2d_no_overlap.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/2d_no_overlap.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VvJL0bOSIm84"
      },
      "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\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w_3yuwV8XtMF",
        "outputId": "e3cb38b6-c273-4a36-dfc6-b956579b9989"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting ortools\n",
            "  Downloading ortools-9.9.3963-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (24.8 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m24.8/24.8 MB\u001b[0m \u001b[31m22.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hCollecting absl-py>=2.0.0 (from ortools)\n",
            "  Downloading absl_py-2.1.0-py3-none-any.whl (133 kB)\n",
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            "\u001b[?25hRequirement already satisfied: numpy>=1.13.3 in /usr/local/lib/python3.10/dist-packages (from ortools) (1.25.2)\n",
            "Requirement already satisfied: pandas>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from ortools) (2.0.3)\n",
            "Collecting protobuf>=4.25.3 (from ortools)\n",
            "  Downloading protobuf-5.26.1-cp37-abi3-manylinux2014_x86_64.whl (302 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m302.8/302.8 kB\u001b[0m \u001b[31m11.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hCollecting immutabledict>=3.0.0 (from ortools)\n",
            "  Downloading immutabledict-4.2.0-py3-none-any.whl (4.7 kB)\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) (2023.4)\n",
            "Requirement already satisfied: tzdata>=2022.1 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2024.1)\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",
            "Installing collected packages: protobuf, immutabledict, absl-py, ortools\n",
            "  Attempting uninstall: protobuf\n",
            "    Found existing installation: protobuf 3.20.3\n",
            "    Uninstalling protobuf-3.20.3:\n",
            "      Successfully uninstalled protobuf-3.20.3\n",
            "  Attempting uninstall: absl-py\n",
            "    Found existing installation: absl-py 1.4.0\n",
            "    Uninstalling absl-py-1.4.0:\n",
            "      Successfully uninstalled absl-py-1.4.0\n",
            "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
            "google-ai-generativelanguage 0.6.2 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-api-core 2.11.1 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0.dev0,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-aiplatform 1.48.0 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-bigquery-connection 1.12.1 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-bigquery-storage 2.24.0 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-datastore 2.15.2 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-firestore 2.11.1 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-functions 1.13.3 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-iam 2.15.0 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-language 2.13.3 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-resource-manager 1.12.3 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "google-cloud-translate 3.11.3 requires protobuf!=3.20.0,!=3.20.1,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "googleapis-common-protos 1.63.0 requires protobuf!=3.20.0,!=3.20.1,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0.dev0,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "grpc-google-iam-v1 0.13.0 requires protobuf!=3.20.0,!=3.20.1,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.19.5, but you have protobuf 5.26.1 which is incompatible.\n",
            "proto-plus 1.23.0 requires protobuf<5.0.0dev,>=3.19.0, but you have protobuf 5.26.1 which is incompatible.\n",
            "tensorflow 2.15.0 requires protobuf!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5,<5.0.0dev,>=3.20.3, but you have protobuf 5.26.1 which is incompatible.\n",
            "tensorflow-metadata 1.15.0 requires protobuf<4.21,>=3.20.3; python_version < \"3.11\", but you have protobuf 5.26.1 which is incompatible.\u001b[0m\u001b[31m\n",
            "\u001b[0mSuccessfully installed absl-py-2.1.0 immutabledict-4.2.0 ortools-9.9.3963 protobuf-5.26.1\n"
          ]
        }
      ],
      "source": [
        "!pip install ortools\n",
        "from ortools.sat.python import cp_model # CP-SAT solver\n",
        "import numpy as np\n",
        "from random import randint\n",
        "import random\n",
        "from math import ceil\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt # Data visualization\n",
        "from matplotlib.patches import Rectangle\n",
        "from google.colab import files\n",
        "\n",
        "import matplotlib.patches as patches\n",
        "\n",
        "#from google.colab import drive\n",
        "#drive.mount('/content/drive')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = {}\n",
