integer-programming-assignment-heuristics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programación Entera: Heurísticas para el Problema de Asignación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Descripción\n",
    "\n",
    "En este trabajo se estudia el problema de asignación de manera detallada, en concreto el de asignación clásico y el de asignación generalizado, analizando el problema de programación lineal además de heurísticas greedy y de búsqueda local. Todo ello se ha hecho apoyandose en el lenguaje *R* y el solver *glpk*. Por último se ha comprobado la validez de los métodos sobre distintos problemas a modo de ejemplo.\n",
    "\n",
    "Este documento forma parte de un grupo de trabajos relacionados con la heuristicas para la resolución de problemas de programación entera. Existen otros tres trabajos referidos al estudio del [problema de la mochila](https://nbviewer.jupyter.org/github/garciparedes/integer-programming-heuristics/blob/master/integer-programming-knapsack-heuristics.ipynb), a [problemas de redes](https://nbviewer.jupyter.org/github/garciparedes/integer-programming-heuristics/blob/master/integer-programming-network-heuristics.ipynb) y a [problemas de localización de servicios](https://nbviewer.jupyter.org/github/garciparedes/integer-programming-heuristics/blob/master/integer-programming-service-location-heuristics.ipynb). El contenido completo del trabajo está publicado en el siguiente repositorio: https://github.com/garciparedes/integer-programming-heuristics \n",
    "\n",
    "#### Autor\n",
    "  \n",
    "  * Sergio García Prado - [garciparedes.me](https://garciparedes.me)\n",
    "  \n",
    "#### Fecha\n",
    "\n",
    "  * Mayo de 2018\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contenidos\n",
    "  \n",
    "  * [Introducción](#Introducción)\n",
    "  * [Problema de Asignación](#Problema-de-Asignación)\n",
    "    * [Asignación Clásico](#Asignación-Clásico)\n",
    "    * [Asignación Generalizado](#Asignación-Generalizado)\n",
    "  * [Conclusiones](#Conclusiones)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introducción\n",
    "\n",
    "El estudio de problemas de programación lineal binaria es un área de investigación muy interesante y enriquecedor, por su amplio campo de apliación en situaciones reales. En este caso, el trabajo se centra en el estudio de problemas de asignación, es decir, aquellos que se basan en la búsqueda de la configuración óptima en algún sentido entre un conjunto de productores y otro de consumidores. \n",
    "\n",
    "Estos problemas modelizan un gran número de situaciones. Entre ellas, una de las más destacadas es la asignación de tareas a un grupo de individuos de tal manera que se minimicen los costes globales de la planificación. \n",
    "\n",
    "La resolución de óptima de problemas de programación lineal binaria conlleva un elevado coste computacional, que en muchos casos se hace inmanejable cuando el tamaño del conjunto de datos de entrada es muy elevado. Esto es cuando hay muchas tareas que asignar a muchos individuos. Por tanto, en la literatura se han propuesto distintas heurísticas, que a pesar de no ofrecer ninguna garantía de optimalidad, en la práctica ofrecen resultados muy cercanos a dicho valor con un coste computacional mucho menor.\n",
    "\n",
    "En este trabajo se han estudiado dos casos concretos del problema de asignación: el referido a **asignación clásico**, donde tanto productores como consumidores sólo pueden relacionarse de manera **uno a uno**, y el referido a **asignación generalizada**, donde un productor puede servir a más de un consumidor, por lo que la relación es **uno a muchos**. Para cada tipo de problema, se ha estudiado el planteamiento exacto, basado en programación lineal, además de una heurística *Greedy* y una mejora basada en búsqueda local. Por último, se ha comprobado la validez de dichos planteamientos aplicando dichas técnicas a una serie de problemas reales.\n",
    "\n",
    "Todo el planteamiento se ha llevado a cabo apoyandose en el lenguaje de computación estadística *R*, sobre el cual se han implementado las diferentes heurísticas, además de resolver los problemas de manera exacta. Para ello se ha utilizado el *solver* de de programación mixta (lineal y entera) **glpk**.\n",
    "\n",
    "A continuación se muestran distintas sentencias para configurar el entorno de desarrollo, así como funciones de lectura de ficheros (`ReadAssignment()` para la lectura de los conjuntos de datos referidos a problemas de asignación clásica, `ReadGeneralizedAssignment()` para los correspondientes problemas de asignación generalizada). Por último, se ha definido un \"wrapper\" denominado `Solve()` para la llamada al solver *glpk*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Configuración del Entorno"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "rm(list = ls())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using the GLPK callable library version 4.65\n"
     ]
    }
   ],
   "source": [
    "library(slam)\n",
    "library(Rglpk)\n",
    "library(magrittr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(repr.matrix.max.rows = 600, repr.matrix.max.cols = 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Constantes y Funciones de Apoyo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset.folder <- \"./data/assignment/\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "ReadAssignment <- function(file.name) {\n",
    "    c <- as.matrix(read.csv(file.name, header = FALSE))\n",
    "    colnames(c) <- NULL\n",
    "    list(\n",
    "        m = dim(c)[1],\n",
    "        n = dim(c)[2],\n",
    "        cost = c\n",
    "    ) %>%\n",
    "    return()\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ReadGeneralizedAssignment <- function(file.name) {\n",
    "    con <- \n",
    "        file.name %>%\n",
    "        file(open = \"r\")\n",
    "    raw <- \n",
    "        con %>%\n",
    "        readLines(warn = FALSE) %>% \n",
    "        strsplit(\"[[:blank:]]\") %>%\n",
    "        unlist() %>%\n",
    "        as.integer()\n",
    "    close(con)\n",
    "    list(m        = raw[1],\n",
    "         n        = raw[2], \n",
    "         cost     = matrix(raw[3:(2 + raw[1] * raw[2])], \n",
    "                           nrow = raw[1], ncol = raw[2], byrow = TRUE),\n",
    "         resource = matrix(raw[(3 + raw[1] * raw[2]):(2 + 2 * raw[1] * raw[2])], \n",
    "                           nrow = raw[1], ncol = raw[2], byrow = TRUE),\n",
    "         capacity = raw[(3 + 2 * raw[1] * raw[2]):length(raw)]\n",
    "        \n",
    "    ) %>%\n",
    "    return()\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Solve <- function(f.obj, f.con, f.dir, f.rhs, ...) {\n",
    "    Rglpk_solve_LP(f.obj, f.con, f.dir, f.rhs, ...)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problema de Asignación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El *problema de asignación* es ampliamente conocido y ha sido estudiado en profundidad en la literatura, principalmente debido a que permite modelizar una gran cantidad de situaciones que se dan en la vida real. Por estas razones es necesario encontrar un modelo matemático que permita representar y estudiar el problema de manera analítica. \n",
    "\n",
    "De manera natural, el problema de asignación puede ser enunciado como el modelo que representa aquellas situaciones en que se tiene dos grupos disjuntos de elementos, tales que el primero de ellos está constituido por productores mientras que el segundo grupo se compone de consumidores. El problema se basa en asignar a cada consumidor un determinado productor, de tal manera que todos ellos queden cubiertos. Este problema puede ser ampliado de muchas maneras, tal y como se verá posteriormente, sin embargo el objetivo último es minimizar (o maximizar) una determinada función de coste (o beneficio) encontrando la configuración óptima de asignaciones. \n",
    "\n",
    "Tal y como se puede apreciar en el párrafo anterior, este problema puede modelizarse como de programación lineal binaria, de tal manera que cada variable represente de si un productor sirve on no a un consumidor restringido a unas determinadas restricciones de capacidad y demanda (dependiendo del modelo concreto). No es difícil darse que este problema es muy similar al [Problema de Transporte](https://es.wikipedia.org/wiki/Problema_de_transporte), tal es así que la diferencia reside en la imposición de que las variables de decisión sean de naturaleza binaria. Por tanto, el problema de transporte puede ser visto como una relajación del problema de asignación.\n",
    "\n",
    "\n",
    "A continuación, se estudirán de manera detallada dos problemas enmarcados en la categoría de problemas de asignación, siendo el primero de ellos el de [Asignación Clásico](#Asignación-Clásico), y el segundo [Asignación Generalizado](#Asignación-Generalizado). Para estos problemas se va a definir el modelo de programación lineal que los representa, para posteriormente añadir el código fuente en el lenguaje *R* que permite la resolución *Exacta* de dichos problemas. Además, se indicarán las heurísticas *Greedy* junto con su correspondiente mejora de *Búsqueda Local*, todas ellas implementadas en el lenguaje *R* para comprobar su efectividad. Por último se han resuelto distintos problemas (referidos a cada modelización) para comprobar la validez de las heurísticas, así como su cercanía a la solución óptima obtenida por el método exacto."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Asignación Clásico"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Descripción:\n",
    "\n",
    "El *problema de asignación clásico* se corresponde con el caso más básico posible, en el cual el número de productores y de consumidores es el mismo, y el objetivo es la búsqueda de la asignación óptima siguiendo la configuración **1 productor a 1 consumidor** de tal manera que se minimice (o maximice) una determinada función de coste.\n",
    "\n",
    "Para ello, la modelización más sencilla es la basada en una matriz binaria de variables de decisión denominada $X$ y formada por $m$ filas que representan a los productores y $n$ columnas que representan a los consumidores. De esta manera se dice que si la posición $x_{ij}$ de la matriz contiene el valor $1$ el productor $i$ servirá al consumidor $j$, mientras que no lo hará si esta posición contiene el valor $0$. Para poder cuantificar el coste (o valor) de cada una de las posiciones de la matriz de decisiones y así encontrar la solución óptima para el problema, nos apoyaremos en una matriz de costes denotada por $C$ y con las mismas dimensiones. Las restricciones sobre las que se define este problema por tanto, pueden ser enunciadas de tal manera que cada productor sirva únicamente a un consumidor, así como que cada consumidor sea servido únicamente por un productor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Modelo:\n",
    "\n",
    "Una vez descrita la notación necesaria para poder modelizar el problema así como una descripción acerca de las restricciones necesarias para que este sea coherente con la realidad que pretender representar, el siguiente paso es indicar su formulación:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "    \\begin{array}{ll@{}ll}\n",
    "      \\text{Minimizar} & \\displaystyle \\sum\\limits_{i=1}^{m}\\sum\\limits_{j=1}^{n} c_{ij} \\cdot x_{ij} \\\\\n",
    "      \\text{sujeto a}  & \\sum\\limits_{j=1}^{n} x_{ij} = 1, & \\forall i \\in \\{1,...,m\\} \\\\\n",
    "                       & \\sum\\limits_{i=1}^{m} x_{ij} = 1, & \\forall j \\in \\{1,...,n\\} \\\\\n",
    "                       & x_{ij} \\in \\{0, 1\\}, \t& \\forall i \\in \\{1,...,m\\}, \\forall j \\in \\{1,...,n\\}\n",
    "    \\end{array}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una vez definido el *problema de asignación clásico* de tal manera que se pueda construir de manera clara y bien definida una función objetivo, así como una matriz de restricciones, el siguiente paso es realizar la codificación pertinente en el lenguaje *R*, la cual se puede consultar en la función `AssignmentExact()`, que tan solo requiere de una matriz de costes para e indicar si el problema el sentido del problema (minimización o maximización) para devolver la solución óptima del problema. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "AssignmentExact <- function(p, ...) { \n",
    "    conditions <- matrix(0, nrow = p$n + p$m, ncol = p$n * p$m)\n",
    "    for (i in 1:p$m) {\n",
    "        conditions[i, seq(p$n) + (i - 1) * p$n] <- 1\n",
    "    }\n",
    "    for (i in (p$m + 1):(p$n + p$m)) {\n",
    "        conditions[i, seq(i - p$m, p$m * p$n, by = p$n)] <- 1\n",
    "    }\n",
    "    Solve(p$cost, conditions, c(rep(\"==\", p$m + p$n)), \n",
    "          rep(1, p$n + p$m),  ...)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Heurísticas:\n",
    "\n",
