colab-notebook.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Genetski algoritmi-Domaci 1",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "jqpfQ-Zk9lJ-",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Prvo domaći iz Genetskih Algoritama\n",
        "\n",
        "\n",
        "## Miloš Milunović RN 17/2016 grupa 302\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "*   Binarni genetski algoritam\n",
        "*   Dvotačkasto ukrštanje\n",
        "*   Inverzija\n",
        "*   Levijeva funkcija broj 13\n",
        "\n",
        "\n",
        "\\begin{equation}\n",
        "f(x, y) = sin^2 3πx + (x − 1)^2(1 + sin^2 3πy) + (y − 1)^2(1 + sin^2 2πy) \\\\\n",
        "interval  -10 < x, y < 10, minimum f(1,1) = 0 \n",
        "\\end{equation}\n"
      ]
    },
    {
      "metadata": {
        "id": "2zoKa6nhAc1f",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 1. Biblioteke"
      ]
    },
    {
      "metadata": {
        "id": "QawUg0JZ-P3V",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "%matplotlib inline\n",
        "\n",
        "import random\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "\n",
        "from mpl_toolkits import mplot3d\n",
        "\n",
        "pi = 3.1415\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "AL3eeIrrAoJ_",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 2. Definicija Levijeve funkcije"
      ]
    },
    {
      "metadata": {
        "id": "1znWiBrCAv-n",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def levy_function(chromosome):\n",
        "  x = chromosome[0]\n",
        "  y = chromosome[1] \n",
        "  \n",
        "  tmp1 = math.pow(math.sin(3*pi*x), 2)\n",
        "  tmp2 = math.pow((x - 1), 2) * (1 + math.pow(math.sin(3*pi*y), 2))\n",
        "  tmp3 = math.pow((y - 1), 2) * (1 + math.pow(math.sin(2*pi*y), 2))\n",
        "\n",
        "  return tmp1 + tmp2 + tmp3\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "vJaGDqW56j-q",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 2.1. 3D Prikaz funkcije"
      ]
    },
    {
      "metadata": {
        "id": "u5Usj6lwCpVN",
        "colab_type": "code",
        "cellView": "both",
        "outputId": "04e5487a-34a9-449c-aa19-6f6eacf07168",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        }
      },
      "cell_type": "code",
      "source": [
        "def l_show(x, y):\n",
        "  tmp1 = math.pow(math.sin(3*pi*x), 2)\n",
        "  tmp2 = math.pow((x - 1), 2) * (1 + math.pow(math.sin(3*pi*y), 2))\n",
        "  tmp3 = math.pow((y - 1), 2) * (1 + math.pow(math.sin(2*pi*y), 2))\n",
        "\n",
        "  return tmp1 + tmp2 + tmp3\n",
        "\n",
        "levy_vectorized = np.vectorize(l_show)\n",
        "\n",
        "x = np.linspace(-13, 13, 30)\n",
        "y = np.linspace(-13, 13, 30)\n",
        "\n",
        "X, Y = np.meshgrid(x, y)\n",
        "Z = levy_vectorized(X, Y)\n",
        "\n",
        "ax = plt.axes(projection='3d')\n",
        "ax.plot_surface(X, Y, Z, rstride=1, cstride=1,\n",
        "                cmap='plasma', edgecolor='none')\n",
        "ax.set_title('Levijeva funkcija br.13');\n",
        "\n",
        "ax.view_init(50, 35)\n",
        "\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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5Y3iFEJgz30ObnFPnysShRv9b0Y9hngPSrYZt2xQKbgJ2FNGkOVfLIuUi0yXglxO6pPsS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060FU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\nx/VIkoSuB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UKogoMk+SB4WI6PrrkYmkO+oiELIpYLhYqKhIAtQM0X8SwwMiqWKbF0p4qi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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "liuOBEbIIBBi",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "\n",
        "# 3. Funkcija za kodovanje i dekodovanje hromozoma\n"
      ]
    },
    {
      "metadata": {
        "id": "f-p9lf0FIf5P",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "\n",
        "def bin_encode(chromosome, bin_val, min_val, precision):\n",
        "  \n",
        "  ret = \"\"\n",
        "  for g in chromosome:\n",
        "    val = round((g - min_val)/bin_val)  \n",
        "    ret += bin(val)[2:].rjust(precision,'0')\n",
        "  return ret\n",
        "\n",
        "def bin_encode_chromosomes(chromosomes, precision, max_val, min_val):\n",
        "  \n",
        "  bin_val = (max_val - min_val) / (2**precision-1) \n",
        "  \n",
        "  bin_chromosomes = [ bin_encode(c, bin_val, min_val, precision) for c in chromosomes]\n",
        "  return bin_chromosomes\n",
        "\n",
        "\n",
        "\n",
