authors/fdabrandao/vpsolver/vpsolver.ipynb

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      "source": [
        "# VPSolver: Cutting & Packing Problems\n",
        "[![vpsolver.ipynb](https://img.shields.io/badge/github-%23121011.svg?logo=github)](https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/vpsolver/vpsolver.ipynb) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/vpsolver/vpsolver.ipynb) [![Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/vpsolver/vpsolver.ipynb) [![Gradient](https://assets.paperspace.io/img/gradient-badge.svg)](https://console.paperspace.com/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/vpsolver/vpsolver.ipynb) [![Open In SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/vpsolver/vpsolver.ipynb) [![Hits](https://h.ampl.com/https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/vpsolver/vpsolver.ipynb)](https://colab.ampl.com)\n",
        "\n",
        "Description: Solving cutting & packing problems using arc-flow formulations\n",
        "\n",
        "Tags: industry, cutting-stock, bin-packing, vector-packing\n",
        "\n",
        "Notebook author: Filipe Brandão <<fdabrandao@gmail.com>>\n",
        "\n",
        "Model author: Filipe Brandão\n",
        "\n",
        "References:\n",
        "1. [Brandão, F. (2017). Cutting & Packing Problems: General Arc-flow Formulation with Graph Compression.](https://vpsolver.fdabrandao.pt/)"
      ]
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      "source": [
        "# Install dependencies\n",
        "!apt -qq install libgraphviz-dev\n",
        "%pip install -q amplpy pygraphviz pyvpsolver"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
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        "colab": {
          "base_uri": "https://localhost:8080/",
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      "source": [
        "# Google Colab & Kaggle integration\n",
        "from amplpy import AMPL, ampl_notebook\n",
        "\n",
        "ampl = ampl_notebook(\n",
        "    modules=[\"highs\"],  # modules to install\n",
        "    license_uuid=\"default\",  # license to use\n",
        ")  # instantiate AMPL object and register magics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m_IQlwsKYk3t"
      },
      "source": [
        "### Instance preparation:\n",
        "\n",
        "1. Define a multiple-choice vector bin packing instance:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "QXEVfnJzYk3t"
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      "source": [
        "from pyvpsolver import VPSolver, MVP, AFG, MPS\n",
        "\n",
        "Ws, Cs, Qs = [(5180, 9), (5189, 9)], [1, 1], [-1, -1]\n",
        "ws = [[(1120, 1)], [(1250, 1)], [(520, 1)], [(1066, 1)], [(1000, 1)], [(1150, 1)]]\n",
        "b = [9, 5, 91, 18, 11, 64]\n",
        "instance = MVP(Ws, Cs, Qs, ws, b)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pk3rixroYk3u"
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      "source": [
        "2. Build an arc-flow graph for the instance defined above:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
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          "text": [
            "VPSolver 3.1.3, Copyright (C) 2013-2016, Filipe Brandao\n",
            "Build (method = -3)\n",
            "  #dp: 163\n",
            "  Step-3' Graph: 50 vertices and 199 arcs (0.00s)\n",
            "  Step-4' Graph: 39 vertices and 132 arcs (0.00s)\n",
            "  #V4/#V3 = 0.78\n",
            "  #A4/#A3 = 0.66\n",
            "Ready! (0.00s)\n"
          ]
        },
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            "text/plain": [
              "<IPython.core.display.SVG object>"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "afg = AFG(instance)\n",
        "from IPython.display import SVG\n",
        "\n",
        "afg.draw(\"graph_vbp.svg\", lpaths=True, graph_attrs={\"size\": \"8,8\"})\n",
        "SVG(\"graph_vbp.svg\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IawMOAIkYk3x"
      },
      "source": [
        "### Model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
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        "%%ampl_eval\n",
        "reset;\n",
        "set V;\n",
        "set A dimen 4;\n",
        "var Flow{A} integer >= 0;\n",
        "\n",
        "set Targets;\n",
        "param Cost{Targets};\n",
        "param Quantity{Targets};\n",
        "minimize TotalCost:\n",
        "    sum{t in Targets} Cost[t] * Flow[t,'S',-1,-1];\n",
        "s.t. BinQuantity{t in Targets: Quantity[t] >= 0}:\n",
        "    Flow[t,'S',-1,-1] <= Quantity[t];\n",
        "\n",
        "set Items;\n",
        "param Demand{Items};\n",