    "La dificultad práctica que surge mediante la resolución exacta del problema se debe principalemente al coste computacional necesario para llegar a la solución deseada cuando el tamaño de la matriz de costes es elevado. Por tanto, existen otras técnicas conocidas como heurísticas que a pesar de no suministrar un resultado óptimo en todos los casos, generan resultados próximos a él con un coste computacinal mucho menor. Es por ello que a continuación se van a enunciar dos heurísticas que permiten resolver el problema en un tiempo mucho menor. Primeramente describiremos el funcionamiento de la heuristica *Greedy* para posteriormente realizar una mejora sobre ella con el método de *Busqueda Local*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Greedy:\n",
    "\n",
    "La heurística *Greedy* recibe ese nombre precisamente debido por su método de comportamiento. La traducción a lenguaje Castellano podría ser algo así como *hambriento* o *voraz* ya que esta nunca \"retrocede\" y cambia una decisión tomada. Es decir, una vez fijada una asignación entre unos determinados productores y consumidores, esta no cambia para buscar otra configuración más cercana al óptimo real. Esto hace que el la implementación algorítmica de la solución Greedy sea extremadamente eficiente, ofreciendo resultados razonables. La regla de decisión que utiliza es la elección de la asignación que más minimiza (o maximiza) la función de coste de entre todas las posibles asignaciones coherentes en esa iteracción. Esto quiere decir que si un productor ya ha sido utilizado, no tendrá sentido estudiar si se puede asignar a otro consumidor, y viceversa. \n",
    "\n",
    "A continaución se ilustra la implementación realizada de la heurística *Greedy*, recogida en la función `AssignmentGreedy()`, que tan solo requiere de la matriz de costes así como de la métrica a optimizar, para devolver una solución aproximada en un tiempo reducido:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "AssignmentGreedy <- function(p) {   \n",
    "    demand <- rep(1, dim(p$cost)[1])\n",
    "    capacity <- rep(1, dim(p$cost)[2]) \n",
    "    sol <- list(solution = matrix(0, nrow = p$m, ncol = p$n), \n",
    "                objval = 0, slack = capacity)\n",
    "    while (!all(demand == 0)) {\n",
    "        ij <- which(p$cost == min(p$cost[sol$slack > 0, demand > 0]), arr.ind = TRUE)\n",
    "        ij.slice <- which(sol$slack[ij[, 1]] > 0 & demand[ij[, 2]] > 0)[1]\n",
    "        i <- ij[ij.slice, 1]\n",
    "        j <- ij[ij.slice, 2]\n",
    "        inc <- min(sol$slack[i], demand[j])    \n",
    "        \n",
    "        sol$solution[i, j] <- sol$solution[i, j] + inc\n",
    "        sol$slack[i] <- sol$slack[i] - inc\n",
    "        demand[j] <- demand[j] - inc\n",
    "        sol$objval <- sol$objval + p$cost[i, j, drop = TRUE] * inc\n",
    "    }\n",
    "    return(sol)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Búsqueda Local:\n",
    "\n",
    "La heurística de *Búsqueda Local* en realidad es una técnica para optimizar soluciones iniciales y tratar de mejorar en la medida de lo posible (un entorno local) la solución inicial. Esto se lleva a cabo de la siguiente manera: Partiendo de una solución inicial que asumimos factible, el método trata de realizar una permutación entre los consumidores de dos productores de tal manera que el coste se reduzca. Al igual que sucedía en el caso de la heurística *Greedy*, ahora también se sigue la misma filosofía, en el sentido de que en cada iteracción del método, se realiza el cambio que mayor beneficio proporciona.\n",
    "\n",
    "La implementación de esta solución se ha dividido en tres partes, partiendo inicialmente de una solución obtenida por el método *Greedy*. El siguiente paso a realizar es definir la heurística de mejora o beneficio, la cual se ha llevado a cabo en la función `GreedyLocalSearchImprovement()`, que dados dos pares de índices (referidos dos asignaciónes (productor, consumidor)). Este beneficio se calcula de la siguiente manera: \n",
    "\n",
    "$$(c_{i_1j_2} + c_{i_2j_1}) - (c_{i_1j_1} + c_{i_2j_2})$$\n",
    "\n",
    "Es decir, el beneficio será el nuevo coste de la asignación (dos primeros términos) menos el coste anterior de la asignación (dos últimos términos). Una vez calculados dichos valores, es necesario quedarse con el máximo de entre todos ellos, lo cual se lleva a cabo a partir de la función `GreedyLocalSearchBest()`. El último paso es el de realizar el cambio. Dicho cambio se realiza en la función que controla el algoritmo de búsqueda local (finaliza cuando ya no hay nuevos cambios que mejoren el la función objetivo). Esta función se ha denotado por `AssignmentGreedyLocalSearch()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "GreedyLocalSearchImprovement <- function(change.1, change.2, cost) {\n",
    "    (cost[change.1[, drop = FALSE]] + cost[change.2[, drop = FALSE]]) -\n",
    "    (cost[change.1[1], change.2[2]] + cost[change.2[1], change.1[2]])\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "GreedyLocalSearchBest <- function(cost, changes) {\n",
    "    best = list(v = 0, i = 0, j = 0)\n",
    "    for (i in 1:(nrow(changes) - 1)) {\n",
    "        for(j in (i + 1):nrow(changes)) {\n",
    "            v.temp <- GreedyLocalSearchImprovement(changes[i, ,drop = FALSE], \n",
    "                                                   changes[j, , drop = FALSE],\n",
    "                                                   cost)\n",
    "            if (best$v < v.temp) {\n",
    "                best$v <- v.temp\n",
    "                best$i <- i\n",
    "                best$j <- j\n",
    "            }\n",
    "        }\n",
    "    }\n",
    "    return(best)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "AssignmentGreedyLocalSearch <- function(p) {    \n",
    "    sol <- AssignmentGreedy(p)\n",
    "        \n",
    "    changes <- which(sol$solution != 0, arr.ind = TRUE)\n",
    "    best <- GreedyLocalSearchBest(p$cost, changes)\n",
    "    while(best$v > 0) {\n",
    "\n",
    "        sol$solution[changes[best$i, , drop = FALSE]] <- 0\n",
    "        sol$solution[changes[best$j, , drop = FALSE]] <- 0\n",
    "        \n",
    "        temp <- changes[best$i, 2]\n",
    "        changes[best$i, 2] <- changes[best$j, 2]\n",
    "        changes[best$j, 2] <- temp\n",
    "        \n",
    "        sol$solution[changes[best$i, , drop = FALSE]] <- 1\n",
    "        sol$solution[changes[best$j, , drop = FALSE]] <- 1\n",
    "        \n",
    "        sol$objval <- sol$objval - best$v\n",
    "        \n",
    "        best <- GreedyLocalSearchBest(p$cost, changes)\n",
    "    }\n",
    "    return(sol)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación se va a demostrar la validez de los algoritmos implementados mediante la prueba sobre tres problemas de minimización de tamaño $15x15$ los cuales se definen a partir de la matriz de costes. Nótese que en estos casos no es necesario indicar en el procedimiento de resolución exacta que la solución dada debe ser binaria y no real, debido a la *propiedad de integridad* que asegura que si los coeficientes de un problema de transporte son enteras, entonces los valores de las variables de decisión también lo serán. Dado que el problema de asignación clásico es una caracterización del problema de transporte, esta condición también se cumplirá. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### matriz.15x15.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "matriz.15x15.1 <- ReadAssignment(paste0(dataset.folder, \"matriz_15x15_1.csv\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>135</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{lllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 135\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   135\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    0    0    1    0    0    0    0     0     0     0     0\n",
       " [2,]    0    0    0    0    0    0    0    1    0     0     0     0     0\n",
       " [3,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [4,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       " [5,]    0    0    0    0    0    0    0    0    0     0     1     0     0\n",
       " [6,]    0    0    0    0    0    0    0    0    1     0     0     0     0\n",
       " [7,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       " [8,]    1    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [9,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[10,]    0    0    0    0    0    0    0    0    0     0     0     1     0\n",
       "[11,]    0    0    0    1    0    0    0    0    0     0     0     0     0\n",
       "[12,]    0    0    0    0    0    0    1    0    0     0     0     0     0\n",
       "[13,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
       "[14,]    0    0    0    0    0    0    0    0    0     1     0     0     0\n",
       "[15,]    0    1    0    0    0    0    0    0    0     0     0     0     0\n",
       "      [,14] [,15]\n",
       " [1,]     0     0\n",
       " [2,]     0     0\n",
       " [3,]     0     1\n",
       " [4,]     0     0\n",
       " [5,]     0     0\n",
       " [6,]     0     0\n",
       " [7,]     0     0\n",
       " [8,]     0     0\n",
       " [9,]     1     0\n",
       "[10,]     0     0\n",
       "[11,]     0     0\n",
       "[12,]     0     0\n",
       "[13,]     0     0\n",
       "[14,]     0     0\n",
       "[15,]     0     0\n",
       "\n",
       "$objval\n",
       "[1] 135\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentExact(matriz.15x15.1)\n",
    "list(solution = matrix(s$solution, nrow = matriz.15x15.1$n), \n",
    "     objval   = s$optimum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>218</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{lllllllllllllll}\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 218\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   218\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       " [2,]    0    0    0    0    0    0    0    1    0     0     0     0     0\n",
       " [3,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [4,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       " [5,]    0    0    0    0    0    0    0    0    0     0     1     0     0\n",
       " [6,]    0    0    0    0    0    0    1    0    0     0     0     0     0\n",
       " [7,]    0    0    0    0    0    0    0    0    0     0     0     1     0\n",
       " [8,]    0    0    0    0    1    0    0    0    0     0     0     0     0\n",
       " [9,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[10,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
       "[11,]    0    0    0    1    0    0    0    0    0     0     0     0     0\n",
       "[12,]    1    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[13,]    0    0    0    0    0    0    0    0    1     0     0     0     0\n",
       "[14,]    0    0    0    0    0    0    0    0    0     1     0     0     0\n",
       "[15,]    0    1    0    0    0    0    0    0    0     0     0     0     0\n",
       "      [,14] [,15]\n",
       " [1,]     0     0\n",
       " [2,]     0     0\n",
       " [3,]     0     1\n",
       " [4,]     0     0\n",
       " [5,]     0     0\n",
       " [6,]     0     0\n",
       " [7,]     0     0\n",
       " [8,]     0     0\n",
       " [9,]     1     0\n",
       "[10,]     0     0\n",
       "[11,]     0     0\n",
       "[12,]     0     0\n",
       "[13,]     0     0\n",
       "[14,]     0     0\n",
       "[15,]     0     0\n",
       "\n",
       "$objval\n",
       "[1] 218\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentGreedy(matriz.15x15.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>144</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{lllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
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       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
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       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 144\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
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       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   144\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    0    0    0    0    0    0    0     0     0     1     0\n",
       " [2,]    0    0    0    0    0    0    0    1    0     0     0     0     0\n",
       " [3,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [4,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       " [5,]    0    0    0    0    0    0    0    0    0     0     1     0     0\n",
       " [6,]    0    0    0    0    0    0    0    0    1     0     0     0     0\n",
       " [7,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       " [8,]    0    0    0    0    1    0    0    0    0     0     0     0     0\n",
       " [9,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[10,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
