Genetic_Algorithm.ipynb

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  "metadata": {
    "colab": {
      "name": "CI_CW_Q1.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
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        "id": "V3V_8wXMcGCH"
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      "source": [
        "<img src=\"https://avatars.githubusercontent.com/u/61354833\" align=\"left\" width=\"70\" height=\"70\">\n",
        "\n",
        "Code by [TomMakesThings](https://github.com/TomMakesThings/Computational-Intelligence-Genetic-Algorithm)"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "# **About**\n",
        "\n",
        "#### **Problem Definition**\n",
        "This code solves the following multi-objective optimisation problem using the elitist non-dominated sorting genetic algorithm (NSGA-II)\n",
        "\n",
        "$min\\{f_{1}, f_{2}\\}$\n",
        "\n",
        "### $f_{1} = \\frac{(\\frac{x_{1}}{2})^2 + (\\frac{x_{2}}{4})^2 + (x_{3})^2}{3}$\n",
        "\n",
        "### $f_{2} = \\frac{(\\frac{x_{1}}{2} - 1)^2 + (\\frac{x_{2}}{4} - 1)^2 + (x_{3} - 1)^2}{3}$\n",
        "\n",
        "For $-4.0 \\le x_{1}, x_{2}, x_{3} \\le 4.0$\n",
        "\n",
        "<br>\n",
        "\n",
        "#### **Implementation**\n",
        "\n",
        "**Encoding**\n",
        "\n",
        "The decision variables for each individual ($x_{1}, x_{2}, x_{3}$) are set up for minimization with gray coding. This is an encoding in which adjacent numbers have a single digit differing by 1.\n",
        "\n",
        "| Binary | Gray Code |\n",
        "| ------ | --------- |\n",
        "| 000    | 000       |\n",
        "| 001    | 001       |\n",
        "| 010    | 011       |\n",
        "| 011    | 010       |\n",
        "| 100    | 110       |\n",
        "| 101    | 111       |\n",
        "| 110    | 101       |\n",
        "| 111    | 100       |\n",
        "\n",
        "<br>\n",
        "\n",
        "**Population Initialisation and Evaluation**\n",
        "\n",
        "A population of 25 individuals is created and each is assigned a random 10-bit string when initialized. They are then evaluated to determine their fitness. First the gray code values are converted to real values within the range $[-4, 4]$ using equation:\n",
        "\n",
        "$x_{i} = a_{i} + (b_{i} - a_{i}) \\times \\frac{c_{i}}{2^l - 1}$\n",
        "\n",
        "<sub>where:</sub>\n",
        "- <sub>$a_{i}$ is the lower bound $-4$</sub>\n",
        "- <sub>$b_{i}$ is the upper bound $4$</sub>\n",
        "- <sub>$c_{i}$ is the integer value of the gray code</sub>\n",
        "- <sub>l is the length of each gene</sub>\n",
        "\n",
        "<br>\n",
        "\n",
        "Then using the decoded values, $f_{1}$ and $f_{2}$ are calculated.\n",
        "\n",
        "| Individual | $x_{1}$    | $x_{2}$    | $x_{3}$    | $f_{1}$  | $f_{2}$  |\n",
        "| ---------- | ---------- | ---------- | ---------- | -------- | -------- |\n",
        "| 1          | 1100000101 | 1110111000 | 1101000010 | 0.371571 | 0.433807 |\n",
        "| 2          | 1110111000 | 1101001011 | 1110101100 | 1.05772  | 0.319697 |\n",
        "| ...        | ...        | ...        | ...        | ...      | ...      |\n",
        "| 24         | 1001111110 | 0110110001 | 0010111100 | 2.78652  | 4.50792  |\n",
        "| 25         | 0010011011 | 0101100100 | 0000001110 | 5.49692  | 9.91497  |\n",
        "\n",
        "<br>\n",
        "\n",
