TSP_Example.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "TSP Example",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/djrmarques/genetic_tsp/blob/master/TSP_Example.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-zJeTkoYdaP-",
        "colab_type": "text"
      },
      "source": [
        "# Simple genetic algorithm application on a TSP problem\n",
        "Super simple genetic algorithm example to solve the TSP.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5x8_4OlhdYbm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.spatial.distance import pdist, squareform\n",
        "from itertools import starmap\n",
        "from tqdm import tqdm\n",
        "from numba import njit"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p3W-fQZqdsIg",
        "colab_type": "text"
      },
      "source": [
        "## Create a simple TSP problem"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gg89unmKdk_L",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "max_coord =  50  # Upper limit of the coordinates\n",
        "np.random.seed(50)\n",
        "\n",
        "def create_cities(n_cities):\n",
        "  \"\"\" Creates a random set of cities \"\"\"\n",
        "  city_coords = np.random.randint(1, max_coord, size=(n_cities, 2))\n",
        "  distance_matrix = squareform(pdist(city_coords))\n",
        "  return city_coords, distance_matrix\n",
        "\n",
        "n_cities = 5\n",
        "city_coords, distance_matrix = create_cities(n_cities)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iTcEtrA3hiWX",
        "colab_type": "text"
      },
      "source": [
        "### Show the distance matrix"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mfQQwCq6heEF",
        "colab_type": "code",
        "outputId": "663bc2c1-390c-4c0a-991c-c2672465468d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        }
      },
      "source": [
        "distance_matrix"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.  , 39.22, 15.13, 51.11, 28.23],\n",
              "       [39.22,  0.  , 26.63, 39.62, 46.87],\n",
              "       [15.13, 26.63,  0.  , 37.64, 24.33],\n",
              "       [51.11, 39.62, 37.64,  0.  , 33.  ],\n",
              "       [28.23, 46.87, 24.33, 33.  ,  0.  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1US-ruF2hmiR",
        "colab_type": "text"
      },
      "source": [
        "### Plot the cities\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9lHRb4ajhd56",
        "colab_type": "code",
        "outputId": "cee25217-c566-481b-b433-6395f8a9adb7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "plt.scatter(city_coords[:, 0], city_coords[:, 1])\n",
        "plt.title(\"City coordinates\")\n",
        "plt.show()"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PSvaIJmfgc1k",
        "colab_type": "text"
      },
      "source": [
        "## Defining a chromosome and the fitness function\n",
        "A solution is going to be defined by the sequence of the cities: \n",
        "- Example: [0, 2, 3, 1,4]\n",
        "- The fitness of the solution is the total distance\n",
        "\n",
        "**Objective is to minimize the distance**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bB30mOJDfc_j",
        "colab_type": "code",
        "outputId": "724e2c5c-e1d1-4e19-fc34-61dfc0bf2cb9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "def get_fitness(path):\n",
        "  \"\"\" Calculates and returns the fitness value of a particular sequence \"\"\"\n",
        "  stacked_path = np.stack((path, np.roll(path, -1)))\n",
        "  return distance_matrix[stacked_path[0, :], stacked_path[1, :]].sum()\n",
        "\n",
        "# Defining an example path\n",
        "example_path = np.array([0, 4, 2, 3, 1])\n",
        "print(f\"Path: {example_path} | Traveled Distance: {int(get_fitness(example_path))}\")"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Path: [0 4 2 3 1] | Traveled Distance: 169\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4X0yKx3esr-S",
        "colab_type": "text"
      },
      "source": [
        "## Defining crossover operation\n",
        "\n",
        "A crossover operation will be used to combine two individuals and yield an offspring, sharing characteristics from both parents.\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tSevZKAbs2gJ",
        "colab_type": "code",
        "outputId": "576cc1bf-770f-4389-bed5-daa36ae9c06e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 156
        }
      },
      "source": [
        "@njit\n",
        "def crossover(sequence1, sequence2):\n",
        "    \"\"\" Creates an offspring by mixing the genetic material of two parents \"\"\"\n",