       "[11,]    0    0    0    1    0    0    0    0    0     0     0     0     0\n",
       "[12,]    1    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[13,]    0    0    0    0    0    0    1    0    0     0     0     0     0\n",
       "[14,]    0    0    0    0    0    0    0    0    0     1     0     0     0\n",
       "[15,]    0    1    0    0    0    0    0    0    0     0     0     0     0\n",
       "      [,14] [,15]\n",
       " [1,]     0     0\n",
       " [2,]     0     0\n",
       " [3,]     0     1\n",
       " [4,]     0     0\n",
       " [5,]     0     0\n",
       " [6,]     0     0\n",
       " [7,]     0     0\n",
       " [8,]     0     0\n",
       " [9,]     1     0\n",
       "[10,]     0     0\n",
       "[11,]     0     0\n",
       "[12,]     0     0\n",
       "[13,]     0     0\n",
       "[14,]     0     0\n",
       "[15,]     0     0\n",
       "\n",
       "$objval\n",
       "[1] 144\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentGreedyLocalSearch(matriz.15x15.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tal y como se puede apreciar a la vista de los resultados, para el problema [matriz.15x15.1](#matriz.15x15.1), la solución óptima ($135$) siempre es menor que la obtenida por los métodos *Greedy* ($218$) y *Búsqueda Local* ($144$). Sin embargo, tal y como era de esperar, la solución optimizada a partir de la búsqueda local mejora de manera sustancial el resultado *Greedy*. A pesar de no llegar a tomar el valor óptimo, está muy cercano de manera relativa."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### matriz.15x15.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "matriz.15x15.2 <- ReadAssignment(paste0(dataset.folder, \"matriz_15x15_2.csv\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
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       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>125</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{lllllllllllllll}\n",
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       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 125\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
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       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
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       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   125\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    0    0    1    0    0    0    0     0     0     0     0\n",
       " [2,]    0    0    0    0    0    0    1    0    0     0     0     0     0\n",
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       " [4,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [5,]    0    0    0    1    0    0    0    0    0     0     0     0     0\n",
       " [6,]    1    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [7,]    0    1    0    0    0    0    0    0    0     0     0     0     0\n",
       " [8,]    0    0    0    0    0    0    0    0    0     0     0     1     0\n",
       " [9,]    0    0    0    0    0    0    0    0    0     1     0     0     0\n",
       "[10,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       "[11,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       "[12,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
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       "[14,]    0    0    0    0    0    0    0    0    0     0     1     0     0\n",
       "[15,]    0    0    0    0    0    0    0    0    1     0     0     0     0\n",
       "      [,14] [,15]\n",
       " [1,]     0     0\n",
       " [2,]     0     0\n",
       " [3,]     0     0\n",
       " [4,]     0     1\n",
       " [5,]     0     0\n",
       " [6,]     0     0\n",
       " [7,]     0     0\n",
       " [8,]     0     0\n",
       " [9,]     0     0\n",
       "[10,]     0     0\n",
       "[11,]     0     0\n",
       "[12,]     0     0\n",
       "[13,]     1     0\n",
       "[14,]     0     0\n",
       "[15,]     0     0\n",
       "\n",
       "$objval\n",
       "[1] 125\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentExact(matriz.15x15.2)\n",
    "list(solution = matrix(s$solution, nrow = matriz.15x15.2$m),\n",
    "     objval   = s$optimum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>146</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{lllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 146\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   146\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    0    0    0    0    0    0    0     0     0     1     0\n",
       " [2,]    0    0    0    0    0    0    1    0    0     0     0     0     0\n",
       " [3,]    0    0    0    0    0    0    0    1    0     0     0     0     0\n",
       " [4,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [5,]    0    0    0    1    0    0    0    0    0     0     0     0     0\n",
       " [6,]    0    0    0    0    0    0    0    0    0     1     0     0     0\n",
       " [7,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       " [8,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [9,]    0    1    0    0    0    0    0    0    0     0     0     0     0\n",
       "[10,]    1    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[11,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       "[12,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
       "[13,]    0    0    0    0    1    0    0    0    0     0     0     0     0\n",
       "[14,]    0    0    0    0    0    0    0    0    0     0     1     0     0\n",
       "[15,]    0    0    0    0    0    0    0    0    1     0     0     0     0\n",
       "      [,14] [,15]\n",
       " [1,]     0     0\n",
       " [2,]     0     0\n",
       " [3,]     0     0\n",
       " [4,]     0     1\n",
       " [5,]     0     0\n",
       " [6,]     0     0\n",
       " [7,]     0     0\n",
       " [8,]     1     0\n",
       " [9,]     0     0\n",
       "[10,]     0     0\n",
       "[11,]     0     0\n",
       "[12,]     0     0\n",
       "[13,]     0     0\n",
       "[14,]     0     0\n",
       "[15,]     0     0\n",
       "\n",
       "$objval\n",
       "[1] 146\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentGreedy(matriz.15x15.2)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>146</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{lllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 146\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   146\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    0    0    0    0    0    0    0     0     0     1     0\n",
       " [2,]    0    0    0    0    0    0    1    0    0     0     0     0     0\n",
       " [3,]    0    0    0    0    0    0    0    1    0     0     0     0     0\n",
       " [4,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [5,]    0    0    0    1    0    0    0    0    0     0     0     0     0\n",
       " [6,]    0    0    0    0    0    0    0    0    0     1     0     0     0\n",
       " [7,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       " [8,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [9,]    0    1    0    0    0    0    0    0    0     0     0     0     0\n",
       "[10,]    1    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[11,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       "[12,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
       "[13,]    0    0    0    0    1    0    0    0    0     0     0     0     0\n",
       "[14,]    0    0    0    0    0    0    0    0    0     0     1     0     0\n",
       "[15,]    0    0    0    0    0    0    0    0    1     0     0     0     0\n",
       "      [,14] [,15]\n",
       " [1,]     0     0\n",
       " [2,]     0     0\n",
       " [3,]     0     0\n",
       " [4,]     0     1\n",
       " [5,]     0     0\n",
       " [6,]     0     0\n",
       " [7,]     0     0\n",
       " [8,]     1     0\n",
       " [9,]     0     0\n",
       "[10,]     0     0\n",
       "[11,]     0     0\n",
       "[12,]     0     0\n",
       "[13,]     0     0\n",
       "[14,]     0     0\n",
       "[15,]     0     0\n",
       "\n",
       "$objval\n",
       "[1] 146\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentGreedyLocalSearch(matriz.15x15.2)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tal y como se puede apreciar a la vista de los resultados, para el problema [matriz.15x15.2](#matriz.15x15.2), la solución óptima ($125$) siempre es menor que la obtenida por los métodos *Greedy* ($146$) y *Búsqueda Local* ($146$). En este caso, la optimización por búsqueda local no consigue mejorar la solución *Greedy* obtenida inicialmente. Sin embargo, esta solución se encuentra cerca del óptimo. Una situación que se da en muchos casos es que cuando las soluciones iniciales (en este caso la obtenida por el método *Greedy*) se encuentran cerca del valor óptimo, son difíciles de optimizar por métodos de búsqueda local, ya que el espacio de posibles alternativas de mejora es reducido."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### matriz.15x15.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "matriz.15x15.3 <- ReadAssignment(paste0(dataset.folder, \"matriz_15x15_3.csv\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
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       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>153</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
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       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 153\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
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       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   153\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
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       "[15,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
       "      [,14] [,15]\n",
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       " [2,]     0     0\n",
       " [3,]     0     0\n",
       " [4,]     0     0\n",
       " [5,]     0     1\n",
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       "\n",
       "$objval\n",
       "[1] 153\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentExact(matriz.15x15.3)\n",
    "list(solution = matrix(s$solution, nrow = matriz.15x15.3$m),\n",
    "     objval   = s$optimum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
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       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>205</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
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       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 205\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
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       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   205\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
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       "[15,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       "      [,14] [,15]\n",
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       "[10,]     0     0\n",
       "[11,]     0     0\n",
       "[12,]     0     0\n",
       "[13,]     0     1\n",
       "[14,]     0     0\n",
       "[15,]     0     0\n",
       "\n",
       "$objval\n",
       "[1] 205\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentGreedy(matriz.15x15.3)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
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       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>156</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{lllllllllllllll}\n",
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       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
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       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 156\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   156\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [2,]    0    0    0    0    0    0    0    0    0     0     1     0     0\n",
       " [3,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       " [4,]    0    0    0    0    0    0    0    0    0     0     0     1     0\n",
       " [5,]    1    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [6,]    0    0    0    0    0    0    0    0    1     0     0     0     0\n",
       " [7,]    0    0    0    0    1    0    0    0    0     0     0     0     0\n",
       " [8,]    0    0    0    0    0    0    0    0    0     1     0     0     0\n",
       " [9,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       "[10,]    0    1    0    0    0    0    0    0    0     0     0     0     0\n",
       "[11,]    0    0    0    1    0    0    0    0    0     0     0     0     0\n",
       "[12,]    0    0    0    0    0    0    1    0    0     0     0     0     0\n",
