Snake_CP.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/OptimizationExpert/Pyomo/blob/main/Snake_CP.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fntyf_g_YElb"
      },
      "source": [
        "Developed by Alireza Soroudi\n",
        "alireza.soroudi@gmail.com\n",
        "\n",
        "Linkedin News letter : https://www.linkedin.com/newsletters/optimization-in-open-source-6874020019009859585/\n",
        "\n",
        "Git hub: https://github.com/OptimizationExpert/Pyomo"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FwTzUa-VH1ro",
        "outputId": "526d774e-648e-4b07-b306-aa2440d832db"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: ortools in /usr/local/lib/python3.10/dist-packages (9.11.4210)\n",
            "Requirement already satisfied: absl-py>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from ortools) (2.1.0)\n",
            "Requirement already satisfied: numpy>=1.13.3 in /usr/local/lib/python3.10/dist-packages (from ortools) (1.26.4)\n",
            "Requirement already satisfied: pandas>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from ortools) (2.2.2)\n",
            "Requirement already satisfied: protobuf<5.27,>=5.26.1 in /usr/local/lib/python3.10/dist-packages (from ortools) (5.26.1)\n",
            "Requirement already satisfied: immutabledict>=3.0.0 in /usr/local/lib/python3.10/dist-packages (from ortools) (4.2.0)\n",
            "Requirement already satisfied: python-dateutil>=2.8.2 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2024.2)\n",
            "Requirement already satisfied: tzdata>=2022.7 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2024.2)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.2->pandas>=2.0.0->ortools) (1.16.0)\n"
          ]
        }
      ],
      "source": [
        "import pandas as pd\n",
        "!pip install ortools\n",
        "from ortools.sat.python import cp_model\n",
        "import matplotlib.pyplot as plt # Data visualization\n",
        "import random\n",
        "import numpy as np\n",
        "import time\n",
        "from google.colab import drive\n",
        "#drive.mount('/content/drive')\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        },
        "id": "PCA1dBYJH8wz",
        "outputId": "7f819770-f74a-4951-b2fb-2c35690f4ed6"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "dic = {}\n",
        "counter = 0\n",
        "N = 17\n",
        "n = N**2\n",
        "\n",
        "nr, nc = N, N\n",
        "for r in range(nr):\n",
        "  for c in range(nc):\n",
        "    counter+=1\n",
        "    dic[counter] = (c,r,1)\n",
        "    if c==(N-1)/2 and r not in [1 , (N-1)/2, N-2]:\n",
        "      dic[counter] = (c,r,0)\n",
        "\n",
        "\n",
        "plt.figure(figsize=(5,5))\n",
        "for counter, (r,c,v) in dic.items():\n",
        "  plt.scatter(r,c,s=v*120,c='k',marker='s', alpha =1)\n",
        "  if v==0 :\n",
        "    plt.scatter(r,c,s=120,c='grey',marker='s', alpha =0.2)\n",
        "\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "plt.tight_layout()\n",
        "plt.grid()\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def distance(n:int,m:int,data:dict)-> int:\n",
        "  x1,y1 = data[n][0],data[n][1]\n",
        "  x2,y2 = data[m][0],data[m][1]\n",
        "  return int(100*(10000**(2-data[n][2]-data[m][2])) * np.sqrt( (x1-x2)**2+(y1-y2)**2))/100"
      ],
      "metadata": {
        "id": "jPInUR7VouYV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "distance(4,5,dic), len(dic)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5YdEZfuq-bcP",
        "outputId": "38d6c555-42f1-489a-f8de-74bf76dc2315"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1.0, 289)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AeesyXV7Q-yP",
        "outputId": "edf8f2e7-e521-498c-e0d5-5815eb6b0c0b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "17"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "\n",