        "Individuals are sorted into fronts using the efficient non-dominated sorting algorithm. First the population is copied, then sorted based on $f_{1}$. If the $f_{1}$ are equal, then sort on $f_{2}$. The first solution is assigned to front 1. All further solutions are compared the current front, starting with front 1. If they are dominated by at least 1 solution in the current front, a new front is created with this individual. Otherwise check the next front. If all fronts are checked, a new front is created containing this individual. \n",
        "\n",
        "| Individual | $x_{1}$    | $x_{2}$    | $x_{3}$    | $f_{1}$  | $f_{2}$  | Front |\n",
        "| ---------- | ---------- | ---------- | ---------- | -------- | -------- | - |\n",
        "| 1          | 1100000101 | 1110111000 | 1101000010 | 0.371571 | 0.433807 | 1 |\n",
        "| 2          | 1110111000 | 1101001011 | 1110101100 | 1.05772  | 0.319697 | 1 |\n",
        "| ...        | ...        | ...        | ...        | ...      | ...      | ... |\n",
        "| 24         | 1001111110 | 0110110001 | 0010111100 | 2.78652  | 4.50792  | 7 |\n",
        "| 25         | 0010011011 | 0101100100 | 0000001110 | 5.49692  | 9.91497  | 8 |\n",
        "\n",
        "<br>\n",
        "\n",
        "Once the individuals are separated into fronts, the crowding distance for individuals in each front is calculated. Solutions at the end of each front are assigned infinite distance, while those in between are assigned the average side length of its two neighbouring solutions.\n",
        "\n",
        "| Individual | $x_{1}$    | $x_{2}$    | $x_{3}$    | $f_{1}$  | $f_{2}$  | Front | Crowding Distance |\n",
        "| ---------- | ---------- | ---------- | ---------- | -------- | -------- | - | -|\n",
        "| 1          | 1100000101 | 1110111000 | 1101000010 | 0.371571 | 0.433807 | 1 | $\\infty$ |\n",
        "| 2          | 1110111000 | 1101001011 | 1110101100 | 1.05772  | 0.319697 | 1 | 1| \n",
        "| ...        | ...        | ...        | ...        | ...      | ...      | ... | ... |\n",
        "| 24         | 1001111110 | 0110110001 | 0010111100 | 2.78652  | 4.50792  | 7 | $\\infty$ |\n",
        "| 25         | 0010011011 | 0101100100 | 0000001110 | 5.49692  | 9.91497  | 8 | $\\infty$ |\n",
        "\n",
        "<br>\n",
        "\n",
        "**Mate Selection**\n",
        "\n",
        "Pairs of parents are selected through binary tournament selection until 25 offspring are produced. For each selected parent, two individuals are randomly selected from the population to compete. An individual is chosen if it dominates the other. If they are in the same front, the individual with the largest crowding distance is selected. If these are also equal, the selected individual is randomly chosen.\n",
        "\n",
        "<br>\n",
        "\n",
        "**Crossover and Mutation**\n",
        "\n",
        "Uniform crossover is applied to parent pairs at a chance of 0.9. If no crossover occurs, parents’ genes are directly transferred to resulting offspring. Mutation is applied to the created offspring at a chance inversely proportionate to the chromosome size, i.e. $p = \\frac{1}{L}$.\n",
        "\n",
        "<br>\n",
        "\n",
        "**Selection**\n",
        "\n",
        "Parents and offspring populations are combined and sorted into fronts using non-dominated sorting. Individuals are assigned a crowding distance and individuals within each front are sorted by crowding distance in descending order. Fronts are combined into a list in ascending order, and the top 25 individuals are selected for the next population."
