examples/binh_and_korn_multiobjective.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e86c731f",
   "metadata": {},
   "source": [
    "# Binh and Korn function\n",
    "\n",
    "---\n",
    "Description:\n",
    "\n",
    "- Optimization (min)\n",
    "- Multi-objective (2)\n",
    "- Constraints (2)\n",
    "---\n",
    "\n",
    "\n",
    "The goal is to **minimize** the following equations:\n",
    "\n",
    "\\begin{cases}\n",
    "      f_{1}\\left(x,y\\right) = 4x^{2} + 4y^{2}, \\\\\n",
    "      f_{2}\\left(x,y\\right) = \\left(x - 5\\right)^{2} + \\left(y - 5\\right)^{2} \\\\\n",
    "\\end{cases}\n",
    "\n",
    "subject to constraints:\n",
    "\n",
    "\\begin{cases}\n",
    "      C_{1}\\left(x,y\\right) = \\left(x - 5\\right)^{2} + y^{2} \\leq 25, \\\\\n",
    "      C_{2}\\left(x,y\\right) = \\left(x - 8\\right)^{2} + \\left(y + 3\\right)^{2} \\geq 7.7 \\\\\n",
    "\\end{cases}\n",
    "\n",
    "where:\n",
    "\n",
    "\\begin{cases}\n",
    "      -15\\le x \\le 30, \\\\\n",
    "      -15\\le y \\le 30. \\\\\n",
    "\\end{cases}\n",
    "\n",
    "The Pareto-optimal solutions are constituted by solutions:\n",
    "    $ x=y ∈ [0.0, 3.0] \\text{  and  } x ∈ [3.0, 5.0], y=3.0.$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01ca38a9",
   "metadata": {},
   "source": [
    "### First we import python libraries and set up the directory of our code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c7e604f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os, sys\n",
    "import numpy as np\n",
    "from math import fsum\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "PROJECT_DIR = os.path.abspath('..')\n",
    "sys.path.append(PROJECT_DIR)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43fefefc",
   "metadata": {},
   "source": [
    "### Here we import all our custom GA code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "efc9d4c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import main classes.\n",
    "from pygenalgo.genome.gene import Gene\n",
    "from pygenalgo.genome.chromosome import Chromosome\n",
    "from pygenalgo.engines.standard_ga import StandardGA\n",
    "from pygenalgo.engines.auxiliary import pareto_front\n",
    "\n",
    "from pygenalgo.operators.genetic_operator import GeneticOperator\n",
    "\n",
    "# Import Selection Operator(s).\n",
    "from pygenalgo.operators.selection.linear_rank_selector import LinearRankSelector\n",
    "\n",
    "# Import Crossover Operator(s).\n",
    "from pygenalgo.operators.crossover.uniform_crossover import UniformCrossover\n",
    "\n",
    "# Import Mutation Operator(s).\n",
    "from pygenalgo.operators.mutation.random_mutator import RandomMutator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e39820c",
   "metadata": {},
   "source": [
    "### Define the multi-objective function, which plays the role of the 'fitness' function.\n",
    "\n",
    "We use a combination of the **weighted sum** and **penalty methods**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f81a99ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Multi-objective function.\n",
    "def fun_Binh_Korn(individual: Chromosome, f_min: bool = True):\n",
    "    \n",
    "    # Set the penalty coefficient.\n",
    "    rho = 5.0\n",
    "    \n",
    "    # Extract the data values as 'x' and 'y', for parsimony.\n",
    "    x, y = individual.values()\n",
    "    \n",
    "    # Compute each objective function.\n",
    "    f1 = 4.0 * (x**2 + y**2)\n",
    "    f2 = (x - 5.0)**2 + (y - 5.0)**2\n",
    "    \n",
    "    # Compute the constraints.\n",
    "    C1 = max(0.0, (x - 5.0)**2 + y**2 - 25.0)**2\n",
    "    C2 = min(0.0, (x - 8.0)**2 + (y + 3.0)**2 - 7.7)**2\n",
    "    \n",
    "    # Compute the final value.\n",
    "    f_val = fsum([0.5*f1, 0.5*f2, rho*(C1 + C2)])\n",
    "    \n",
    "    # Condition for termination.\n",
    "    solution_found = False\n",
    "\n",
    "    # Assign the fitness value (check for minimization).\n",
    "    fit_value = -f_val if f_min else f_val\n",
    "    \n",
    "    # Return the solution tuple.\n",
    "    return fit_value, solution_found\n",
    "# _end_def_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d36e08b",
   "metadata": {},
   "source": [
    "Then we set the GA parameters, such as the genes, the number of chromosomes, etc. Note that in this case the genes have the same\n",
    "range so we define a single random function, set by 'boundary_xy'. Moreover, we set the parameters for the GA engine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "49db5662",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Random number generator.\n",
    "rng = np.random.default_rng()\n",
    "\n",
    "# Random function that enforce the boundaries in x/y.\n",
    "boundary_xy = lambda: rng.uniform(-15.0, 30.0)\n",
    "\n",
    "# Define the number of chromosomes.\n",
    "N = 100\n",
    "\n",
    "# Draw random samples for the initial points.\n",
    "xy_init = rng.uniform(-15.0, 30.0, size=(N, 2))\n",
    "\n",
    "# Initial population.\n",
    "population = [Chromosome([Gene(xy_init[i, 0], boundary_xy),\n",
    "                          Gene(xy_init[i, 1], boundary_xy)], np.nan, True)\n",