        "def bin_decode(chromosome, bin_val, min_val, precision):\n",
        "\n",
        "  ret = []\n",
        "  for idx in range(0, len(chromosome), precision):\n",
        "    g = int(chromosome[idx:idx + precision], 2)\n",
        "    ret.append(g * bin_val + min_val)\n",
        "    \n",
        "  return ret\n",
        "\n",
        "def bin_decode_chromosomes(chromosomes, precision, max_val, min_val):\n",
        "  \n",
        "  bin_val = (max_val - min_val) / (2**precision-1) \n",
        "\n",
        "  bin_chromosomes = [ bin_decode(c, bin_val, min_val, precision) for c in chromosomes]\n",
        "  return bin_chromosomes\n",
        "\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "9z1OzOS9IhAM",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 4. Funkcija za dvotačkasto ukrštanje\n",
        "Nasumično biramo dve tačke ukrštanja. Novi hromozomi (h3, h4) će biti sastavljeni od delova ulaznih hromozoma (h1, h2). I to na sledeći način:\n",
        "\n",
        "> * h3 dobija genetski materijal od h1 od početka do prve presečne tačke i od druge presečne tačke do kraja \n",
        "a genetski materijal od h2 dobija od prve do druge presečne tačke\n",
        "\n",
        "\n",
        "> * h4 dobija genetski materijal od h2 od početka do prve presečne tačke i od druge presečne tačke do kraja \n",
        "a genetski materijal od h1 dobija od prve do druge presečne tačke\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "H3yux1gVIhJz",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def two_point_crossover(pairs):\n",
        "  length = len(pairs[0])\n",
        "  children = []\n",
        "  \n",
        "  for (a,b) in pairs:  \n",
        "   \n",
        "      r1 = random.randrange(0, length)\n",
        "      r2 = random.randrange(0, length)\n",
        "      \n",
        "      if r1 < r2:\n",
        "        children.append(a[:r1] + b[r1:r2] + a[r2:])\n",
        "        children.append(b[:r1] + a[r1:r2] + b[r2:])\n",
        "      else:\n",
        "        children.append(a[:r2] + b[r2:r1] + a[r1:])\n",
        "        children.append(b[:r2] + a[r2:r1] + b[r1:])\n",
        "    \n",
        "  return children  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "y7pmXQGXIhUP",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 5. Mutacija inverzijom\n",
        "\n",
        "Nasumično biramo dve  tačke u hromozomu i genetski materijal koji se nalazi između te dve tačke invertujemo.\n",
        "\n",
        "\n",
        "\n",
        "> primer: h = [ 1110101000 ]\n",
        "<br>nasumično izabrani indeksi: r1 = 3, r2 = 6\n",
        "<br>rezultat nakon mutacije: [1111010000]\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "LMj39G3iIhbf",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def inv_mutation(chromosomes, mutation_rate):\n",
        "  mutated_chromosomes = []\n",
        "  \n",
        "  for chromosome in chromosomes:\n",
        "    \n",
        "    if random.random() < mutation_rate:\n",
        "      r1 = random.randrange(0, len(chromosome) - 1)\n",
        "      r2 = random.randrange(0, len(chromosome) - 1)\n",
        "      \n",
        "      if r1 < r2:\n",
        "        mutated_chromosomes.append(chromosome[:r1] + chromosome[r1:r2][::-1] + chromosome[r2:])\n",
        "      else:\n",
        "        mutated_chromosomes.append(chromosome[:r2] + chromosome[r2:r1][::-1] + chromosome[r1:])\n",
        "        \n",
        "    else:\n",
        "      mutated_chromosomes.append(chromosome)\n",
        "      \n",
        "\n",
        "  return mutated_chromosomes"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "82xmJg83OUYn",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 6. Generisanje populacije\n"
      ]
    },
    {
      "metadata": {
        "id": "Z3Qnt1hHaZ7r",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def generate_inital_chromosomes(length, max, min, pop_size):\n",
        "  return [ [random.uniform(min,max) for j in range(length)] for i in range(pop_size)]\n",
        "\n",
        "def population_stats(costs):\n",
        "  return costs[0], sum(costs)/len(costs)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Rot7GYZIIhjl",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 7. Funkcije za rangiranje i odabir hromozoma\n",
        "\n",
        "Jedinke se rangiraju po vrednosti funkcije troška funkcijom **rank_chromosomes**.</br>\n",
        "Zatim se funkcijom **natural_selection** ostavljamo samo prvih *n_keep* jedinki.</br>\n",
        "Funkcija **pairing** uparuje roditeljske hromozome po principu najbolji i sledeći najbolji..."