        "\n",
        "    # Size of the chromosomes\n",
        "    n_jobs = sequence1.shape[0]\n",
        "\n",
        "    # Select two crossover points\n",
        "    crossover_points = np.random.choice(n_jobs, 2)\n",
        "    crossover_points.sort()\n",
        "    c1, c2 = crossover_points\n",
        "\n",
        "    # Create offspring\n",
        "    new_sequence = sequence1.copy()\n",
        "    for i in range(c1, c2):\n",
        "        gen_to_change = sequence2[i]\n",
        "        for j in range(n_jobs):\n",
        "            if gen_to_change == new_sequence[j]:\n",
        "                new_sequence[j] = new_sequence[i]\n",
        "                new_sequence[i] = gen_to_change\n",
        "                break\n",
        "\n",
        "    return new_sequence\n",
        "\n",
        "n_cities = 10\n",
        "\n",
        "city_coords, distance_matrix = create_cities(n_cities)\n",
        "\n",
        "\n",
        "# Create two parents\n",
        "parent1 = np.arange(n_cities)\n",
        "parent2 = parent1.copy()\n",
        "np.random.shuffle(parent1)\n",
        "np.random.shuffle(parent2)\n",
        "\n",
        "# Create offpring\n",
        "offspring = crossover(parent1, parent2)\n",
        "\n",
        "# Assert that all the elements are unique\n",
        "assert offspring.shape[0] == np.unique(offspring.shape[0])\n",
        "\n",
        "\n",
        "print(\"Chromosomes\")\n",
        "print(\"Parent 1 :\", parent1)\n",
        "print(\"Parent 2 :\", parent2)\n",
        "print(\"Offspring:\", offspring)\n",
        "\n",
        "print(\"Fitness\")\n",
        "print(\"Parent 1  fitness:\", round(get_fitness(parent1)))\n",
        "print(\"Parent 2  fitness:\", round(get_fitness(parent2)))\n",
        "print(\"Offspring fitness:\", round(get_fitness(offspring)))"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Chromosomes\n",
            "Parent 1 : [8 1 4 5 2 7 3 6 0 9]\n",
            "Parent 2 : [6 1 5 0 7 8 4 2 9 3]\n",
            "Offspring: [6 1 5 0 7 8 3 2 4 9]\n",
            "Fitness\n",
            "Parent 1  fitness: 268.0\n",
            "Parent 2  fitness: 328.0\n",
            "Offspring fitness: 256.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X0czfbFiEPZd",
        "colab_type": "text"
      },
      "source": [
        "## Selection Method\n",
        "How are we going to select the parents to crossover?\n",
        "\n",
        "- Roulete Wheel Selection: Fittest members are more likely to be chosen"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PvxqnT0ME2wt",
        "colab_type": "code",
        "outputId": "e0083e4e-81c9-4e57-f643-535e134df814",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        }
      },
      "source": [
        "np.random.seed(50)\n",
        "np.set_printoptions(precision=2)\n",
        "\n",
        "fitness_array = np.arange(1, 50, 1, dtype=float)\n",
        "\n",
        "# Define the selection pressure: Probabiltieis change over the genrations\n",
        "beta=0.1\n",
        "fitness_array *= -beta\n",
        "probs = np.exp(fitness_array)\n",
        "probs /= probs.sum()\n",
        "\n",
        "# Plot\n",
        "plt.figure(figsize=(10, 5))\n",
        "lines = plt.plot(probs)\n",
        "plt.xlabel(\"Fitness Level\")\n",
        "plt.ylabel(\"Probability of selection\")\n",
        "plt.title(\"Probability of selection as function of fitness\")\n",
        "plt.show()"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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WRwzP5d63V1FRXRPrckRERKQDUUjbSxcdMZTNJRX8931d3FZERERaj0LaXjpieC779srk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\n",
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PSpFsY0Dny9c",
        "colab_type": "text"
      },
      "source": [
        "## Run Genetic algorithm\n",
        "\n",
        "1. Create Random Population\n",
        "2. Evalute Fitness\n",
        "3. Select Parents\n",
        "4. Apply Crossover operation on parents until a new generation is created\n",
        "3. Repeat 2-4 until generation limit\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tm62SnZOhx5z",
        "colab_type": "text"
      },
      "source": [
        "### Create new set of cities"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NZ_D-fFPeFaf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Creating a new city\n",
        "np.random.seed(42)\n",
        "\n",
        "n_cities = 20\n",
        "\n",
        "# New city coordinates and distance matrix\n",
        "city_coords, distance_matrix = create_cities(n_cities)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uAbNUWIWh12s",