       "[13,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[14,]    0    0    0    0    0    0    0    1    0     0     0     0     0\n",
       "[15,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
       "      [,14] [,15]\n",
       " [1,]     1     0\n",
       " [2,]     0     0\n",
       " [3,]     0     0\n",
       " [4,]     0     0\n",
       " [5,]     0     0\n",
       " [6,]     0     0\n",
       " [7,]     0     0\n",
       " [8,]     0     0\n",
       " [9,]     0     0\n",
       "[10,]     0     0\n",
       "[11,]     0     0\n",
       "[12,]     0     0\n",
       "[13,]     0     1\n",
       "[14,]     0     0\n",
       "[15,]     0     0\n",
       "\n",
       "$objval\n",
       "[1] 156\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- AssignmentGreedyLocalSearch(matriz.15x15.3)\n",
    "list(solution = matrix(s$solution, nrow = matriz.15x15.3$m),\n",
    "     objval  = s$objval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tal y como se puede apreciar a la vista de los resultados, para el problema [matriz.15x15.3](#matriz.15x15.3), la solución óptima ($153$) siempre es menor que la obtenida por los métodos *Greedy* ($205$) y *Búsqueda Local* ($156$). Sin embargo, tal y como era de esperar, la solución optimizada a partir de la búsqueda local mejora de manera sustancial el resultado *Greedy*. A pesar de no llegar a tomar el valor óptimo, está muy cercano de manera relativa."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Asignación Generalizado"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Descripción:\n",
    "\n",
    "El *problema de asignación generalizado* en cierto sentido, es una ampliación respecto del descrito en la sección anterior. Esto es la modificación de una la restricción impuesta a los productores, de tal manera que estos ya no estén restringidos a la servir a un único consumidor. Esto se puede modelizar en el enfoque relacional de bases de datos como una la relación **1 productor a muchos consumidores**. Sin embargo, la restricción no se elimina por completo, sino que se fija en una determinada \"capacidad\" de trabajo por cada productor. Tal y como es de esperar (y para que tenga sentido la anterior afirmación), también será necesario añadir una matriz extra que refleje las unidades de capacidad necesarias por cada productor para poder poder servir a cada consumidor.\n",
    "\n",
    "Tal y como sucedía con el problema anterior, en este caso también se cumple la idea de que el problema de asignación generalizado se puede ver como el caso del problema del transporte, para el cual las variables de decisión son de naturaleza binaria. Nótese que en este caso el modelo se encuntra \"más cercano aún\" ya que las capacidades no son todas ellas iguales a $1$, cosa que si sucede con las demandas.\n",
    "\n",
    "Ahora que ya se ha ilustrado el contexto del problema, el siguiente paso es definir las variables necesarias para poder modelizarlo y que este puedas ser estudiado de manera analítica. Al igual que para el problema de asignación clásico, se tiene una matriz de decisión binaria $X$ de $m$ filas y $n$ columnas referida a las asignaciones entre el productor $i$ y el consumidor $j$. La matriz de costes $C$ a minimizar (o maximizar) también es equivalente. Las diferencias residen una nueva matriz de capacidades con las mismas dimensiones que las anteriores y que denotaremos por $R$ (del inglés *resources*) y que indica en la posición $r_{ij}$ la cantidad de recursos necesarios para que el productor $i$ pueda satisfacer al consumidor $j$. Estos deberán ser menores o iguales a la capacidad de cada productor, que almacenaremos en un vector de longitud igual al número de productores y que denotaremor por $b$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Modelo:\n",
    "\n",
    "Una vez descrita la notación pertinente, así como las modificaciones sobre el problema de asignación clásico para llegar al problema de asignación generalizado, el siguiente paso es añadir el modelo matemático de programación lineal que representa el problema. La formulación del mismo se indica a continuación:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "    \\begin{array}{ll@{}ll}\n",
    "      \\text{Minimizar} & \\displaystyle \\sum\\limits_{i=1}^{m}\\sum\\limits_{j=1}^{n} c_{ij} \\cdot x_{ij} \\\\\n",
    "      \\text{sujeto a}  & \\sum\\limits_{i=1}^{m} x_{ij} = 1, & \\forall j \\in \\{1,...,n\\} \\\\\n",
    "                       & \\sum\\limits_{j=1}^{n} r_{ij} x_{ij} \\leq b_{i}, & \\forall i \\in \\{1,...,m\\} \\\\\n",
    "                       & x_{ij} \\in \\{0, 1\\}, \t& \\forall i \\in \\{1,...,m\\}, \\forall j \\in \\{1,...,n\\}\n",
    "    \\end{array}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una vez definido el modelo, es sencillo realizar la implementación pertinente en el lenguaje *R*. Esto se ha llevado a cabo en la función `GeneralizedAssignmentExact()` que calcula una solución exacta y para el problema de asignación generalizado:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "GeneralizedAssignmentExact <- function(p, ...) {\n",
    "    conditions <- matrix(0, nrow = p$n + p$m, ncol = p$n * p$m)\n",
    "    for (i in 1:p$m) {\n",
    "        conditions[i, seq(p$n) + (i - 1) * p$n] <- p$resource[i, ]\n",
    "    }\n",
    "    for (i in (p$m + 1):(p$n + p$m)) {\n",
    "        conditions[i, seq(i - p$m, p$m * p$n, by = p$n)] <- 1\n",
    "    }\n",
    "    Solve(t(p$cost), conditions, c(rep(\"<=\", p$m), rep(\"==\", p$n)), \n",
    "          c(p$capacity, rep(1, p$n)), types = \"B\", max = TRUE, ...)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Heurísticas:\n",
    "\n",
    "Debido al elevado coste computacional necesario para la resolución de manera exacta de problemas de asignación generalizada cuando el tamaño del problema es grande, a continuación se van a enunciar dos heurísticas que permiten resolver el problema de manera aproximada en un tiempo razonable. La primera de ellas está basada en el método *Greedy* del cual se ha hablado en la anterior sección, mientras que el segundo se refiere a otra heurística de mejora basada en *Búsqueda Local*, la cual también se describió en la anterior sección.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Greedy de Martello-Toth:\n",
    "\n",
    "Este método, al igual que el descrito en la sección anterior, se basa en la asinación de productores y consumidores de manera *voraz* y sin tener en cuenta decisiones pasadas. Sin embargo, en el caso anterior no era necesario tener en cuenta la capacidad restante de los consumidores para llegar a una solución factible, algo que en este caso si que lo es. Por tanto, la heurística *Greedy* que se ha utilizado se basa en la selección de la configuración que la capacidad libre total de los productores, y de entre estas, se selecciona la que más ganancia proporcione en el sentido del problema (minimizar o maximizar). Mediante la utilización de esta heurística, se asegura la obtención de una solución factible del problema. Sin embargo, las garantías de optimalidad en este caso son más difusas que en el caso del problema anterior.\n",
    "\n",
    "La función `GeneralizedAssignmentGreedy()` implementa el cálculo de la heurística *Greedy Martello-Toth* tal y como se ha descrito en el párrafo anterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "GeneralizedAssignmentGreedy <- function(p) {    \n",
    "    sol <- list(solution = matrix(0, nrow = p$m, ncol = p$n), \n",
    "                objval = 0, slack = p$capacity)\n",
    "    while(!all(colSums(sol$solution) == 1)) {\n",
    "        max.resource <- max(sol$slack - p$resource[,colSums(sol$solution) == 0])\n",
    "        \n",
    "        ij <- which(sol$slack - p$resource == max.resource, arr.ind = TRUE)\n",
    "        ij <- ij[colSums(sol$solution[, ij[,2], drop = FALSE]) == 0, , drop = FALSE]\n",
    "        ij <- ij[which.max(p$cost[ij]), ,drop = FALSE]\n",
    "        \n",
    "        sol$solution[ij[1], ij[2]] <- 1\n",
    "        sol$slack[ij[1]] <- sol$slack[ij[1]] - p$resource[ij[1], ij[2]]\n",
    "        sol$objval <- sol$objval + p$cost[ij[1], ij[2]]\n",
    "    }\n",
    "    return(sol)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Búsqueda Local:\n",
    "\n",
    "La heurística de *búsqueda local* para el problema de asignación generalizado, se basa en las mismas ideas que para el caso del problema de asignación clásico. Sin embargo, al igual que sucede con la heurística greedy, en este caso el intercambio de asignaciones debe tener en cuenta la capacidad de los productores. Esto se lleva a cabo mediante la verificación de que el nuevo intercambio cumplirá las restricciones de capacidad del productor.\n",
    "\n",
    "La implementación de esta solución se ha dividido en tres partes, partiendo inicialmente de una solución obtenida por el método *Greedy*. El siguiente paso a realizar es definir la heurística de mejora o beneficio, la cual se ha llevado a cabo en la función `GeneralizedAssignmentGreedyLocalSearchmprovement()`, que dados dos pares de índices (referidos dos asignaciónes (productor, consumidor)). Dado que en este caso el problema de asignación calculará la mejora de beneficio de forma opuesta. Este beneficio se calcula de la siguiente manera: \n",
    "\n",
    "$$- (c_{i_1j_2} + c_{i_2j_1}) + (c_{i_1j_1} + c_{i_2j_2})$$\n",
    "\n",
    "Es decir, el beneficio será el nuevo coste de la asignación (dos primeros términos) menos el coste anterior de la asignación (dos últimos términos). Una vez calculados dichos valores, es necesario quedarse con el máximo de entre todos ellos, lo cual se lleva a cabo a partir de la función `GeneralizedAssignmentGreedyLocalSearchBest()`. El último paso es el de realizar el cambio. Dicho cambio se realiza en la función que controla el algoritmo de búsqueda local (finaliza cuando ya no hay nuevos cambios que mejoren el la función objetivo). Esta función se ha denotado por `GeneralizedAssignmentGreedyLocalSearch()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "GeneralizedAssignmentGreedyLocalSearchmprovement <- function(change.1, change.2, cost) {\n",
    "    return( - (cost[change.1[, drop = FALSE]] + cost[change.2[, drop = FALSE]]) +\n",
    "              (cost[change.1[1], change.2[2]] + cost[change.2[1], change.1[2]]))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "GeneralizedAssignmentGreedyLocalSearchBest <- function(p, changes, slack) {\n",
    "    best = list(v = 0, i = 0, j = 0)\n",
    "    for (i in 1:(nrow(changes) - 1)) {\n",
    "        for(j in (i + 1):nrow(changes)) {\n",
    "            if ((slack[changes[i, , drop = FALSE][1]] + p$resource[changes[i, , drop = FALSE]] - \n",
    "                     p$resource[changes[i, 1], changes[j, 2]] > 0) & \n",
    "                (slack[changes[j, , drop = FALSE][1]] + p$resource[changes[j, , drop = FALSE]] - \n",
    "                     p$resource[changes[j, 1], changes[i, 2]] > 0)) { \n",
    "                    \n",
    "                    v.temp <- GeneralizedAssignmentGreedyLocalSearchmprovement(changes[i, ,drop = FALSE], \n",
    "                                                                     changes[j, , drop = FALSE],\n",
    "                                                                     p$cost)\n",
    "                    if (best$v < v.temp) {\n",
    "                        best$v <- v.temp\n",
    "                        best$i <- i\n",
    "                        best$j <- j\n",
    "                    }\n",
    "                }\n",
    "        }\n",
    "    }\n",
    "    return(best)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "GeneralizedAssignmentGreedyLocalSearch <- function(p) {\n",
    "    sol <- GeneralizedAssignmentGreedy(p)\n",
    "    \n",
    "    changes <- which(sol$solution != 0, arr.ind = TRUE)\n",
    "    slack <- rowSums(sol$solution * p$resource)\n",
    "    best <- GeneralizedAssignmentGreedyLocalSearchBest(p, changes, sol$slack)\n",
    "    while(best$v > 0) {\n",
    "        \n",
    "        sol$solution[changes[best$i, , drop = FALSE]] <- 0\n",
    "        sol$solution[changes[best$j, , drop = FALSE]] <- 0\n",
    "        sol$slack[changes[best$i][1]] <- sol$slack[changes[best$i][1]] + p$resource[changes[best$i, , drop = FALSE]]\n",
    "        sol$slack[changes[best$j][1]] <- sol$slack[changes[best$j][1]] + p$resource[changes[best$j, , drop = FALSE]]\n",
    "        \n",
    "        temp <- changes[best$i, 2]\n",
    "        changes[best$i, 2] <- changes[best$j, 2]\n",
    "        changes[best$j, 2] <- temp\n",
    "        \n",
    "        sol$solution[changes[best$i, , drop = FALSE]] <- 1\n",
    "        sol$solution[changes[best$j, , drop = FALSE]] <- 1\n",
    "        \n",
    "        sol$slack[changes[best$i][1]] <- sol$slack[changes[best$i][1]] - p$resource[changes[best$i, , drop = FALSE]]\n",
    "        sol$slack[changes[best$j][1]] <- sol$slack[changes[best$j][1]] - p$resource[changes[best$j, , drop = FALSE]]\n",
