Search/09-Local_Search_Genetic_Algorithm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "<div class='alert alert-success'>\n",
    "    <h1 align=\"center\">Local Search Algorithms: Genetic Algorithm for N-Queens</h1> \n",
    "    <h3 align=\"center\">Artificial Intelligece Course (Fall 2021)</h3>\n",
    "    <h5 align=\"center\">Seyed Naser RAZAVI <a href='http://www.snrazavi.ir/ai-slides/'>(website)</a></h5>\n",
    "</div>"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "import tqdm\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import clear_output\n",
    "\n",
    "from nqueens import NQueensStatePermutation as NQueensState\n",
    "from nqueens import create_animation\n",
    "\n",
    "# for animation\n",
    "from matplotlib import rc\n",
    "rc('animation', html='html5')\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (6, 6)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## N-Queens Problem\n",
    "- **Goal**: Place N queens on a N-by-N chess board so that no two queens can attack each other.\n",
    "- Thus a solution requires that no two queens share the same row, column or diagonal.\n",
    "\n",
    "<p align=\"center\">\n",
    "    <img src=\"imgs/Four-Queens-Local-Search.png\" width=\"80%\">\n",
    "</p>\n",
    "<h6 align=\"center\">4-Queens problem</h6>"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Problem formulation: First formulation\n",
    "- **States**: each column contains only one queen.\n",
    "- **Actions**: move a queen to another row in its column.\n",
    "- **State Space Size**: $N^N$\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Problem formulation: Second formulation (Permuatation)\n",
    "- **States**: each column and each row contains only one queen.\n",
    "- **Actions**: move a queen to another row in its column which is not occupied.\n",
    "- **State Space Size**: $N!$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "state = NQueensState.random_state(N=8)\n",
    "print(state)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[3, 4, 5, 7, 2, 6, 8, 1] <3>\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "state.plot(show_conflicts=True)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "best_neighbor = state.best_neighbor()\n",
    "best_neighbor.plot(show_conflicts=True)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "best_neighbor"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "NQueensStatePermutation(queens=[8, 4, 5, 7, 2, 6, 3, 1])"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Genetic Algorithm\n",
    "<img src=\"imgs/genetic_algorithm.png\" width=\"80%\">"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Selection, Crossover, Mutation\n",
    "<img src='imgs/GA_cycle.png' width='100%'>"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "class GeneticAlgorithm:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.population = []    \n",
    "        self.history, self.bests, self.means = [], [], []\n",
    "\n",
    "    def tournament_selection(self, k=2):\n",
    "        samples = [random.choice(self.population) for _ in range(k)]\n",
    "        return min(samples, key=lambda x: x.conflicts())\n",
    "\n",
    "    @staticmethod\n",
    "    def mutate(chromosome):\n",
    "        \"\"\" Swap mutation which randomly swaps two genes.\"\"\"\n",
    "        N = chromosome.N\n",
    "        offspring = NQueensState(queens=chromosome.queens)\n",
    "        i = random.randint(0, N - 2)\n",
    "        j = random.randint(i + 1, N - 1)\n",
    "\n",
    "        p = random.random()\n",
    "        if p < 0.8:\n",
    "            offspring.queens[i], offspring.queens[j] = offspring.queens[j], offspring.queens[i]\n",
    "        elif p < 0.9:\n",
    "            offspring.queens[i: j + 1] = reversed(offspring.queens[i: j + 1])\n",
    "        else:\n",
    "            random.shuffle(offspring.queens[i: j + 1])\n",
    "\n",
    "        offspring.conflicts()\n",
    "        return offspring\n",
    "\n",
    "    @staticmethod\n",
    "    def crossover(parent1, parent2):\n",
    "        \"\"\"Order 1 crossover.\"\"\"\n",
    "\n",
    "        def next(idx, N):\n",
    "            return (idx + 1) % N\n",
    "\n",
    "        N = parent1.N\n",
    "        child1 = NQueensState(queens=parent1.queens)\n",
    "        child2 = NQueensState(queens=parent2.queens)\n",
    "\n",
    "        i = random.randint(0,   N - 2)\n",
    "        j = random.randint(i+1, N - 1)\n",
    "\n",
    "        # create child1\n",
    "        k1 = k2 = j\n",
    "        count = j - i\n",
    "        while count < N:\n",
    "            if parent2.queens[k1] not in child1.queens[i:j]:\n",
    "                child1.queens[k2] = parent2.queens[k1]\n",
    "                k1 = next(k1, N)\n",
    "                k2 = next(k2, N)\n",