      ]
    },
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        "<div markdown=\"1\" align=\"center\">\n",
        "\n",
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)\n",
        "\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "htD3iKr36qm4"
      },
      "source": [
        "**Evolution**\n",
        "\n",
        "The algorithm is run for 30 generations causing the individuals to converge towards the Pareto frontier.  This is the shape formed by the optimal solutions in the objective space. In this case it is convex as this is a minimisation problem. To evaluate performance across generations, hypervolume is calculated using the worst objective values as a reference point. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "twEYbw7n7GsB"
      },
      "source": [
        "<div align=\"center\">\n",
        "\n",
        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)\n",
        "\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JXWFeHr5fuEQ"
      },
      "source": [
        "# **Imports**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PkquYkaj5DTE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "53873663-9e46-469e-d507-f6b9c2a40c82"
      },
      "source": [
        "!pip install deap\n",
        "\n",
        "import array\n",
        "import random\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plot\n",
        "import matplotlib.cm as cm\n",
        "\n",
        "from deap import base, creator, tools\n",
        "from deap.benchmarks.tools import hypervolume\n",
        "from sympy.combinatorics.graycode import random_bitstring, gray_to_bin, bin_to_gray"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting deap\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/0a/eb/2bd0a32e3ce757fb26264765abbaedd6d4d3640d90219a513aeabd08ee2b/deap-1.3.1-cp36-cp36m-manylinux2010_x86_64.whl (157kB)\n",
            "\r\u001b[K     |██                              | 10kB 12.0MB/s eta 0:00:01\r\u001b[K     |████▏                           | 20kB 17.9MB/s eta 0:00:01\r\u001b[K     |██████▎                         | 30kB 12.4MB/s eta 0:00:01\r\u001b[K     |████████▍                       | 40kB 10.3MB/s eta 0:00:01\r\u001b[K     |██████████▍                     | 51kB 5.1MB/s eta 0:00:01\r\u001b[K     |████████████▌                   | 61kB 5.6MB/s eta 0:00:01\r\u001b[K     |██████████████▋                 | 71kB 5.9MB/s eta 0:00:01\r\u001b[K     |████████████████▊               | 81kB 6.1MB/s eta 0:00:01\r\u001b[K     |██████████████████▊             | 92kB 6.3MB/s eta 0:00:01\r\u001b[K     |████████████████████▉           | 102kB 6.5MB/s eta 0:00:01\r\u001b[K     |███████████████████████         | 112kB 6.5MB/s eta 0:00:01\r\u001b[K     |█████████████████████████       | 122kB 6.5MB/s eta 0:00:01\r\u001b[K     |███████████████████████████▏    | 133kB 6.5MB/s eta 0:00:01\r\u001b[K     |█████████████████████████████▏  | 143kB 6.5MB/s eta 0:00:01\r\u001b[K     |███████████████████████████████▎| 153kB 6.5MB/s eta 0:00:01\r\u001b[K     |████████████████████████████████| 163kB 6.5MB/s \n",
            "\u001b[?25hRequirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from deap) (1.18.5)\n",
            "Installing collected packages: deap\n",
            "Successfully installed deap-1.3.1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XOzN0LJUbb3B"
      },
      "source": [
        "# **Constants**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w7Kypd_lCws7"
      },
      "source": [
        "# Binary length\n",
        "BITS = 10\n",
        "# -4.0 <= x1,x2,x3 <= 4.0\n",
        "LOWER_BOUND, UPPER_BOUND = - 4, 4\n",
        "# Number of genes (decision variables)\n",
        "DECISION_VARIABLES = 3\n",
        "\n",
        "POPULATION_SIZE = 25\n",
        "NUMBER_OF_GENERATIONS = 30\n",
        "OFFSPRING_SIZE = 25\n",
        "CROSS_PROBABILITY = 0.9\n",
        "MUTATION_PROBABILITY = 1/(BITS * DECISION_VARIABLES)\n",
        "\n",
        "random.seed(10)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GFIvtG2RbqpB"
      },
      "source": [
        "# **Functions**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OrIyolea4DjL"
      },
      "source": [
        "def gray_to_real(gray, lower, upper):\n",
        "  \"\"\" Converts between gray coding to a real value in range [lower, upper] \"\"\"\n",
        "  l = len(gray)\n",
        "  # Converts to binary, then integer\n",