    "        sol$objval <- sol$objval + best$v\n",
    "        best <- GeneralizedAssignmentGreedyLocalSearchBest(p, changes, sol$slack)\n",
    "    }\n",
    "    return(sol)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplos\n",
    "\n",
    "Para verificar la validez de las implementaciones realizadas, en esta sección se han aplicado sobre $5$ problemas de asignación generalizada para así poder comparar los resultados obtenidos. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### gap2.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "gap2.1 <- ReadGeneralizedAssignment(\"./data/assignment/gap2_1.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>434</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>38</li>\n",
       "\t<li>50</li>\n",
       "\t<li>51</li>\n",
       "\t<li>43</li>\n",
       "\t<li>54</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllll}\n",
       "\t 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 434\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 38\n",
       "\\item 50\n",
       "\\item 51\n",
       "\\item 43\n",
       "\\item 54\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   434\n",
       "$slack\n",
       ":   1. 38\n",
       "2. 50\n",
       "3. 51\n",
       "4. 43\n",
       "5. 54\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    0    1    0    0    1    0    0    1     0     0     0     0     0\n",
       "[2,]    0    0    0    0    0    0    1    0    0     1     0     0     0     0\n",
       "[3,]    1    0    0    0    1    0    0    0    0     0     0     0     1     0\n",
       "[4,]    0    0    0    1    0    0    0    1    0     0     0     0     0     0\n",
       "[5,]    0    1    0    0    0    0    0    0    0     0     1     1     0     1\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20]\n",
       "[1,]     0     0     0     0     0     1\n",
       "[2,]     0     1     0     0     1     0\n",
       "[3,]     0     0     1     0     0     0\n",
       "[4,]     1     0     0     1     0     0\n",
       "[5,]     0     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 434\n",
       "\n",
       "$slack\n",
       "[1] 38 50 51 43 54\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentExact(gap2.1)\n",
    "list(solution = matrix(s$solution, nrow = gap2.1$m, byrow = TRUE),\n",
    "     objval   = s$optimum,\n",
    "     slack    = s$auxiliary$primal[1:gap2.1$m])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>377</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>14</li>\n",
       "\t<li>14</li>\n",
       "\t<li>13</li>\n",
       "\t<li>13</li>\n",
       "\t<li>10</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllll}\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 377\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 14\n",
       "\\item 14\n",
       "\\item 13\n",
       "\\item 13\n",
       "\\item 10\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   377\n",
       "$slack\n",
       ":   1. 14\n",
       "2. 14\n",
       "3. 13\n",
       "4. 13\n",
       "5. 10\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    0    1    0    0    0    0    0    1     0     0     1     0     0\n",
       "[2,]    0    0    0    0    0    0    1    0    0     0     0     0     0     0\n",
       "[3,]    0    0    0    0    0    1    0    1    0     0     0     0     1     0\n",
       "[4,]    1    0    0    1    0    0    0    0    0     1     0     0     0     0\n",
       "[5,]    0    1    0    0    1    0    0    0    0     0     1     0     0     1\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20]\n",
       "[1,]     0     0     0     1     0     0\n",
       "[2,]     1     1     0     0     1     0\n",
       "[3,]     0     0     0     0     0     1\n",
       "[4,]     0     0     1     0     0     0\n",
       "[5,]     0     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 377\n",
       "\n",
       "$slack\n",
       "[1] 14 14 13 13 10\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GeneralizedAssignmentGreedy(gap2.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>432</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>4</li>\n",
       "\t<li>2</li>\n",
       "\t<li>4</li>\n",
       "\t<li>7</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 432\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 7\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   432\n",
       "$slack\n",
       ":   1. 2\n",
       "2. 4\n",
       "3. 2\n",
       "4. 4\n",
       "5. 7\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    0    0    0    0    0    0    0    1     0     1     1     0     0\n",
       "[2,]    0    0    0    0    0    0    1    0    0     1     0     0     0     0\n",
       "[3,]    1    0    0    0    0    1    0    0    0     0     0     0     1     0\n",
       "[4,]    0    0    0    1    0    0    0    1    0     0     0     0     0     0\n",
       "[5,]    0    1    1    0    1    0    0    0    0     0     0     0     0     1\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20]\n",
       "[1,]     0     0     0     0     0     1\n",
       "[2,]     0     1     0     0     1     0\n",
       "[3,]     0     0     1     0     0     0\n",
       "[4,]     1     0     0     1     0     0\n",
       "[5,]     0     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 432\n",
       "\n",
       "$slack\n",
       "[1] 2 4 2 4 7\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "GeneralizedAssignmentGreedyLocalSearch(gap2.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el problema [gap2.1](#gap2.1) las soluciones obtenidas han sido las siguientes: el resultado exacto del problema es ($434$), el resultado obtenido por el método *Greedy* propuesto por Martello-Toth es ($377$), que tras la heurística de *Búsqueda Local* toma el valor ($432$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### gap4.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "gap4.1 <- ReadGeneralizedAssignment(\"./data/assignment/gap4_1.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>656</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>70</li>\n",
       "\t<li>71</li>\n",
       "\t<li>79</li>\n",
       "\t<li>61</li>\n",
       "\t<li>63</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 656\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 70\n",
       "\\item 71\n",
       "\\item 79\n",
       "\\item 61\n",
       "\\item 63\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   656\n",
       "$slack\n",
       ":   1. 70\n",
       "2. 71\n",
       "3. 79\n",
       "4. 61\n",
       "5. 63\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    0    0    0    0    0    1    0    0     0     0     0     0     0\n",
       "[2,]    0    1    0    0    1    0    0    0    0     0     1     0     1     0\n",
       "[3,]    0    0    0    0    0    0    0    1    1     0     0     0     0     1\n",
       "[4,]    1    0    0    0    0    0    0    0    0     1     0     0     0     0\n",
       "[5,]    0    0    1    1    0    1    0    0    0     0     0     1     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     1     0     0     1     0     0     0     0     0     0     0     1\n",
       "[2,]     0     1     1     0     0     0     0     0     0     0     0     0\n",
       "[3,]     0     0     0     0     1     0     0     0     0     1     0     0\n",
       "[4,]     0     0     0     0     0     1     0     1     1     0     1     0\n",
       "[5,]     0     0     0     0     0     0     1     0     0     0     0     0\n",
       "     [,27] [,28] [,29] [,30]\n",
       "[1,]     0     1     0     0\n",
       "[2,]     0     0     1     0\n",
       "[3,]     1     0     0     0\n",
       "[4,]     0     0     0     0\n",
       "[5,]     0     0     0     1\n",
       "\n",
       "$objval\n",
       "[1] 656\n",
       "\n",
       "$slack\n",
       "[1] 70 71 79 61 63\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentExact(gap4.1)\n",
    "list(solution = matrix(s$solution, nrow = gap4.1$m, byrow = TRUE),\n",
    "     objval   = s$optimum,\n",
    "     slack    = s$auxiliary$primal[1:gap4.1$m])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>541</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>19</li>\n",
       "\t<li>28</li>\n",
       "\t<li>11</li>\n",
       "\t<li>20</li>\n",
       "\t<li>20</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllll}\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 541\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 19\n",
       "\\item 28\n",
       "\\item 11\n",
       "\\item 20\n",
       "\\item 20\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   541\n",
       "$slack\n",
       ":   1. 19\n",
       "2. 28\n",
       "3. 11\n",
       "4. 20\n",
       "5. 20\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    1    0    0    0    0    0    0    0    1     0     0     1     0     0\n",
       "[2,]    0    0    0    0    1    0    1    0    0     0     1     0     1     0\n",
       "[3,]    0    0    0    0    0    1    0    0    0     0     0     0     0     1\n",
       "[4,]    0    0    0    1    0    0    0    0    0     1     0     0     0     0\n",
       "[5,]    0    1    1    0    0    0    0    1    0     0     0     0     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0     0     1     1     0     0     0\n",
       "[3,]     0     0     0     0     1     0     1     0     0     0     0     1\n",
       "[4,]     0     1     1     1     0     0     0     0     0     1     0     0\n",
       "[5,]     1     0     0     0     0     1     0     0     0     0     1     0\n",
       "     [,27] [,28] [,29] [,30]\n",
       "[1,]     0     1     1     1\n",
       "[2,]     0     0     0     0\n",
       "[3,]     1     0     0     0\n",
       "[4,]     0     0     0     0\n",
       "[5,]     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 541\n",
       "\n",
       "$slack\n",
       "[1] 19 28 11 20 20\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentGreedy(gap4.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval,\n",
    "     slack    = s$slack)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>650</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>10</li>\n",
       "\t<li>1</li>\n",
       "\t<li>5</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 650\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 10\n",
       "\\item 1\n",
       "\\item 5\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   650\n",
       "$slack\n",
       ":   1. 10\n",
       "2. 1\n",
       "3. 5\n",
       "4. 3\n",
       "5. 4\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    0    0    0    0    0    1    0    1     0     1     0     0     0\n",
       "[2,]    0    1    0    0    1    0    0    0    0     0     0     1     1     0\n",
       "[3,]    0    0    0    0    0    0    0    1    0     0     0     0     0     1\n",
       "[4,]    1    0    0    0    0    0    0    0    0     1     0     0     0     0\n",
       "[5,]    0    0    1    1    0    1    0    0    0     0     0     0     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     1     0     0     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     1     1     0     0     0     0     0     0     0     0     0\n",
       "[3,]     0     0     0     0     1     0     0     0     0     1     0     1\n",
       "[4,]     0     0     0     1     0     0     0     1     1     0     1     0\n",
       "[5,]     0     0     0     0     0     1     1     0     0     0     0     0\n",
       "     [,27] [,28] [,29] [,30]\n",
       "[1,]     0     1     1     0\n",
       "[2,]     0     0     0     0\n",
       "[3,]     1     0     0     0\n",
       "[4,]     0     0     0     0\n",
       "[5,]     0     0     0     1\n",
       "\n",
       "$objval\n",
       "[1] 650\n",
       "\n",
       "$slack\n",
       "[1] 10  1  5  3  4\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentGreedyLocalSearch(gap4.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval,\n",
    "     slack    = s$slack)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el problema [gap4.1](#gap4.1) las soluciones obtenidas han sido las siguientes: el resultado exacto del problema es ($656$), el resultado obtenido por el método *Greedy* propuesto por Martello-Toth es ($541$), que tras la heurística de *Búsqueda Local* toma el valor ($650$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### gap6.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "gap6.1 <- ReadGeneralizedAssignment(\"./data/assignment/gap6_1.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>761</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>37</li>\n",
       "\t<li>39</li>\n",
       "\t<li>44</li>\n",
       "\t<li>49</li>\n",
       "\t<li>48</li>\n",
       "\t<li>44</li>\n",