        "N = 10\n",
        "rects = range(N)\n",
        "\n",
        "for rec in rects:\n",
        "  data[rec,'l']= random.randint(1,7)\n",
        "  data[rec,'w']= random.randint(1,5)\n",
        "\n",
        "\n",
        "data"
      ],
      "metadata": {
        "id": "zp3BLJ8Jxjxh",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "df75e086-91a4-4ab4-832b-815cde819ce4"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{(0, 'l'): 7,\n",
              " (0, 'w'): 1,\n",
              " (1, 'l'): 5,\n",
              " (1, 'w'): 2,\n",
              " (2, 'l'): 2,\n",
              " (2, 'w'): 3,\n",
              " (3, 'l'): 3,\n",
              " (3, 'w'): 2,\n",
              " (4, 'l'): 3,\n",
              " (4, 'w'): 5,\n",
              " (5, 'l'): 7,\n",
              " (5, 'w'): 4,\n",
              " (6, 'l'): 6,\n",
              " (6, 'w'): 4,\n",
              " (7, 'l'): 2,\n",
              " (7, 'w'): 4,\n",
              " (8, 'l'): 1,\n",
              " (8, 'w'): 2,\n",
              " (9, 'l'): 2,\n",
              " (9, 'w'): 4}"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "{(0, 'l'): 7,\n",
        " (0, 'w'): 1,\n",
        " (1, 'l'): 5,\n",
        " (1, 'w'): 2,\n",
        " (2, 'l'): 2,\n",
        " (2, 'w'): 3,\n",
        " (3, 'l'): 3,\n",
        " (3, 'w'): 2,\n",
        " (4, 'l'): 3,\n",
        " (4, 'w'): 5,\n",
        " (5, 'l'): 7,\n",
        " (5, 'w'): 4,\n",
        " (6, 'l'): 6,\n",
        " (6, 'w'): 4,\n",
        " (7, 'l'): 2,\n",
        " (7, 'w'): 4,\n",
        " (8, 'l'): 1,\n",
        " (8, 'w'): 2,\n",
        " (9, 'l'): 2,\n",
        " (9, 'w'): 4}"
      ],
      "metadata": {
        "id": "mou99sP2yjCZ"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "AxZSoOv2-NEu"
      },
      "outputs": [],
      "source": [
        "KOLORS = [\"#1f77b4\", \"#ff7f0e\", \"#2ca02c\", \"#d62728\", \"#9467bd\",\n",
        "            \"#8c564b\", \"#e377c2\", \"#7f7f7f\", \"#bcbd22\", \"#17becf\",\n",
        "            \"#aec7e8\", \"#ffbb78\", \"#98df8a\", \"#ff9896\", \"#c5b0d5\",\n",
        "            \"#c49c94\", \"#f7b6d2\", \"#c7c7c7\", \"#dbdb8d\", \"#9edae5\",\n",
        "            \"#8c6d31\", \"#9c9ede\", \"#637939\", \"#e7cb94\", \"#b5cf6b\",\n",
        "            \"#cedb9c\", \"#c7c7c7\", \"#bd9e39\", \"#e7969c\", \"#7b4173\"]"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n"
      ],
      "metadata": {
        "id": "lqw1iTmuft6T"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model = cp_model.CpModel()\n",
        "solver = cp_model.CpSolver()\n",
        "Lmax = 20\n",
        "Wmax = 10\n",
        "x = {i:model.NewIntVar(0,Lmax-data[i,'l']  , f\"X_{i}\") for i in rects}\n",
        "y = {i:model.NewIntVar(0,Wmax-data[i,'w']  , f\"Y_{i}\") for i in rects}\n",
        "\n",
        "\n",
        "X_list = [model.NewIntervalVar(x[i],data[i,'l'] , x[i]+data[i,'l'], f\"Xinterval_{i}\") for i in rects]\n",
        "Y_list = [model.NewIntervalVar(y[i],data[i,'w'] , y[i]+data[i,'w'], f\"Yinterval_{i}\") for i in rects]\n",
        "model.AddNoOverlap2D(X_list, Y_list)\n",
        "\n",
        "status = solver.Solve(model)\n",
        "if status == cp_model.FEASIBLE:\n",
        "  print(\"feasible\")\n",
        "elif status == cp_model.OPTIMAL:\n",
        "  print(\"optimal\")\n",
        "elif status == cp_model.INFEASIBLE:\n",
        "  print(\"INFEASIBLE\")\n",
        "elif status == cp_model.UNKNOWN:\n",
        "  print(\"UNKNOWN\")\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1u74WJiO3-3W",
        "outputId": "2f0ba8b4-886f-4804-d8ed-d7f749e6aa38"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "optimal\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt # Data visualization\n",
        "from matplotlib.patches import Rectangle\n",
        "plt.figure(figsize=(8,6))\n",
        "\n",
        "for i in rects:\n",
        "  x0,y0 = solver.value(x[i]), solver.value(y[i])\n",
        "  plt.gca().add_patch(Rectangle((x0,y0), data[i,'l'],data[i,'w'],linewidth=1,edgecolor='k',facecolor=KOLORS[i], alpha =0.2))\n",
        "  plt.text(x0+0.5*data[i,'l'],y0+0.5*data[i,'w'], s= str(i))\n",
        "\n",
        "\n",
        "# Create a figure\n",
        "\n",
        "# Set limits\n",
        "plt.xlim(0, 22)\n",
        "plt.ylim(0, 12)\n",
        "plt.tight_layout()\n",
        "plt.xticks(range(25))\n",
        "plt.yticks(range(12))\n",
        "\n",
        "# Show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 601
        },
        "id": "A8PQBlL4QJrj",
        "outputId": "2d02d5e9-ce4c-4356-a244-3c53f6cb09b9"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n"
      ],
      "metadata": {
        "id": "KVj_xEHrn2k0"
      },
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yJdhHr-DIlur"
      },
      "source": []
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}