        "colab_type": "text"
      },
      "source": [
        "### Solve with genetic algorithm"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kqsQqkecsqRP",
        "colab_type": "code",
        "outputId": "fb139d90-ff75-4ab8-9537-c86084626457",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 341
        }
      },
      "source": [
        "np.random.seed()\n",
        "\n",
        "# Genetic algorithm parameters\n",
        "n_pop = 30000\n",
        "n_its = 300\n",
        "\n",
        "# Creates initial population \n",
        "population = np.tile(np.arange(n_cities), (n_pop, 1))\n",
        "np.apply_along_axis(arr=population, func1d=np.random.shuffle, axis=1)\n",
        "\n",
        "# Fitness per generation placeholder array\n",
        "fitness_per_generation = np.zeros(n_its + 1)\n",
        "\n",
        "# Evaluate the fitness of every member of the population\n",
        "fitness_list = np.apply_along_axis(arr=population, func1d=get_fitness, axis=1)\n",
        "\n",
        "# Get the best element\n",
        "best_element_id = np.argmax(fitness_list)\n",
        "\n",
        "# Save best fitness and best solution\n",
        "best_fitness = fitness_list[best_element_id]\n",
        "best_solution = population[best_element_id]\n",
        "\n",
        "# Save the best fitness \n",
        "fitness_per_generation[0] = best_fitness\n",
        "\n",
        "# Start genetic algorithm\n",
        "for i in tqdm(range(1, n_its+1)):\n",
        "\n",
        "  # Select the parents. Members with lower fitness will be more likely to be chosen\n",
        "  selection_pressure = -0.05\n",
        "  fitness_list *= selection_pressure\n",
        "  probs = np.exp(fitness_list)\n",
        "  probs /= probs.sum()\n",
        "\n",
        "  # Select the parents based on the probability\n",
        "  parents_index = np.random.choice(np.arange(n_pop), p=probs, size=(n_pop, 2))\n",
        "  parents = population[parents_index]\n",
        "\n",
        "  # Create new generation\n",
        "  population = np.array(list(starmap(crossover, parents)))\n",
        "  # Evaluate the fitness of every member of the population\n",
        "  fitness_list = np.apply_along_axis(arr=population, func1d=get_fitness, axis=1)\n",
        "\n",
        "  # Get the best element\n",
        "  best_element_id = np.argmax(fitness_list)\n",
        "  generation_best_fitness = fitness_list[best_element_id]\n",
        "\n",
        "  # Append best element to fittest by generation\n",
        "  fitness_per_generation[i] = generation_best_fitness\n",
        "\n",
        "  # Saves the best results\n",
        "  if generation_best_fitness < best_fitness:\n",
        "    best_fitness = generation_best_fitness\n",
        "    best_solution = population[best_element_id]\n",
        "\n",
        "  # print(f\"Generation {i} | Fitness: {generation_best_fitness}\")\n",
        "\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(fitness_per_generation)\n",
        "plt.show()"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 300/300 [08:43<00:00,  1.72s/it]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wi49fuoSNOw/x+dXP0VhTyUVLW3nX6+ce/TkpJZ7fdYifPLebZ7YdYPehLt6z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\n",
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QuTjnyvs4tN_",
        "colab_type": "text"
      },
      "source": [
        "## View the final result"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g6dGdN-E4wXC",
        "colab_type": "code",
        "outputId": "ba780f4c-87e0-4021-d62d-23805a006de2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 724
        }
      },
      "source": [
        "plt.figure(figsize=(12, 12))\n",
        "x = np.append(city_coords[best_solution][:, 0], city_coords[best_solution][:, 0][0])\n",
        "y = np.append(city_coords[best_solution][:, 1], city_coords[best_solution][:, 1][0])\n",
        "plt.plot(x, y, label=\"path\")\n",
        "plt.scatter(city_coords[:, 0], city_coords[:, 1], c=\"red\", label=\"cities\")\n",
        "plt.title(f\"Fitness: {int(best_fitness)}\")\n",
        "plt.legend(fontsize=18, bbox_to_anchor=(1.18, 1.05))\n",
        "plt.show()"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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u6gbtrGrQD07p2ynnAwDALpQXAF7D18ehSYPjNWlwvKobWrSoY1jZA//eoIfe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S6NPZvVIiTAyTwt3JcKoPAiIn7P4TA82qMRk1LasGn/SfpNSGPT/pN2l1Vixe2Sc0u0+FZExBjD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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x864 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}