        "  binary = gray_to_bin(gray)\n",
        "  integer = int(binary, 2)\n",
        "  # Converts to real-valued\n",
        "  x = lower + (upper - lower) * (1 / (2**l  - 1)) * integer\n",
        "  return x"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3m_j9-02Jwy7"
      },
      "source": [
        "def evaluation(individual):\n",
        "  \"\"\" Evaluation function \"\"\"\n",
        "  # An individual's genes\n",
        "  g1, g2, g3 = individual[0], individual[1], individual[2]\n",
        "  # Converts from gray code to real-valued\n",
        "  x1, x2, x3 = gray_to_real(g1, LOWER_BOUND, UPPER_BOUND), gray_to_real(g2, LOWER_BOUND, UPPER_BOUND), gray_to_real(g3, LOWER_BOUND, UPPER_BOUND)\n",
        "  f1 = ((x1/2)**2 + (x2/4)**2 + x3**2) / 3\n",
        "  f2 = (((x1/2) - 1)**2 + ((x2/4) - 1)**2 + (x3 - 1)**2) / 3\n",
        "  return f1, f2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "McWs-d8ScFIN"
      },
      "source": [
        "def check_dominated(individual, current_front):\n",
        "  # Compare with individuals in current front starting from last\n",
        "  for compare_ind in current_front[::-1]:\n",
        "    if compare_ind.fitness.dominates(individual.fitness):\n",
        "      return True\n",
        "  return False\n",
        "\n",
        "def sequential_search(ind, fronts):\n",
        "  # Current front to check\n",
        "  front_index = 0\n",
        "  while True:\n",
        "    current_front = fronts[front_index]\n",
        "    dominated = check_dominated(ind, current_front)\n",
        "    if not dominated:\n",
        "      # Adds individual to current front\n",
        "      fronts[front_index].append(ind)\n",
        "      return fronts\n",
        "    front_index += 1\n",
        "    if front_index + 1 > len(fronts):\n",
        "      # Add individual to new front\n",
        "      new_front = [ind]\n",
        "      fronts.append(new_front)\n",
        "      return fronts\n",
        "\n",
        "def efficient_ND_sort(population):\n",
        "  \"\"\" Efficient non-dominated sorting \"\"\"\n",
        "  # Copies population to prevent population changing\n",
        "  copy_population = toolbox.clone(population)\n",
        "  # Sort population by f1, then by f2 is f1 is equal\n",
        "  copy_population.sort(key=lambda ind: (ind.fitness.values[0], ind.fitness.values[1]))\n",
        "  # Assigns best f1 to front 1\n",
        "  fronts = [[copy_population[0]]]\n",
        "  copy_population.remove(copy_population[0])\n",
        "  for ind in copy_population:\n",
        "    fronts = sequential_search(ind, fronts)\n",
        "  return fronts"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HMrycPJ9OT9u"
      },
      "source": [
        "def assignCrowdingDist(front):\n",
        "  \"\"\" Deap function to assign crowding distance to individuals in a front \"\"\"\n",
        "  if len(front) == 0:\n",
        "    return\n",
        "  distances = [0.0] * len(front)\n",
        "  crowd = [(ind.fitness.values, i) for i, ind in enumerate(front)]\n",
        "\n",
        "  nobj = len(front[0].fitness.values)\n",
        "\n",
        "  for i in range(nobj):\n",
        "      crowd.sort(key=lambda element: element[0][i])\n",
        "      distances[crowd[0][1]] = float(\"inf\")\n",
        "      distances[crowd[-1][1]] = float(\"inf\")\n",
        "      if crowd[-1][0][i] == crowd[0][0][i]:\n",
        "          continue\n",
        "      norm = nobj * float(crowd[-1][0][i] - crowd[0][0][i])\n",
        "      for prev, cur, next in zip(crowd[:-2], crowd[1:-1], crowd[2:]):\n",
        "          distances[cur[1]] += (next[0][i] - prev[0][i]) / norm\n",
        "\n",
        "  for i, dist in enumerate(distances):\n",
        "      front[i].fitness.crowding_dist = dist"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ROydNlNQkcVs"
      },
      "source": [
        "def compete(first, second):\n",
        "  # Comparision based on dominance\n",
        "  if first.fitness.dominates(second.fitness):\n",
        "    return first\n",
        "  elif second.fitness.dominates(first.fitness):\n",
        "    return second\n",
        "  # Comparision based on crowding distance\n",
        "  if first.fitness.crowding_dist > second.fitness.crowding_dist:\n",
        "    return first\n",
        "  elif first.fitness.crowding_dist < second.fitness.crowding_dist:\n",