        "KOLORS  = [\"red\", \"green\", \"blue\", \"orange\", \"purple\", \"cyan\", \"magenta\",\n",
        "    \"yellow\", \"lime\", \"pink\", \"brown\", \"gray\", \"olive\", \"navy\", \"teal\"\n",
        "]\n",
        "N"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "8zbesxN6yW5D"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3-7GCM8FgGYj",
        "outputId": "6a9581a7-059c-4732-b62d-41181e952dfa"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "FEASIBLE\n",
            "Time  243.34406638145447\n",
            "Min of objective function: 130.0\n",
            "\n"
          ]
        }
      ],
      "source": [
        "def main() -> None:\n",
        "    # Creates the model.\n",
        "\n",
        "    model = cp_model.CpModel()\n",
        "\n",
        "    nodes = [i for i in dic.keys() if dic[i][2]==1]\n",
        "    x={(i,j):model.NewBoolVar(f\"flow_{i}_{j}\") for i in nodes for j in nodes if distance(i,j,dic)== 1}\n",
        "    assign = {i: model.NewBoolVar(f\"assign_{i}\") for i in nodes}\n",
        "\n",
        "\n",
        "    endpoint = {i: model.NewBoolVar(f\"end_{i}\") for i in nodes if dic[i][1] not in [0,N-1] and dic[i][0] not in [0,N-1]}\n",
        "    startpoint = {i: model.NewBoolVar(f\"st_{i}\") for i in nodes if dic[i][1] in [0,N-1] or dic[i][0] in [0,N-1]}\n",
        "\n",
        "    linked= {(i,j): model.NewBoolVar(f\"linked_{i}_{j}\") for i in startpoint for j in endpoint}\n",
        "\n",
        "\n",
        "    ###################################################################################################\n",
        "    arcs= [ (i,j,v) for (i,j),v in x.items()] + [(i,i,assign[i].Not()) for i in nodes] + [(i,j,v) for (i,j),v in linked.items()]\n",
        "    model.AddCircuit(arcs)\n",
        "\n",
        "    boundry_nodes_right = [v for i,v in assign.items() if i in startpoint and dic[i][1] >= N/2]\n",
        "    model.AddExactlyOne(boundry_nodes_right)\n",
        "\n",
        "    boundry_nodes_all = [v for i,v in assign.items() if i in startpoint]\n",
        "    model.AddExactlyOne(boundry_nodes_all)\n",
        "\n",
        "\n",
        "    boundry_nodes = [v for i,v in startpoint.items()]\n",
        "    model.AddExactlyOne(boundry_nodes)\n",
        "\n",
        "\n",
        "    nonboundry_nodes = [v for v in endpoint.values()]\n",
        "    model.AddExactlyOne(nonboundry_nodes)\n",
        "\n",
        "    nonboundry_nodes_left = [v for i,v in endpoint.items()]\n",
        "    model.AddExactlyOne(nonboundry_nodes_left)\n",
        "\n",
        "\n",
        "    for (i,j),v in linked.items():\n",
        "      model.Add(v <= assign[i])\n",
        "      model.Add(v <= assign[j])\n",
        "      model.Add(v >= startpoint[i] + endpoint[j] - 1)\n",
        "      model.Add(v <= startpoint[i])\n",
        "      model.Add(v <= endpoint[j])\n",
        "\n",
        "\n",
        "    ################################### Non Touching ################################################################\n",
        "    for (i,j),v in x.items():\n",
        "      if (j,i) in x and i>j:\n",
        "        model.Add(assign[i]+assign[j]<=  1+ v + x[j,i] )\n",
        "    ###################################################################################################\n",
        "\n",
        "    expressions_of = [v for v in assign.values()]\n",
        "    model.Maximize(cp_model.LinearExpr.Sum(expressions_of))\n",
        "\n",
        "    solver = cp_model.CpSolver()\n",
        "    solver.parameters.subsolvers[:] = ['core', 'pseudo_costs', 'no_lp']\n",
        "    solver.parameters.max_time_in_seconds = 240\n",
        "    solver.parameters.num_search_workers = 4\n",
        "    status = solver.solve(model)\n",
        "    print(solver.StatusName(status))\n",
        "\n",
        "    if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:\n",
        "        return solver,x, assign, startpoint, endpoint\n",