       "\t<li>42</li>\n",
       "\t<li>43</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 761\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 37\n",
       "\\item 39\n",
       "\\item 44\n",
       "\\item 49\n",
       "\\item 48\n",
       "\\item 44\n",
       "\\item 42\n",
       "\\item 43\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   761\n",
       "$slack\n",
       ":   1. 37\n",
       "2. 39\n",
       "3. 44\n",
       "4. 49\n",
       "5. 48\n",
       "6. 44\n",
       "7. 42\n",
       "8. 43\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    0    0    0    0    1    0    0    0     0     0     0     0     0\n",
       "[2,]    0    0    0    0    0    0    1    0    0     0     0     0     0     0\n",
       "[3,]    0    0    0    0    0    0    0    1    0     0     0     0     0     0\n",
       "[4,]    1    0    0    0    1    0    0    0    0     0     0     0     0     0\n",
       "[5,]    0    0    0    0    0    0    0    0    0     0     0     0     0     1\n",
       "[6,]    0    0    1    0    0    0    0    0    0     0     0     0     1     0\n",
       "[7,]    0    1    0    1    0    0    0    0    0     0     0     0     0     0\n",
       "[8,]    0    0    0    0    0    0    0    0    1     1     1     1     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     1     0     1     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     1     0     0     1     1     0     0     1     0     0     0\n",
       "[3,]     0     0     0     0     0     0     0     1     0     0     0     0\n",
       "[4,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[5,]     0     0     0     0     0     0     0     0     0     0     1     0\n",
       "[6,]     0     0     0     0     0     0     0     0     0     1     0     1\n",
       "[7,]     0     0     0     1     0     0     0     0     0     0     0     0\n",
       "[8,]     0     0     0     0     0     0     1     0     0     0     0     0\n",
       "     [,27] [,28] [,29] [,30] [,31] [,32]\n",
       "[1,]     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0\n",
       "[3,]     0     0     0     0     0     0\n",
       "[4,]     0     0     0     0     0     1\n",
       "[5,]     0     0     1     1     0     0\n",
       "[6,]     1     0     0     0     0     0\n",
       "[7,]     0     1     0     0     1     0\n",
       "[8,]     0     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 761\n",
       "\n",
       "$slack\n",
       "[1] 37 39 44 49 48 44 42 43\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentExact(gap6.1)\n",
    "list(solution = matrix(s$solution, nrow = gap6.1$m, byrow = TRUE),\n",
    "     objval   = s$optimum,\n",
    "     slack    = s$auxiliary$primal[1:gap6.1$m])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>664</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>26</li>\n",
       "\t<li>9</li>\n",
       "\t<li>14</li>\n",
       "\t<li>25</li>\n",
       "\t<li>24</li>\n",
       "\t<li>14</li>\n",
       "\t<li>21</li>\n",
       "\t<li>20</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllll}\n",
       "\t 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 664\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 26\n",
       "\\item 9\n",
       "\\item 14\n",
       "\\item 25\n",
       "\\item 24\n",
       "\\item 14\n",
       "\\item 21\n",
       "\\item 20\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   664\n",
       "$slack\n",
       ":   1. 26\n",
       "2. 9\n",
       "3. 14\n",
       "4. 25\n",
       "5. 24\n",
       "6. 14\n",
       "7. 21\n",
       "8. 20\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    1    0    0    0    0    1    1    0    0     0     0     0     0     0\n",
       "[2,]    0    0    0    0    1    0    0    0    0     0     0     0     0     0\n",
       "[3,]    0    1    0    0    0    0    0    0    0     0     0     0     0     0\n",
       "[4,]    0    0    0    0    0    0    0    0    0     0     1     1     0     0\n",
       "[5,]    0    0    0    0    0    0    0    0    1     0     0     0     0     1\n",
       "[6,]    0    0    0    0    0    0    0    0    0     0     0     0     1     0\n",
       "[7,]    0    0    0    1    0    0    0    0    0     0     0     0     0     0\n",
       "[8,]    0    0    1    0    0    0    0    1    0     1     0     0     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     1     1     0     1     1     0     0     0\n",
       "[3,]     0     0     1     1     0     0     0     0     0     0     0     0\n",
       "[4,]     0     1     0     0     0     0     0     0     0     0     0     0\n",
       "[5,]     1     0     0     0     0     0     0     0     0     0     0     1\n",
       "[6,]     0     0     0     0     0     0     0     0     0     0     1     0\n",
       "[7,]     0     0     0     0     0     0     0     0     0     1     0     0\n",
       "[8,]     0     0     0     0     0     0     1     0     0     0     0     0\n",
       "     [,27] [,28] [,29] [,30] [,31] [,32]\n",
       "[1,]     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0\n",
       "[3,]     0     0     0     0     1     0\n",
       "[4,]     0     0     0     0     0     1\n",
       "[5,]     0     0     0     0     0     0\n",
       "[6,]     1     1     0     1     0     0\n",
       "[7,]     0     0     1     0     0     0\n",
       "[8,]     0     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 664\n",
       "\n",
       "$slack\n",
       "[1] 26  9 14 25 24 14 21 20\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentGreedy(gap6.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval,\n",
    "     slack    = s$slack)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>746</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>5</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>4</li>\n",
       "\t<li>7</li>\n",
       "\t<li>6</li>\n",
       "\t<li>6</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 746\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 5\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 4\n",
       "\\item 7\n",
       "\\item 6\n",
       "\\item 6\n",
       "\\item 2\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   746\n",
       "$slack\n",
       ":   1. 5\n",
       "2. 3\n",
       "3. 1\n",
       "4. 4\n",
       "5. 7\n",
       "6. 6\n",
       "7. 6\n",
       "8. 2\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    0    0    0    0    1    0    0    1     0     0     1     0     0\n",
       "[2,]    0    0    0    0    0    0    1    0    0     1     0     0     0     0\n",
       "[3,]    0    1    0    0    0    0    0    0    0     0     0     0     0     0\n",
       "[4,]    1    0    0    0    0    0    0    0    0     0     0     0     0     0\n",
       "[5,]    0    0    0    0    0    0    0    0    0     0     0     0     0     1\n",
       "[6,]    0    0    1    0    0    0    0    0    0     0     0     0     1     0\n",
       "[7,]    0    0    0    1    0    0    0    0    0     0     0     0     0     0\n",
       "[8,]    0    0    0    0    1    0    0    1    0     0     1     0     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     1     1     0     0     1     0     0     0\n",
       "[3,]     0     0     1     0     0     0     0     0     0     0     0     0\n",
       "[4,]     0     1     0     0     0     0     0     0     0     0     0     0\n",
       "[5,]     0     0     0     0     0     0     0     1     0     0     1     0\n",
       "[6,]     0     0     0     0     0     0     0     0     0     1     0     1\n",
       "[7,]     1     0     0     1     0     0     0     0     0     0     0     0\n",
       "[8,]     0     0     0     0     0     0     1     0     0     0     0     0\n",
       "     [,27] [,28] [,29] [,30] [,31] [,32]\n",
       "[1,]     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0\n",
       "[3,]     1     0     0     1     0     0\n",
       "[4,]     0     0     0     0     1     1\n",
       "[5,]     0     0     1     0     0     0\n",
       "[6,]     0     1     0     0     0     0\n",
       "[7,]     0     0     0     0     0     0\n",
       "[8,]     0     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 746\n",
       "\n",
       "$slack\n",
       "[1] 5 3 1 4 7 6 6 2\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentGreedyLocalSearch(gap6.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval,\n",
    "     slack    = s$slack)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el problema [gap6.1](#gap6.1) las soluciones obtenidas han sido las siguientes: el resultado exacto del problema es ($761$), el resultado obtenido por el método *Greedy* propuesto por Martello-Toth es ($664$), que tras la heurística de *Búsqueda Local* toma el valor ($746$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### gap8.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "gap8.1 <- ReadGeneralizedAssignment(\"./data/assignment/gap8_1.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>1133</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>48</li>\n",
       "\t<li>53</li>\n",
       "\t<li>52</li>\n",
       "\t<li>52</li>\n",
       "\t<li>45</li>\n",
       "\t<li>50</li>\n",
       "\t<li>53</li>\n",
       "\t<li>46</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "\t 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 1133\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 48\n",
       "\\item 53\n",
       "\\item 52\n",
       "\\item 52\n",
       "\\item 45\n",
       "\\item 50\n",
       "\\item 53\n",
       "\\item 46\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   1133\n",
       "$slack\n",
       ":   1. 48\n",
       "2. 53\n",
       "3. 52\n",
       "4. 52\n",
       "5. 45\n",
       "6. 50\n",
       "7. 53\n",
       "8. 46\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    1    1    0    0    0    0    0    0    0     0     0     0     0     0\n",
       "[2,]    0    0    0    0    0    0    0    0    0     0     1     0     1     0\n",
       "[3,]    0    0    0    0    0    0    1    0    0     0     0     0     0     0\n",
       "[4,]    0    0    0    1    0    0    0    0    1     0     0     0     0     0\n",
       "[5,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0\n",
       "[6,]    0    0    0    0    1    1    0    1    0     0     0     0     0     0\n",
       "[7,]    0    0    0    0    0    0    0    0    0     1     0     0     0     1\n",
       "[8,]    0    0    1    0    0    0    0    0    0     0     0     1     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     1     0     0     0     0     0     0     0     0     0     1     0\n",
       "[2,]     0     0     0     0     0     0     0     1     0     1     0     0\n",
       "[3,]     0     0     0     1     0     0     0     0     0     0     0     0\n",
       "[4,]     0     0     1     0     1     0     0     0     0     0     0     0\n",
       "[5,]     0     0     0     0     0     0     1     0     0     0     0     1\n",
       "[6,]     0     1     0     0     0     1     0     0     0     0     0     0\n",
       "[7,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[8,]     0     0     0     0     0     0     0     0     1     0     0     0\n",
       "     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]\n",
       "[1,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     1     0     0     1     0     0     0\n",
       "[3,]     0     0     0     0     1     0     1     0     0     0     0     0\n",
       "[4,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[5,]     0     0     0     1     0     0     0     0     0     0     0     0\n",
       "[6,]     0     0     0     0     0     0     0     0     0     1     0     1\n",
       "[7,]     1     0     1     0     0     0     0     1     0     0     0     0\n",
       "[8,]     0     1     0     0     0     0     0     0     0     0     1     0\n",
       "     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]\n",
       "[1,]     0     0     0     1     0     1     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0     0     0     0     0\n",
       "[3,]     0     0     1     0     0     0     1     1     0     0\n",
       "[4,]     0     0     0     0     0     0     0     0     0     1\n",
       "[5,]     1     1     0     0     0     0     0     0     1     0\n",
       "[6,]     0     0     0     0     0     0     0     0     0     0\n",
       "[7,]     0     0     0     0     0     0     0     0     0     0\n",
       "[8,]     0     0     0     0     1     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 1133\n",
       "\n",
       "$slack\n",
       "[1] 48 53 52 52 45 50 53 46\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentExact(gap8.1)\n",
    "list(solution = matrix(s$solution, nrow = gap8.1$m, byrow = TRUE),\n",
    "     objval   = s$optimum,\n",