        "    return second\n",
        "  # Random selection\n",
        "  if random.random() <= 0.5:\n",
        "    return first\n",
        "  return second\n",
        "\n",
        "def binaryTournament(population, pair_number):\n",
        "  \"\"\" Binary tournament selection\n",
        "  Prevents the same individuals being repeatedly selected \"\"\"\n",
        "  # Pairs of selected individuals\n",
        "  selected = []\n",
        "  # Copies population\n",
        "  copy_pop = [ind for ind in population]\n",
        "\n",
        "  # Number of parent pairs\n",
        "  for i in range(pair_number):\n",
        "    # Randomly select two individuals\n",
        "    first = random.choice(copy_pop)\n",
        "    # Remove from population to prevent repeat selection\n",
        "    copy_pop.remove(first)\n",
        "    # Checks if all individuals selected\n",
        "    if (len(copy_pop) == 0):\n",
        "      # Adds more individuals for selection\n",
        "      copy_pop = [ind for ind in population]\n",
        "    second = random.choice(copy_pop)\n",
        "    copy_pop.remove(second)\n",
        "    if (len(copy_pop) == 0):\n",
        "      copy_pop = [ind for ind in population]\n",
        "    first_parent = compete(first, second)\n",
        "\n",
        "    # Randomly select two more individuals\n",
        "    first = random.choice(copy_pop)\n",
        "    copy_pop.remove(first)\n",
        "    if (len(copy_pop) == 0):\n",
        "      copy_pop = [ind for ind in population]\n",
        "    second = random.choice(copy_pop)\n",
        "    if (len(copy_pop) == 0):\n",
        "      copy_pop = [ind for ind in population]\n",
        "    copy_pop.remove(second)\n",
        "    second_parent = compete(first, second)\n",
        "    selected.append([first_parent, second_parent])\n",
        "    \n",
        "  return selected"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WQUSAC4KPfs2"
      },
      "source": [
        "def flipMutation(individual, probability=0.1):\n",
        "  # Iterates through decision variables\n",
        "  for i in range(len(individual)):\n",
        "    # Creates updated decision variable\n",
        "    new_var = \"\"\n",
        "    # Iterates through bits in decision variable\n",
        "    for bit in individual[i]:\n",
        "      new_bit = bit\n",
        "      # Flip bit\n",
        "      if random.random() <= probability:\n",
        "        if bit == '0':\n",
        "          new_bit = '1'\n",
        "        if bit == '1':\n",
        "          new_bit = '0'\n",
        "      new_var += new_bit\n",
        "    # Updates mutated decision variable\n",
        "    individual[i] = new_var\n",
        "  return individual"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p2PyM19pbxl4"
      },
      "source": [
        "# **Run the Genetic Algorithm**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CcvWHXX2-Kvb"
      },
      "source": [
        "# Creates a fitness for minimization of a problem with 2 objectives\n",
        "creator.create(\"FitnessMin\", base.Fitness, weights=(-1.0, -1.0))\n",
        "# Creates class Individual with fitness set for minimization\n",
        "creator.create(\"Individual\", list, fitness=creator.FitnessMin)\n",
        "\n",
        "toolbox = base.Toolbox()\n",
        "\n",
        "# Generation function for decision variables using 10 bit gray coding\n",
        "toolbox.register(\"gray_code\", random_bitstring, BITS)\n",
        "# Initializers for individual and population\n",
        "toolbox.register(\"individual\", tools.initRepeat, creator.Individual, toolbox.gray_code, DECISION_VARIABLES)\n",
        "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)\n",
        "\n",
        "# Genetic operators\n",
        "toolbox.register(\"evaluate\", evaluation) # Uses evaluation function\n",
        "toolbox.register(\"sort\", efficient_ND_sort) # Non-dominated sorting into fronts\n",
        "toolbox.register(\"crowd\", assignCrowdingDist) # Assign crowding distance to each individual of the list\n",
        "toolbox.register(\"tournament\", binaryTournament) # Tournament selection\n",
        "toolbox.register(\"mate\", tools.cxUniform, indpb=0.5) # Uniform crossover with 50% chance of exchange\n",