        "\n",
        "    else:\n",
        "        print(\"No solution found.\")\n",
        "\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "  st= time.time()\n",
        "  solver, x,assign, startpoint, endpoint = main()\n",
        "  print(\"Time \", time.time()-st)\n",
        "  print(f\"Min of objective function: {solver.objective_value}\\n\")\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dic[144],dic[145]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uFvsnExmVsFm",
        "outputId": "49b3a72a-632b-40bc-c42e-a6fe7fb60b75"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((7, 8, 1), (8, 8, 1))"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "plt.figure(figsize=(5,5))\n",
        "for counter, (r,c,v) in dic.items():\n",
        "  plt.scatter(r,c,s=v*120,c='k',marker='s', alpha =0.3)\n",
        "  if v==0 :\n",
        "    plt.scatter(r,c,s=120,c='grey',marker='s', alpha =0.2)\n",
        "\n",
        "#for counter, (r,c,v) in dic.items():\n",
        "#  plt.text(r,c,s=str(counter), alpha =0.5)\n",
        "c=0\n",
        "for i,v in assign.items():\n",
        "  r,c = dic[i][0], dic[i][1]\n",
        "  plt.text(r,c,s=str(i), fontsize=7)\n",
        "\n",
        "  if solver.value(v) == 0:\n",
        "    plt.scatter(r,c,s=120,c='k',marker='s', alpha =1)\n",
        "\n",
        "\n",
        "\n",
        "for (i,j),v in x.items():\n",
        "  if solver.value(v)>0:\n",
        "      x1,y1 = dic[i][0],dic[i][1]\n",
        "      x2,y2 = dic[j][0],dic[j][1]\n",
        "      plt.plot([x1,x2],[y1,y2], lw=3, c='r', alpha=1,zorder = 2)\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "plt.tight_layout()\n",
        "plt.grid()"
      ],
      "metadata": {
        "id": "CdJ3xVASb1I0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        },
        "outputId": "8afc6ebb-de77-44b6-f454-59f309d32095"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "plt.figure(figsize=(5,5))\n",
        "for counter, (r,c,v) in dic.items():\n",
        "  plt.scatter(r,c,s=v*120,c='k',marker='s', alpha =1)\n",
        "  if v==0 :\n",
        "    plt.scatter(r,c,s=120,c='grey',marker='s', alpha =0.2)\n",
        "\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "plt.tight_layout()\n",
        "plt.grid()\n",
        "\n",
        "st = sum([i*solver.Value(v) for i,v in startpoint.items()])\n",
        "ep = sum([i*solver.Value(v) for i,v in endpoint.items()])\n",
        "print(st,ep)\n",
        "contin = True\n",
        "counter = 1\n",
        "while contin:\n",
        "  for (i,j),v in x.items():\n",
        "    if solver.Value(v)>0 and j==st:\n",
        "      x1,y1 = dic[i][0],dic[i][1]\n",
        "      x2,y2 = dic[j][0],dic[j][1]\n",
        "      plt.scatter(x1,y1,s=120,c='gold',marker='s', alpha =1, zorder=2)\n",
        "      plt.plot([x1,x2],[y1,y2], lw=3, c='r', alpha=1,zorder = 2)\n",
        "      st = i\n",
        "      #plt.savefig(f'/content/drive/MyDrive/img/graph{counter}.png')\n",
        "      counter+=1\n",
        "      if i ==ep:\n",
        "        contin = False\n",
        "        break\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        },
        "id": "JUbiAwf8HU4Z",
        "outputId": "ae52b543-d69f-4991-e517-8716423a6c33"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "154 19\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(5,5))\n",
        "for counter, (r,c,v) in dic.items():\n",
        "  plt.scatter(r,c,s=v*120,c='k',marker='s', alpha =1)\n",
        "  if v==0 :\n",
        "    plt.scatter(r,c,s=120,c='grey',marker='s', alpha =0.2)\n",
        "\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "plt.tight_layout()\n",
        "plt.grid()\n"
      ],
      "metadata": {
        "id": "htXqH72cl_x0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        },
        "outputId": "bf92af3d-e621-4825-e7fe-f5416b2b1fdc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}