    "              for i in range(N)]\n",
    "\n",
    "# Create the StandardGA object that will carry on the optimization.\n",
    "test_GA = StandardGA(initial_pop=population,\n",
    "                     fit_func=fun_Binh_Korn,\n",
    "                     select_op=LinearRankSelector(),\n",
    "                     mutate_op=RandomMutator(),\n",
    "                     crossx_op=UniformCrossover())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "407dd6cb",
   "metadata": {},
   "source": [
    "### Optimization process.\n",
    "\n",
    "Here we call the GA object (either directly, or through the method run()). We set a number of parameter, such as the maximum iterations (i.e. epochs), tolerance for the fitness convergences, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "32636518",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial Avg. Fitness = -1198505.1280\n",
      "Final   Avg. Fitness = -47526.1252\n",
      "Elapsed time: 2.182 seconds.\n"
     ]
    }
   ],
   "source": [
    "test_GA(epochs=250, elitism=True, f_tol=1.0e-6, adapt_probs=True, verbose=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "64a98568",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=1.00038, y=1.00219\n",
      "\n",
      "f1(x, y) = 8.02058\n",
      "f2(x, y) = 31.97945\n"
     ]
    }
   ],
   "source": [
    "# Extract the data values as 'x' and 'y', for parsimony.\n",
    "x, y = test_GA.best_chromosome().values()\n",
    "\n",
    "# Compute the final objective functions.\n",
    "f1_opt = 4.0 * (x**2 + y**2)\n",
    "f2_opt = (x - 5.0)**2 + (y - 5.0)**2\n",
    "\n",
    "# Print the resutls.\n",
    "print(f\"x={x:.5f}, y={y:.5f}\", end='\\n\\n')\n",
    "print(f\"f1(x, y) = {f1_opt:.5f}\")\n",
    "print(f\"f2(x, y) = {f2_opt:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41ebe5cf",
   "metadata": {},
   "source": [
    "### Visualize the adapted probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "04d13bf5",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(test_GA.stats[\"prob_crossx\"],\n",
    "         'ro:', markersize=5, label=\"crossover\")\n",
    "\n",
    "plt.plot(test_GA.stats[\"prob_mutate\"],\n",
    "         'bd:', markersize=5, label=\"mutation\")\n",
    "\n",
    "plt.xlabel(\"Epochs\")\n",
    "\n",
    "plt.ylabel(\"Probability\")\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70610133",
   "metadata": {},
   "source": [
    "### Compute the Pareto Frontier (solutions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "182e6675",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a list that will hold points that satisfy both constraints.\n",
    "points = []\n",
    "\n",
    "# Generate a 2D grid sample on [-15.0, 30].\n",
    "for x in np.linspace(-15.0, 30.0, 100):\n",
    "    \n",
    "    for y in np.linspace(-15.0, 30.0, 100):\n",
    "    \n",
    "        # Compute the constraints.\n",
    "        C1 = (x - 5.0)**2 + y**2 <= 25.0\n",
    "        C2 = (x - 8.0)**2 + (y + 3.0)**2 >= 7.7\n",
    "\n",
    "        # If both constraints are satisfied.\n",
    "        if C1 and C2:\n",
    "\n",
    "            # Evaluate both functions.\n",
    "            f1 = 4.0 * (x**2 + y**2)\n",
    "            f2 = (x - 5.0)**2 + (y - 5.0)**2\n",
    "\n",
    "            # Keep the point in the list.\n",
    "            points.append((f1, f2))\n",
    "        # _end_if_\n",
    "    # _end_for_\n",
    "# _end_for_\n",
    "\n",
    "# Estimate the pareto front points.\n",
    "pareto_points = pareto_front(points)\n",
    "\n",
    "# Convert lists to numpy.\n",
    "points = np.array(points)\n",
    "pareto_points = np.array(pareto_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "654e7453",
   "metadata": {},
   "source": [
    "### Visualize the solution on the Pareto plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "29b6ee5c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a new figure.\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "# Plot the Pareto front.\n",
    "plt.plot(pareto_points[:, 0],\n",
    "         pareto_points[:, 1],\n",
    "         'ro:', alpha=0.5, label=\"Pareto Frontier\")\n",
    "\n",
    "# Plot all the feasible solutions.\n",
    "plt.scatter(x=points[:, 0],\n",
    "            y=points[:, 1],\n",
    "            s=5, marker='o', label=\"Feasible Solutions\")\n",
    "\n",
    "# Plot the optimal solution from the GA.\n",
    "plt.plot(f1_opt, f2_opt,\n",
    "         'k*', markersize=10, alpha=0.8, label=\"PyGenAlgo optimal\")\n",
    "\n",
    "# Tidy up the plot.\n",
    "plt.title(\"Binh and Korn Test Case No.2\")\n",
    "plt.xlabel(r\"$\\mathbf{f1(x,y)}$\")\n",
    "plt.ylabel(r\"$\\mathbf{f2(x,y)}$\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "\n",
    "plt.savefig(\"Binh_and_Korn_optimal.pdf\", format=\"pdf\", dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9f76d72",
   "metadata": {},
   "source": [
    "### End of file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "70c8e340-f19c-4364-b2b1-1d12f169c292",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv_tf",
   "language": "python",
   "name": "venv_tf"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}