        "toolbox.register(\"mutate\", flipMutation, probability=MUTATION_PROBABILITY) # Flip mutation with chance = 1 / chromosome length"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O86_mkiqspXF"
      },
      "source": [
        "def main():\n",
        "  stats = tools.Statistics()\n",
        "  logbook = tools.Logbook()\n",
        "  logbook.header = \"generation\", \"x1\", \"x2\", \"x3\", \"f1\", \"f2\", \"front_number\", \"crowding_distance\"\n",
        "\n",
        "  # Initiate the population\n",
        "  pop = toolbox.population(POPULATION_SIZE)\n",
        "  # Hypervolume over generations\n",
        "  hypervolumes = []\n",
        "\n",
        "  # Evaluate fitness of population\n",
        "  invalid_individuals = [ind for ind in pop if not ind.fitness.valid]\n",
        "  fitnesses = list(map(toolbox.evaluate, pop))\n",
        "  for ind, fit in zip(invalid_individuals, fitnesses):\n",
        "    ind.fitness.values = fit\n",
        "\n",
        "  # Find the worst f1 and f2 values\n",
        "  copy_pop = toolbox.clone(pop)\n",
        "  # Sort population by f1 and f2\n",
        "  copy_pop.sort(key=lambda x: x.fitness.values[0], reverse=True)\n",
        "  worst_f1 = copy_pop[0].fitness.values[0]\n",
        "  copy_pop.sort(key=lambda x: x.fitness.values[1], reverse=True)\n",
        "  worst_f2 = copy_pop[0].fitness.values[1]\n",
        "  # Sets reference point for hypervolume\n",
        "  reference = [worst_f1, worst_f2]\n",
        "  print(\"Worst f1: \" + str(worst_f1))\n",
        "  print(\"Worst f2: \" + str(worst_f2))\n",
        "  print(\"\\n\")\n",
        "\n",
        "  # Sort population into fronts\n",
        "  fronts = toolbox.sort(pop)\n",
        "  updated_pop = []\n",
        "  for i in range(len(fronts)):\n",
        "    front = fronts[i]\n",
        "    # Assign crowding distance to individuals in each front\n",
        "    toolbox.crowd(front)\n",
        "    for ind in front:\n",
        "      updated_pop.append(ind)\n",
        "      # Print out individuals and fitness\n",
        "      logbook.record(generation=0, x1=ind[0], x2=ind[1], x3=ind[2], f1=ind.fitness.values[0], f2=ind.fitness.values[1], front_number=i+1, crowding_distance=ind.fitness.crowding_dist)\n",
        "      print(logbook.stream)\n",
        "  print(\"\\n\")\n",
        "  # Updates population so that individuals have crowding distance\n",
        "  pop = updated_pop\n",
        "\n",
        "  # Calculates hypervolume of generation 0\n",
        "  hv = hypervolume(fronts[0], reference)\n",
        "  hypervolumes.append(hv)\n",
        "\n",
        "  for generation in range(1, NUMBER_OF_GENERATIONS + 1):\n",
        "    # Selects parents through tournament selection\n",
        "    parent_pairs = toolbox.tournament(pop, len(pop))\n",
        "    parents = []\n",
        "    offspring = []\n",
        "    for pair in parent_pairs:\n",
        "      # Makes copies of parents to modify\n",
        "      parent1 = toolbox.clone(pair[0])\n",
        "      parent2 = toolbox.clone(pair[1])\n",
        "      offspring1 = toolbox.clone(parent1)\n",
        "      offspring2 = toolbox.clone(parent2)\n",
        "      # Cross over\n",
        "      if random.random() <= CROSS_PROBABILITY:\n",
        "        toolbox.mate(offspring1, offspring2)\n",
        "      # Mutate both offspring\n",
        "      toolbox.mutate(offspring1)\n",
        "      toolbox.mutate(offspring2)\n",
        "      parents.append(parent1)\n",
        "      offspring.append(offspring1)\n",
        "      parents.append(parent2)\n",
        "      offspring.append(offspring2)\n",
        "    # Caps to 25 offspring\n",
        "    offspring = offspring[:OFFSPRING_SIZE]\n",
        "    parents = parents[:OFFSPRING_SIZE]\n",
        "  \n",
        "    # Offspring still have parent's fitness\n",
        "    parent_f1 = [off.fitness.values[0] for off in offspring]\n",
        "    parent_f2 = [off.fitness.values[1] for off in offspring]\n",
        "    # Offspring fitness is updated\n",
        "    fitnesses = list(map(toolbox.evaluate, offspring))\n",
        "    for off, fit in zip(offspring, fitnesses):\n",
        "      off.fitness.values = fit\n",
        "\n",
        "    # Print graph\n",
        "    if generation == 1 or generation == NUMBER_OF_GENERATIONS:\n",
        "      offspring_f1 = [off.fitness.values[0] for off in offspring]\n",
        "      offspring_f2 = [off.fitness.values[1] for off in offspring]\n",