    "     slack    = s$auxiliary$primal[1:gap8.1$m])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>990</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>8</li>\n",
       "\t<li>16</li>\n",
       "\t<li>14</li>\n",
       "\t<li>17</li>\n",
       "\t<li>6</li>\n",
       "\t<li>12</li>\n",
       "\t<li>8</li>\n",
       "\t<li>16</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "\t 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 990\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 8\n",
       "\\item 16\n",
       "\\item 14\n",
       "\\item 17\n",
       "\\item 6\n",
       "\\item 12\n",
       "\\item 8\n",
       "\\item 16\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   990\n",
       "$slack\n",
       ":   1. 8\n",
       "2. 16\n",
       "3. 14\n",
       "4. 17\n",
       "5. 6\n",
       "6. 12\n",
       "7. 8\n",
       "8. 16\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    1    0    1    0    0    0    0    0     1     0     0     0     0\n",
       "[2,]    1    0    1    0    0    0    0    0    0     0     0     0     1     0\n",
       "[3,]    0    0    0    0    0    0    1    0    0     0     0     0     0     0\n",
       "[4,]    0    0    0    0    0    0    0    1    1     0     0     0     0     0\n",
       "[5,]    0    0    0    0    0    0    0    0    0     0     0     1     0     0\n",
       "[6,]    0    0    0    0    1    1    0    0    0     0     0     0     0     0\n",
       "[7,]    0    0    0    0    0    0    0    0    0     0     0     0     0     1\n",
       "[8,]    0    0    0    0    0    0    0    0    0     0     1     0     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     0     0     1     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[3,]     0     1     0     0     0     1     0     1     0     0     0     0\n",
       "[4,]     0     0     0     1     0     0     0     0     0     0     0     0\n",
       "[5,]     0     0     0     0     0     0     1     0     0     0     0     0\n",
       "[6,]     0     0     0     0     1     0     0     0     1     0     0     1\n",
       "[7,]     0     0     0     0     0     0     0     0     0     1     1     0\n",
       "[8,]     1     0     0     0     0     0     0     0     0     0     0     0\n",
       "     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]\n",
       "[1,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0     0     0     1     0     0     0\n",
       "[3,]     0     0     0     0     1     0     1     0     0     0     0     0\n",
       "[4,]     0     0     0     0     0     0     0     0     0     0     0     1\n",
       "[5,]     1     0     0     1     0     0     0     1     0     0     0     0\n",
       "[6,]     0     0     0     0     0     0     0     0     0     1     0     0\n",
       "[7,]     0     0     1     0     0     1     0     0     0     0     1     0\n",
       "[8,]     0     1     0     0     0     0     0     0     0     0     0     0\n",
       "     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]\n",
       "[1,]     1     0     0     0     0     1     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0     1     1     0     0\n",
       "[3,]     0     0     0     0     0     0     0     0     0     0\n",
       "[4,]     0     1     0     1     0     0     0     0     0     0\n",
       "[5,]     0     0     0     0     0     0     0     0     1     1\n",
       "[6,]     0     0     0     0     0     0     0     0     0     0\n",
       "[7,]     0     0     0     0     0     0     0     0     0     0\n",
       "[8,]     0     0     1     0     1     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 990\n",
       "\n",
       "$slack\n",
       "[1]  8 16 14 17  6 12  8 16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentGreedy(gap8.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval,\n",
    "     slack    = s$slack)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>1100</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>4</li>\n",
       "\t<li>2</li>\n",
       "\t<li>4</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\\\\n",
       "\t 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 1100\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | \n",
       "| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   1100\n",
       "$slack\n",
       ":   1. 1\n",
       "2. 2\n",
       "3. 1\n",
       "4. 2\n",
       "5. 4\n",
       "6. 2\n",
       "7. 4\n",
       "8. 1\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\n",
       "[1,]    0    1    0    0    0    0    0    0    0     1     0     0     0     0\n",
       "[2,]    0    0    1    0    0    0    0    0    0     0     1     0     1     0\n",
       "[3,]    0    0    0    0    0    0    1    0    0     0     0     0     0     0\n",
       "[4,]    0    0    0    0    0    0    0    0    1     0     0     0     0     0\n",
       "[5,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0\n",
       "[6,]    1    0    0    0    1    1    0    1    0     0     0     0     0     0\n",
       "[7,]    0    0    0    0    0    0    0    0    0     0     0     0     0     1\n",
       "[8,]    0    0    0    1    0    0    0    0    0     0     0     1     0     0\n",
       "     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]\n",
       "[1,]     1     0     0     0     1     0     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[3,]     0     1     0     0     0     0     0     0     0     0     0     0\n",
       "[4,]     0     0     1     1     0     0     0     0     0     0     0     0\n",
       "[5,]     0     0     0     0     0     1     1     0     0     0     0     1\n",
       "[6,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[7,]     0     0     0     0     0     0     0     0     1     1     1     0\n",
       "[8,]     0     0     0     0     0     0     0     1     0     0     0     0\n",
       "     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]\n",
       "[1,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[2,]     0     0     0     0     0     1     0     0     1     0     0     1\n",
       "[3,]     1     0     0     0     1     0     1     0     0     0     0     0\n",
       "[4,]     0     0     0     0     0     0     0     1     0     0     0     0\n",
       "[5,]     0     0     0     1     0     0     0     0     0     0     0     0\n",
       "[6,]     0     0     0     0     0     0     0     0     0     1     0     0\n",
       "[7,]     0     0     1     0     0     0     0     0     0     0     1     0\n",
       "[8,]     0     1     0     0     0     0     0     0     0     0     0     0\n",
       "     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]\n",
       "[1,]     0     0     0     0     0     1     0     1     0     0\n",
       "[2,]     0     0     0     0     0     0     0     0     0     0\n",
       "[3,]     0     0     1     0     0     0     0     0     0     0\n",
       "[4,]     0     1     0     1     0     0     0     0     0     0\n",
       "[5,]     1     0     0     0     0     0     0     0     1     1\n",
       "[6,]     0     0     0     0     0     0     1     0     0     0\n",
       "[7,]     0     0     0     0     0     0     0     0     0     0\n",
       "[8,]     0     0     0     0     1     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 1100\n",
       "\n",
       "$slack\n",
       "[1] 1 2 1 2 4 2 4 1\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentGreedyLocalSearch(gap8.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval,\n",
    "     slack    = s$slack)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el problema [gap8.1](#gap8.1) las soluciones obtenidas han sido las siguientes: el resultado exacto del problema es ($1133$), el resultado obtenido por el método *Greedy* propuesto por Martello-Toth es ($990$), que tras la heurística de *Búsqueda Local* toma el valor ($1100$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### gap12.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "gap12.1 <- ReadGeneralizedAssignment(\"./data/assignment/gap12_1.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
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       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
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       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>1451</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>75</li>\n",
       "\t<li>63</li>\n",
       "\t<li>71</li>\n",
       "\t<li>73</li>\n",
       "\t<li>65</li>\n",
       "\t<li>72</li>\n",
       "\t<li>68</li>\n",
       "\t<li>68</li>\n",
       "\t<li>73</li>\n",
       "\t<li>69</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 1451\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 75\n",
       "\\item 63\n",
       "\\item 71\n",
       "\\item 73\n",
       "\\item 65\n",
       "\\item 72\n",
       "\\item 68\n",
       "\\item 68\n",
       "\\item 73\n",
       "\\item 69\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   1451\n",
       "$slack\n",
       ":   1. 75\n",
       "2. 63\n",
       "3. 71\n",
       "4. 73\n",
       "5. 65\n",
       "6. 72\n",
       "7. 68\n",
       "8. 68\n",
       "9. 73\n",
       "10. 69\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       " [2,]    0    0    0    0    0    0    0    0    0     1     0     0     0\n",
       " [3,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       " [4,]    0    0    0    0    1    0    1    0    0     0     0     0     0\n",
       " [5,]    0    1    0    0    0    0    0    0    0     0     1     0     0\n",
       " [6,]    0    0    0    0    0    0    0    0    1     0     0     0     0\n",
       " [7,]    0    0    0    0    0    0    0    1    0     0     0     1     0\n",
       " [8,]    1    0    0    1    0    0    0    0    0     0     0     0     0\n",
       " [9,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "[10,]    0    0    0    0    0    0    0    0    0     0     0     0     1\n",
       "      [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]\n",
       " [1,]     0     0     0     0     0     0     0     1     0     0     0     0\n",
       " [2,]     0     1     1     0     0     0     0     0     0     0     0     0\n",
       " [3,]     0     0     0     0     0     0     0     0     0     1     0     0\n",
       " [4,]     0     0     0     0     0     0     0     0     1     0     0     0\n",
       " [5,]     0     0     0     0     0     1     0     0     0     0     0     1\n",
       " [6,]     1     0     0     0     0     0     0     0     0     0     0     0\n",
       " [7,]     0     0     0     0     1     0     0     0     0     0     0     0\n",
       " [8,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [9,]     0     0     0     1     0     0     0     0     0     0     1     0\n",
       "[10,]     0     0     0     0     0     0     1     0     0     0     0     0\n",
       "      [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]\n",
       " [1,]     0     0     1     0     0     0     1     0     0     0     0     0\n",
       " [2,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [3,]     1     0     0     1     0     1     0     0     0     0     0     0\n",
       " [4,]     0     1     0     0     1     0     0     0     0     0     0     0\n",
       " [5,]     0     0     0     0     0     0     0     0     0     1     1     0\n",
       " [6,]     0     0     0     0     0     0     0     1     0     0     0     1\n",
       " [7,]     0     0     0     0     0     0     0     0     1     0     0     0\n",
       " [8,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [9,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "[10,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "      [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]\n",
       " [1,]     0     0     1     1     0     0     0     0     0     0     1     0\n",
       " [2,]     0     0     0     0     1     0     0     0     0     0     0     0\n",
       " [3,]     0     1     0     0     0     0     0     0     0     1     0     0\n",
       " [4,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [5,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [6,]     0     0     0     0     0     0     0     0     1     0     0     0\n",
       " [7,]     0     0     0     0     0     0     0     0     0     0     0     1\n",
       " [8,]     1     0     0     0     0     1     0     0     0     0     0     0\n",
       " [9,]     0     0     0     0     0     0     1     1     0     0     0     0\n",
       "[10,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       "      [,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60]\n",
       " [1,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [2,]     0     0     0     1     0     0     0     0     1     0     0\n",