      ]
    },
    {
      "metadata": {
        "id": "ujBA5vK_Ihpz",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "\n",
        "def rank_chromosomes(cost, chromosomes):\n",
        "  costs = list(map(cost, chromosomes))\n",
        "  ranked  = sorted( list(zip(chromosomes,costs)), key = lambda c:c[1])\n",
        "  \n",
        "  return list(zip(*ranked))\n",
        "\n",
        "def natural_selection(chromosomes, n_keep):\n",
        "  return chromosomes[:n_keep]\n",
        "\n",
        "def pairing(parents):\n",
        "  pairs = []\n",
        "  i = 0\n",
        "  for i in range(0, len(parents), 2):\n",
        "    pairs.append([parents[i], parents[i+1]])\n",
        "      \n",
        "  return pairs"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "9rU0sO9QIhwm",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 8. Main loop - sklopljen genetski algoritam\n",
        "- Generišemo početnu populaciju veličine *population_size* \n",
        "- Vrtimo glavnu petlju maksimalno *max_iter* puta, svaka iteracija petlje je jedna generacija\n",
        "- Rangiramo jedinke po prilagođenosti, funkcijom **rank_chromosomes**\n",
        "- Funkcijom **natural_selection** biramo roditelje\n",
        "- Funkcijom **bin_encode_chromosomes** kodujemo celu roditeljsku populaciju\n",
        "- Funkcijom **pairing** odvajamo parove roditeljskih hromozoma koje ćemo ukrstiti\n",
        "- Metodom *dvotačkastog ukrštanja*, tj funkcijom **two_point_crossover** uparujemo roditeljske hromozome i dobijemo populaciju dece\n",
        "- Spajamo novonastale hromozome sa roditeljskim u novu populaciju *chromosomes* \n",
        "- Na ovoj populaciji vršimo *inverznu mutaciju* funkcijom **inv_mutation** sa zadatim *mutation_rate = 0.3*\n",
        "- Dekodujemo celu populaciju funkcijom **bin_decode_chromosomes**\n",
        "- Proveravamo da li populacija konvergira ili da li smo došli do optimalnog rešenja\n",
        "- Ispisujemo statistike za svaku generaciju: prosečna prilagođenost, najbolji hromozom i sastav najboljeg hromozoma"
      ]
    },
    {
      "metadata": {
        "id": "XXfAPOOUIh3R",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def genetic(cost_func , extent, population_size, mutation_rate = 0.3, chromosome_length = 2, precision = 13, max_iter = 500):\n",
        "  \n",
        "  min_val = extent[0]\n",
        "  max_val = extent[1]\n",
        "  \n",
        "  \n",
        "  avg_list = []\n",
        "  best_list = []\n",
        "  curr_best = 10000\n",
        "  same_best_count = 0\n",
        "  \n",
        "  chromosomes = generate_inital_chromosomes(chromosome_length, max_val, min_val, population_size)\n",
        " \n",
        "  for iter in range(max_iter):\n",
        "      \n",
        "    ranked, costs = rank_chromosomes(cost_func, chromosomes) \n",
        "    \n",
        "    best, average = population_stats(costs)\n",
        "    \n",
        "    parents = natural_selection(ranked, population_size)\n",
        "    \n",
        "    parents = bin_encode_chromosomes(parents, precision, max_val, min_val)  \n",
        "    \n",
        "    pairs = pairing(parents)   \n",
        "    \n",
        "    children = two_point_crossover(pairs)\n",
        "    chromosomes = parents + children    \n",
        "    \n",
        "    chromosomes = inv_mutation(chromosomes, mutation_rate)\n",
        "\n",
        "    chromosomes = bin_decode_chromosomes(chromosomes, precision, max_val, min_val)\n",
        "    \n",
        "    \n",
        "    print(\"Generation: \",iter+1,\" Average: {:.3f}\".format(average),\" Curr best: {:.3f}\".format(best), \n",
        "          \"[X, Y] = {:.3f} {:.3f}\".format(chromosomes[0][0],chromosomes[0][1]))\n",
        "    print(\"-------------------------\")\n",
        "    \n",
        "    avg_list.append(average)\n",
        "    if best < curr_best:\n",
        "      best_list.append(best)\n",
        "      curr_best = best\n",
        "      same_best_count = 0\n",
        "    else:\n",
        "      same_best_count += 1\n",
        "      best_list.append(best)\n",
        "      \n",
        "    \n",
        "    if(cost_func(chromosomes[0]) < 0.05):\n",
        "      \n",
        "      avg_list = avg_list[:iter]\n",
        "      best_list = best_list[:iter]\n",
        "      all_avg_list.append(avg_list)\n",
        "      all_best_list.append(best_list)\n",
        "      generations_list.append(iter)\n",