        "      # Plot parents and offspring fitness\n",
        "      plot.figure()\n",
        "      plot.title('Parents and Offspring Fitness for Generation ' + str(generation))\n",
        "      plot.plot(parent_f1, parent_f2, 'ro', alpha=0.5, label='Parents')\n",
        "      plot.plot(offspring_f1, offspring_f2, 'bo', alpha=0.5, label='Offspring')\n",
        "      plot.xlabel('f1')\n",
        "      plot.ylabel('f2')\n",
        "      plot.legend()\n",
        "\n",
        "    # Combine parents and offspring then sort\n",
        "    combined_pop = parents + offspring\n",
        "    fronts = toolbox.sort(combined_pop)\n",
        "    sorted_pop = []\n",
        "    for i in range(len(fronts)):\n",
        "      front = fronts[i]\n",
        "      # Assign crowding distance to individuals in each front\n",
        "      toolbox.crowd(front)\n",
        "      # Sort individual's in front by crowding distance in descending order\n",
        "      front.sort(key=lambda x: x.fitness.crowding_dist, reverse=True)\n",
        "      for ind in front:\n",
        "        # Ensures individual's are unique to improve diversity\n",
        "        duplicated = False\n",
        "        for ind2 in sorted_pop:\n",
        "          if ind == ind2:\n",
        "            duplicated = True\n",
        "        if not duplicated:\n",
        "          sorted_pop.append(ind)\n",
        "    # Select top individuals\n",
        "    pop = sorted_pop[:POPULATION_SIZE]\n",
        "\n",
        "    # Hypervolume using the worst objective values as the reference point\n",
        "    hv = hypervolume(fronts[0], reference)\n",
        "    hypervolumes.append(hv)\n",
        "\n",
        "    # Print graph\n",
        "    if generation == 1 or generation == NUMBER_OF_GENERATIONS:\n",
        "      # Worst individuals\n",
        "      rejected_pop = sorted_pop[POPULATION_SIZE:]\n",
        "      # Fitness of selected and rejected individuals\n",
        "      selected_f1 = [ind.fitness.values[0] for ind in pop]\n",
        "      selected_f2 = [ind.fitness.values[1] for ind in pop]\n",
        "      rejected_f1 = [ind.fitness.values[0] for ind in rejected_pop]\n",
        "      rejected_f2 = [ind.fitness.values[1] for ind in rejected_pop]\n",
        "\n",
        "      # Plot fronts\n",
        "      plot.figure()\n",
        "      plot.title('Fronts for Generation ' + str(generation))\n",
        "      # Iterable rainbow colour map\n",
        "      colours = iter(cm.hsv(np.linspace(0, 1, len(fronts))))\n",
        "      for f in range(len(fronts)-1, 0, -1):\n",
        "        front_f1s = [ind.fitness.values[0] for ind in fronts[f]]\n",
        "        front_f2s = [ind.fitness.values[1] for ind in fronts[f]]\n",
        "        plot.plot(front_f1s, front_f2s, 'o', color=next(colours), label='Front ' + str(f))\n",
        "      plot.xlabel('f1')\n",
        "      plot.ylabel('f2')\n",
        "      plot.legend(loc='upper left', bbox_to_anchor=(1.05, 1))\n",
        "\n",
        "      # Plot parents and offspring fitness\n",
        "      plot.figure()\n",
        "      plot.title('Selected Solutions Fitness for Generation ' + str(generation))\n",
        "      plot.plot(selected_f1, selected_f2, 'o', alpha=0.5, label='Selected')\n",
        "      plot.plot(rejected_f1, rejected_f2, 'o', alpha=0.5, label='Not selected')\n",
        "      plot.xlabel('f1')\n",
        "      plot.ylabel('f2')\n",
        "      plot.legend()\n",
        "\n",
        "  # Plot hypervolume over generations\n",
        "  hvs = np.array(hypervolumes)\n",
        "  # Makes list of generation numbers same shape as hypervolumes list\n",
        "  gens = np.zeros_like(hvs)\n",
        "  for i in range(0, len(gens)):\n",
        "    gens[i] = i\n",
        "  plot.figure()\n",
        "  plot.title('Hypervolume Over Generations')\n",
        "  plot.plot(gens, hvs, '-*', color='indigo')\n",
        "  plot.xlabel('Generation')\n",
        "  plot.ylabel('Hypervolume')\n",
        "  plot.show()\n",
        "  \n",
        "  return pop"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "21YpgRJoMvs7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "a986057b-367a-4199-a31f-4aab317fb130"
      },
      "source": [
        "# Run the genetic algorithm\n",
        "pop = main()\n",
        "print(\"Population: \" + str(pop))\n",