        "s.t. SatisfyDemand{i in Items}:\n",
        "    sum{(u,v,i,j) in A} Flow[u,v,i,j] >= Demand[i];\n",
        "\n",
        "s.t. FlowConservation{k in V}:\n",
        "    (sum{(u,v,i,j) in A: v == k} Flow[u,v,i,j]) - (sum{(u,v,i,j) in A: u == k} Flow[u,v,i,j]) == 0;"
      ]
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      "metadata": {
        "id": "2x5-wxxlpeTn"
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      "source": [
        "### Data"
      ]
    },
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      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "lm6kasqGYk3y"
      },
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      "source": [
        "graph = afg.graph()\n",
        "ampl.set[\"Items\"] = list(range(len(b)))\n",
        "ampl.param[\"Demand\"] = instance.b\n",
        "ampl.set[\"Targets\"] = graph.Ts\n",
        "ampl.param[\"Cost\"] = instance.Cs\n",
        "ampl.param[\"Quantity\"] = instance.Qs\n",
        "ampl.set[\"V\"] = graph.V\n",
        "ampl.set[\"A\"] = [\n",
        "    (u, v) + l if l != graph.LOSS else (u, v, -1, -1) for u, v, l in graph.A\n",
        "]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QhcC0RiPpjge"
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      "source": [
        "### Solve"
      ]
    },
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      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3e04VuCYizEO",
        "outputId": "6925e248-9396-40e8-9cd7-b9b679adea6a"
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          "text": [
            "HiGHS 1.2.2: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.2.2: optimal solution; objective 33\n",
            "1 branching nodes\n",
            "absmipgap=7.10543e-14, relmipgap=2.15316e-15\n"
          ]
        }
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        "ampl.option[\"solver\"] = \"highs\"\n",
        "ampl.solve()"
      ]
    },
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      "cell_type": "markdown",
      "metadata": {
        "id": "Z4oQXqY7rCFm"
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      "source": [
        "### Extrat solution for the original problem"
      ]
    },
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      "execution_count": 8,
      "metadata": {
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          "base_uri": "https://localhost:8080/"
        },
        "id": "2LDzvKklrJyB",
        "outputId": "884c0aeb-30a1-4dae-cec8-10f1b437ffec"
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          "text": [
            "Bins of type 1: 0 bins\n",
            "Bins of type 2: 33 bins\n",
            "\t11 x [i=3 opt=1, i=3 opt=1, i=3 opt=1, i=3 opt=1, i=3 opt=1, i=3 opt=1, i=4 opt=1, i=5 opt=1]\n",
            "\t15 x [i=3 opt=1, i=6 opt=1, i=6 opt=1, i=6 opt=1, i=6 opt=1]\n",
            "\t4 x [i=1 opt=1, i=1 opt=1, i=2 opt=1, i=3 opt=1, i=6 opt=1]\n",
            "\t1 x [i=1 opt=1, i=3 opt=1, i=4 opt=1, i=4 opt=1, i=4 opt=1]\n",
            "\t1 x [i=2 opt=1, i=3 opt=1, i=4 opt=1, i=4 opt=1, i=4 opt=1]\n",
            "\t1 x [i=1 opt=1, i=3 opt=1, i=3 opt=1, i=3 opt=1, i=3 opt=1, i=3 opt=1, i=4 opt=1]\n"
          ]
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        "values = ampl.get_data(\n",
        "    \"{(u,v,i,j) in A: round(Flow[u,v,i,j]) > 0} round(Flow[u,v,i,j])\"\n",
        ").to_dict()\n",
        "flows = {}\n",
        "for (u, v, i, j), value in values.items():\n",
        "    u = u if isinstance(u, str) else int(u)\n",
        "    v = v if isinstance(v, str) else int(v)\n",
        "    l = graph.LOSS if i == -1 else (int(i), int(j))\n",
        "    flows[u, v, l] = int(value)\n",
        "    assert (u, v, l) in graph.A\n",
        "graph.flow = flows\n",
        "graph.labels = {(u, v, lbl): [lbl] for (u, v, lbl) in graph.A if lbl != graph.LOSS}\n",
        "for i in range(len(Ws)):\n",
        "    total_flow = flows.get((graph.Ts[i], \"S\", graph.LOSS), 0)\n",
        "    sol = graph.extract_solution(graph.S, \"<-\", graph.Ts[i], flow_limit=total_flow)\n",
        "    assert sum(m for m, p in sol) == total_flow\n",
        "    print(\n",
        "        \"Bins of type {0}: {1} {2}\".format(\n",
        "            i + 1, total_flow, [\"bins\", \"bin\"][total_flow == 1]\n",
        "        )\n",
        "    )\n",
        "    for mult, patt in sol:\n",
        "        print(\n",
        "            \"\\t\"\n",
        "            + \"{0} x [{1}]\".format(\n",
        "                mult, \", \".join([f\"i={it+1} opt={opt+1}\" for it, opt in patt])\n",
        "            )\n",
        "        )"
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