        "     \n",
        "      print(\"\\nSolution found ! Chromosome content: [X, Y] = {:.3f} {:.3f}\\n\".format(chromosomes[0][0],chromosomes[0][1]))\n",
        "      return\n",
        "        \n",
        "    if same_best_count > 20:\n",
        "      print(\"\\nStopped due to convergance.Best chromosome [X, Y] = {:.3f} {:.3f}\\n\".format(chromosomes[0][0],chromosomes[0][1]))\n",
        "      \n",
        "      avg_list = avg_list[:iter]\n",
        "      best_list = best_list[:iter]\n",
        "      all_avg_list.append(avg_list)\n",
        "      all_best_list.append(best_list)\n",
        "      generations_list.append(iter)\n",
        "      \n",
        "      return\n",
        "    \n",
        "    if iter == 499:\n",
        "      avg_list = avg_list[:iter]\n",
        "      best_list = best_list[:iter]\n",
        "      all_avg_list.append(avg_list)\n",
        "      all_best_list.append(best_list)\n",
        "      generations_list.append(iter)\n",
        "      \n",
        "      print(\"\\nStopped due to max number of iterations, solution not found. Best chromosome [X, Y] = {:.3f} {:.3f}\\n\".format(chromosomes[0][0],chromosomes[0][1]))\n",
        "      \n",
        "\n",
        "   "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "5CLeZ0oEz7QX",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 9. Iscrtavanje grafikona</br>\n",
        "Iscrtavamo prosečnu i najbolji prilagođenost za svaku generaciju."
      ]
    },
    {
      "metadata": {
        "id": "Uj5EkLRHz7h9",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def display_stats(all_avg_list, all_best_list, generations_list):\n",
        "  \n",
        "  c = 0\n",
        "  colors = ['red', 'green', 'blue', 'yellow', 'orange']\n",
        "  \n",
        "  for average_list in all_avg_list:\n",
        "      x_axis = list(range(generations_list[c]))\n",
        "      y_axis = average_list\n",
        "      plt.plot(x_axis, y_axis, linewidth=3, color=colors[c], label=str(c + 1))\n",
        "      plt.title('Average cost function value', fontsize=19)\n",
        "      plt.xlabel('Generation', fontsize=10)\n",
        "      plt.ylabel('Cost function')\n",
        "      c += 1\n",
        "  plt.legend(loc='upper right')\n",
        "  plt.show()\n",
        "\n",
        "  c = 0\n",
        "\n",
        "  for best_list in all_best_list:\n",
        "      x_axis = list(range(generations_list[c]))\n",
        "      y_axis = best_list\n",
        "      plt.plot(x_axis, y_axis, color=colors[c], label=str(c + 1))\n",
        "      plt.title('Best cost function value', fontsize=19)\n",
        "      plt.xlabel('Generation')\n",
        "      plt.ylabel('Cost function')\n",
        "      c += 1\n",
        "  plt.legend(loc='upper right')\n",
        "  plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "i6ea8eLALxgt",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# 10. Konfigurisanje i poziv genetskog algoritma\n",
        "\n",
        "Argumenti funkcije:\n",
        "\n",
        "\n",
        "1.   Funkcija za minimizaciju (u našem slučaju Levy_function) - *function*\n",
        "2.   Opseg u kome pretražujemo rešenje - *list*\n",
        "3.   Broj hromozoma - *int*\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "Opcioni argumenti:\n",
        "\n",
        "\n",
        "4.   Stopa mutacije - *float*\n",
        "5.   Dužina hromozoma - *int*\n",
        "6.   Na koliko decimala kodujemo X i Y - *int*\n",
        "7.   Maksimalni broj iteracija - *int*\n",
        "\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "aigHUlbI2Xdm",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "number_of_chromosomes = [20, 100, 150]\n",
        "all_avg_list = []\n",
        "generations_list = []\n",
        "all_best_list = []\n",
        "run_number = 5\n",
        "\n",
        "for x in number_of_chromosomes:\n",
        "  \n",
        "  print(\"==========================\")\n",
        "  \n",
        "  for k in range(0, run_number):\n",
        "    \n",
        "    print(\"\\n\", k + 1, \": run of genetic algorithm with \", x ,\" chromosomes.\\n\")    \n",
        "    genetic(levy_function, [10, -10], x)\n",
        "    \n",
        "  display_stats(all_avg_list, all_best_list, generations_list)\n",
        "  all_best_list = []\n",
        "  all_avg_list = []\n",
        "  generations_list = []\n"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}