        "print(\"\\n\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Worst f1: 6.620413767798122\n",
            "Worst f2: 9.914974804010845\n",
            "\n",
            "\n",
            "generation\tx1        \tx2        \tx3        \tf1      \tf2      \tfront_number\tcrowding_distance\n",
            "0         \t1100000101\t1110111000\t1101000010\t0.371571\t0.433807\t1           \tinf              \n",
            "0         \t1110111000\t1101001011\t1110101100\t1.05772 \t0.319697\t1           \t1                \n",
            "0         \t1011110000\t1010000110\t1111001011\t1.12426 \t0.130773\t1           \tinf              \n",
            "0         \t0100101110\t1110000100\t0101000111\t0.398622\t1.85024 \t2           \tinf              \n",
            "0         \t1010100100\t0111000101\t0101101101\t0.630849\t1.37474 \t2           \t0.491982         \n",
            "0         \t1101100000\t0111000001\t1111101010\t0.699373\t0.764215\t2           \t0.588704         \n",
            "0         \t1100110111\t1000010001\t1110110110\t1.28469 \t0.415028\t2           \t0.508018         \n",
            "0         \t1111100001\t1011101000\t1110000000\t1.65908 \t0.393194\t2           \tinf              \n",
            "0         \t0110000100\t0100111000\t0111000101\t0.686344\t3.09723 \t3           \tinf              \n",
            "0         \t1111011011\t1001011111\t0111000101\t0.687636\t1.47845 \t3           \t1                \n",
            "0         \t0101101111\t1110101000\t1010011110\t1.64161 \t1.12385 \t3           \tinf              \n",
            "0         \t0011001000\t1111000110\t1100011011\t0.72137 \t2.4128  \t4           \tinf              \n",
            "0         \t0110101100\t0110101001\t1010000010\t1.63192 \t2.07082 \t4           \t1                \n",
            "0         \t1110010011\t0010010011\t1011010100\t2.99984 \t1.9073  \t4           \tinf              \n",
            "0         \t0010000001\t1100100000\t0110111100\t1.28973 \t4.00168 \t5           \tinf              \n",
            "0         \t1011000100\t0101100010\t0010011001\t2.25304 \t3.78546 \t5           \t0.490349         \n",
            "0         \t0010110010\t0111000101\t1001001001\t3.69324 \t3.55085 \t5           \t0.787748         \n",
            "0         \t1111101100\t1011010101\t1000001010\t5.42137 \t2.87168 \t5           \tinf              \n",
            "0         \t0010110010\t1000110011\t0010000001\t2.07517 \t4.55513 \t6           \tinf              \n",
            "0         \t0101000110\t1000010110\t0010110100\t2.15681 \t4.38783 \t6           \t0.641573         \n",
            "0         \t0101000001\t1100101000\t1000010110\t4.86969 \t3.61032 \t6           \t0.931848         \n",
            "0         \t1000100100\t1000011000\t1000000110\t6.62041 \t3.14143 \t6           \tinf              \n",
            "0         \t0111101001\t1010110100\t0010100010\t2.31381 \t5.04141 \t7           \tinf              \n",
            "0         \t1001111110\t0110110001\t0010111100\t2.78652 \t4.50792 \t7           \tinf              \n",
            "0         \t0010011011\t0101100100\t0000001110\t5.49692 \t9.91497 \t8           \tinf              \n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Population: [['1100000001', '1100001100', '1100000000'], ['1110000000', '1000001111', '1111000011'], ['1101010101', '1010011100', '1100100100'], ['1110010000', '1110011000', '1101101101'], ['1100000001', '1110011000', '1101100000'], ['1100100111', '1101001100', '1100000000'], ['1110010000', '1001000101', '1101101011'], ['1110001000', '1000000011', '1101110001'], ['1110101000', '1010011000', '1101110011'], ['1110010000', '1000000011', '1111000011'], ['1100010001', '1100001100', '1100000000'], ['1100010001', '1110011001', '1100100000'], ['1110010000', '1001000101', '1101001110'], ['1110010000', '1010011100', '1111000011'], ['1100011001', '1100001100', '1100000000'], ['1110010010', '1010011100', '1111000011'], ['1100000001', '0100001100', '1100001000'], ['1010001100', '1000000011', '1111000011'], ['1100010000', '1100001100', '1101110001'], ['1100000001', '1110011001', '1100000000'], ['1100010000', '1111011001', '1101001110'], ['1100010000', '1010011000', '1101001110'], ['1010001100', '1000001111', '1111000011'], ['1100100101', '0101001100', '1100010000'], ['1110000000', '1010011100', '1111000011']]\n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}