       " [3,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [4,]     0     0     0     0     1     0     0     1     0     0     0\n",
       " [5,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [6,]     1     0     0     0     0     0     0     0     0     0     0\n",
       " [7,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [8,]     0     0     0     0     0     0     0     0     0     1     0\n",
       " [9,]     0     0     1     0     0     1     0     0     0     0     1\n",
       "[10,]     0     1     0     0     0     0     1     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 1451\n",
       "\n",
       "$slack\n",
       " [1] 75 63 71 73 65 72 68 68 73 69\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentExact(gap12.1)\n",
    "list(solution = matrix(s$solution, nrow = gap12.1$m, byrow = TRUE),\n",
    "     objval   = s$optimum,\n",
    "     slack    = s$auxiliary$primal[1:gap12.1$m])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
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       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>1260</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>26</li>\n",
       "\t<li>30</li>\n",
       "\t<li>36</li>\n",
       "\t<li>27</li>\n",
       "\t<li>28</li>\n",
       "\t<li>38</li>\n",
       "\t<li>31</li>\n",
       "\t<li>26</li>\n",
       "\t<li>36</li>\n",
       "\t<li>27</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 1260\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 26\n",
       "\\item 30\n",
       "\\item 36\n",
       "\\item 27\n",
       "\\item 28\n",
       "\\item 38\n",
       "\\item 31\n",
       "\\item 26\n",
       "\\item 36\n",
       "\\item 27\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   1260\n",
       "$slack\n",
       ":   1. 26\n",
       "2. 30\n",
       "3. 36\n",
       "4. 27\n",
       "5. 28\n",
       "6. 38\n",
       "7. 31\n",
       "8. 26\n",
       "9. 36\n",
       "10. 27\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
       " [1,]    0    0    0    0    0    0    0    0    1     0     0     0     1\n",
       " [2,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [3,]    0    0    0    1    0    0    0    0    0     0     0     0     0\n",
       " [4,]    0    0    0    0    1    0    0    1    0     0     1     0     0\n",
       " [5,]    0    1    0    0    0    0    1    0    0     1     0     0     0\n",
       " [6,]    0    0    1    0    0    0    0    0    0     0     0     0     0\n",
       " [7,]    1    0    0    0    0    0    0    0    0     0     0     0     0\n",
       " [8,]    0    0    0    0    0    1    0    0    0     0     0     0     0\n",
       " [9,]    0    0    0    0    0    0    0    0    0     0     0     1     0\n",
       "[10,]    0    0    0    0    0    0    0    0    0     0     0     0     0\n",
       "      [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]\n",
       " [1,]     0     0     0     0     1     0     1     0     0     0     0     0\n",
       " [2,]     0     0     0     0     0     0     0     1     0     0     0     0\n",
       " [3,]     0     0     0     0     0     0     0     0     0     1     1     0\n",
       " [4,]     0     0     0     0     0     0     0     0     0     0     0     1\n",
       " [5,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [6,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [7,]     0     1     0     0     0     0     0     0     1     0     0     0\n",
       " [8,]     0     0     0     0     0     1     0     0     0     0     0     0\n",
       " [9,]     0     0     0     1     0     0     0     0     0     0     0     0\n",
       "[10,]     1     0     1     0     0     0     0     0     0     0     0     0\n",
       "      [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]\n",
       " [1,]     0     0     0     0     0     0     1     0     0     0     0     0\n",
       " [2,]     0     0     0     0     0     0     0     0     1     0     1     0\n",
       " [3,]     0     0     0     0     0     1     0     0     0     0     0     0\n",
       " [4,]     0     1     0     0     1     0     0     0     0     0     0     0\n",
       " [5,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [6,]     0     0     0     0     0     0     0     0     0     0     0     1\n",
       " [7,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [8,]     0     0     0     1     0     0     0     0     0     0     0     0\n",
       " [9,]     0     0     0     0     0     0     0     0     0     1     0     0\n",
       "[10,]     1     0     1     0     0     0     0     1     0     0     0     0\n",
       "      [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]\n",
       " [1,]     0     1     0     0     0     0     0     1     0     0     0     0\n",
       " [2,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [3,]     0     0     0     0     0     0     0     0     0     1     0     0\n",
       " [4,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [5,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [6,]     0     0     0     1     0     1     0     0     0     0     0     0\n",
       " [7,]     0     0     0     0     0     0     0     0     1     0     1     1\n",
       " [8,]     0     0     0     0     1     0     0     0     0     0     0     0\n",
       " [9,]     1     0     0     0     0     0     1     0     0     0     0     0\n",
       "[10,]     0     0     1     0     0     0     0     0     0     0     0     0\n",
       "      [,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60]\n",
       " [1,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [2,]     0     1     0     1     0     0     0     0     0     1     0\n",
       " [3,]     1     0     0     0     0     0     0     0     0     0     0\n",
       " [4,]     0     0     0     0     0     0     0     0     0     0     1\n",
       " [5,]     0     0     1     0     0     0     1     0     0     0     0\n",
       " [6,]     0     0     0     0     0     1     0     0     0     0     0\n",
       " [7,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [8,]     0     0     0     0     1     0     0     1     0     0     0\n",
       " [9,]     0     0     0     0     0     0     0     0     1     0     0\n",
       "[10,]     0     0     0     0     0     0     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 1260\n",
       "\n",
       "$slack\n",
       " [1] 26 30 36 27 28 38 31 26 36 27\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentGreedy(gap12.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval,\n",
    "     slack    = s$slack)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$solution</dt>\n",
       "\t\t<dd><table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$objval</dt>\n",
       "\t\t<dd>1433</dd>\n",
       "\t<dt>$slack</dt>\n",
       "\t\t<dd><ol class=list-inline>\n",
       "\t<li>5</li>\n",
       "\t<li>1</li>\n",
       "\t<li>22</li>\n",
       "\t<li>7</li>\n",
       "\t<li>11</li>\n",
       "\t<li>12</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>8</li>\n",
       "\t<li>4</li>\n",
       "</ol>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$solution] \\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "\t 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1\\\\\n",
       "\t 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$objval] 1433\n",
       "\\item[\\$slack] \\begin{enumerate*}\n",
       "\\item 5\n",
       "\\item 1\n",
       "\\item 22\n",
       "\\item 7\n",
       "\\item 11\n",
       "\\item 12\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 8\n",
       "\\item 4\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$solution\n",
       ":   \n",
       "| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | \n",
       "| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \n",
       "\n",
       "\n",
       "\n",
       "$objval\n",
       ":   1433\n",
       "$slack\n",
       ":   1. 5\n",
       "2. 1\n",
       "3. 22\n",
       "4. 7\n",
       "5. 11\n",
       "6. 12\n",
       "7. 3\n",
       "8. 3\n",
       "9. 8\n",
       "10. 4\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$solution\n",
       "      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]\n",
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       " [7,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [8,]     0     0     0     1     0     0     0     0     0     0     0     0\n",
       " [9,]     0     0     0     0     0     0     0     0     1     0     0     0\n",
       "[10,]     1     0     1     0     0     0     0     0     0     0     0     0\n",
       "      [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]\n",
       " [1,]     0     0     0     0     0     0     0     0     0     0     1     0\n",
       " [2,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [3,]     0     1     0     0     0     0     0     0     0     1     0     0\n",
       " [4,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [5,]     0     0     0     0     0     0     0     0     0     0     0     0\n",
       " [6,]     0     0     0     0     0     1     0     0     1     0     0     0\n",
       " [7,]     0     0     0     0     1     0     0     0     0     0     0     1\n",
       " [8,]     1     0     0     1     0     0     0     0     0     0     0     0\n",
       " [9,]     0     0     0     0     0     0     1     1     0     0     0     0\n",
       "[10,]     0     0     1     0     0     0     0     0     0     0     0     0\n",
       "      [,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60]\n",
       " [1,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [2,]     0     1     0     1     0     0     0     0     1     1     0\n",
       " [3,]     1     0     0     0     0     0     0     0     0     0     0\n",
       " [4,]     0     0     0     0     1     0     1     1     0     0     0\n",
       " [5,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [6,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [7,]     0     0     0     0     0     0     0     0     0     0     0\n",
       " [8,]     0     0     1     0     0     0     0     0     0     0     0\n",
       " [9,]     0     0     0     0     0     1     0     0     0     0     1\n",
       "[10,]     0     0     0     0     0     0     0     0     0     0     0\n",
       "\n",
       "$objval\n",
       "[1] 1433\n",
       "\n",
       "$slack\n",
       " [1]  5  1 22  7 11 12  3  3  8  4\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s <- GeneralizedAssignmentGreedyLocalSearch(gap12.1)\n",
    "list(solution = s$solution,\n",
    "     objval   = s$objval,\n",
    "     slack    = s$slack)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el problema [gap12.1](#gap12.1) las soluciones obtenidas han sido las siguientes: el resultado exacto del problema es ($1451$), el resultado obtenido por el método *Greedy* propuesto por Martello-Toth es ($1260$), que tras la heurística de *Búsqueda Local* toma el valor ($1433$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusiones\n",
    "\n",
    "El problema de asignación es un problema que a pesar de su simplicidad contextual, tiene grandes apliaciones en un amplio número de situaciones, es por ello que es necesario seguir estudiando el problema para buscar soluciones heurísticas eficientes y cercanas a la optimalidad. A pesar de las modelizaciones descritas en este trabajo, existen numeros ampliaciones que realizar sobre estas, tales como el aumento de la dimensionalidad del problema o la permisión de distintos valores en la demanda, al igual que ocurre con la asignación generalizada y la capacidad.\n",
    "\n",
    "En cuanto a las modelizaciones descritas en este trabajo, estas permiten la modelización de una gran cantidad de situaciones, por lo que han sido ampliamente estudiadas en la literatura, por lo que existe una gran cantidad de heurísticas cercanas a la optimalidad, tales como las descritas en este trabajo (*Greedy* y *Búsqueda Local*) dado que cuando el tamaño del problema es inmanejable para métodos exactos, dichas heurísticas son la única manera de aproximarnos a soluciones óptimas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Referencias\n",
    "\n",
    "  * [TRC13] Team, R.C., 2013. R: A language and environment for statistical computing.\n",
    "  * [GP18] Sergio García Prado. Programación Entera: Heurísticas, 2018. [github.com/garciparedes/integer-programming-heuristics](https://github.com/garciparedes/integer-programming-heuristics).\n",
    "  * [SA18] Jesús Sáez Aguado. Programación Entera, 2017/18. Facultad de Ciencias: Departamento de Estadística e Investigación Operativa.\n",
    "  * [THBSST17] Theussl, S., Hornik, K., Buchta, C., Schwendinger, F., Schuchardt, H. and Theussl, M.S., 2017. Package ‘Rglpk’.\n",
    "\n",
    "  "
   ]
  }
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