    "                count += 1\n",
    "            else:\n",
    "                k1 = next(k1, N)\n",
    "\n",
    "        child1.conflicts()\n",
    "\n",
    "        # create child2\n",
    "        k1 = k2 = j\n",
    "        count = j - i\n",
    "        while count < N:\n",
    "            if parent1.queens[k1] not in child2.queens[i:j]:\n",
    "                child2.queens[k2] = parent1.queens[k1]\n",
    "                k1 = next(k1, N)\n",
    "                k2 = next(k2, N)\n",
    "                count += 1\n",
    "            else:\n",
    "                k1 = next(k1, N)\n",
    "\n",
    "        child2.conflicts()\n",
    "\n",
    "        return child1, child2\n",
    "    \n",
    "    \n",
    "    def search(self, N=100, pop_size=300, max_generations=200, k=None, pc=0.9, pm=0.8):\n",
    "        if k is None:\n",
    "            k = max(2, int(0.2 * pop_size))\n",
    "\n",
    "        # create random initial population\n",
    "        self.population = [NQueensState.random_state(N=N) for _ in range(pop_size)]\n",
    "\n",
    "        # report statistics\n",
    "        best = min(self.population, key=lambda x: x.conflicts())\n",
    "        mean = sum([x.conflicts() for x in self.population]) / pop_size\n",
    "        self.history.append(best)\n",
    "        self.bests.append(best.conflicts())\n",
    "        self.means.append(mean)\n",
    "\n",
    "        pbar = tqdm.tqdm(range(1, max_generations + 1), \n",
    "                                  desc='Generation 0', \n",
    "                                  total=max_generations)\n",
    "        for i in pbar:\n",
    "            if best.conflicts() == 0: \n",
    "                break\n",
    "\n",
    "            new_population = []\n",
    "\n",
    "            for j in range(pop_size // 2):\n",
    "                # Select parents\n",
    "                parent1 = self.tournament_selection(k)\n",
    "                parent2 = self.tournament_selection(k)\n",
    "\n",
    "                # crossover\n",
    "                if random.random() < pc:\n",
    "                    child1, child2 = self.crossover(parent1, parent2)\n",
    "                else:\n",
    "                    child1 = NQueensState(queens=parent1.queens)\n",
    "                    child2 = NQueensState(queens=parent2.queens)\n",
    "\n",
    "                # mutation\n",
    "                if random.random() < pm:\n",
    "                    child1 = self.mutate(child1)\n",
    "                if random.random() < pm:\n",
    "                    child2 = self.mutate(child2)\n",
    "\n",
    "                new_population += [child1, child2]\n",
    "\n",
    "            self.population = new_population\n",
    "\n",
    "            # report statistics\n",
    "            best = min(self.population, key=lambda x: x.conflicts())\n",
    "            mean = sum([x.conflicts() for x in self.population]) / pop_size\n",
    "            pbar.set_description(f'Generation {i:3d} | best {best.conflicts():3d} | mean {mean:.2f}')\n",
    "\n",
    "            self.history.append(best)\n",
    "            self.bests.append(best.conflicts())\n",
    "            self.means.append(mean)\n",
    "\n",
    "            # Stop if optimal solution found\n",
    "            if best.conflicts == 0: \n",
    "                break\n",
    "\n",
    "        return best\n",
    "     \n",
    "    def __call__(self, N=100, pop_size=300, max_generations=200, k=None, pc=0.9, pm=0.8):\n",
    "        return self.search(N, pop_size, max_generations, k, pc, pm)\n",
    "    \n",
    "    def plot_fitness(self):\n",
    "        plt.figure(figsize=(12, 6))\n",
    "        plt.plot(self.means, label='Average')\n",
    "        plt.plot(self.bests, label='Best')\n",
    "        plt.xlabel('Generation')\n",
    "        plt.ylabel('Fitness')\n",
    "        plt.legend(loc='best')\n",
    "        plt.show()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "# GA parameters\n",
    "N = 30\n",
    "pop_size = 100\n",
    "max_generations = 500\n",
    "\n",
    "p_crossover = 0.9\n",
    "p_mutation = 0.8\n",
    "\n",
    "# run GA\n",
    "ga = GeneticAlgorithm()\n",
    "\n",
    "best_solution = ga(\n",
    "    N=N, \n",
    "    pop_size=pop_size, \n",
    "    max_generations=max_generations,\n",
    "    pc=p_crossover,\n",
    "    pm=p_mutation\n",
    ")\n",
    "\n",
    "# show results\n",
    "print(f\"Best Solution Found with <{best_solution.conflicts()}> conflicts:\\n{best_solution}\")"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "Generation  56 | best   0 | mean 4.07:  11%|█         | 56/500 [00:00<00:05, 88.12it/s]"
     ]
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Best Solution Found with <0> conflicts:\n",
      "[15, 6, 4, 13, 5, 21, 24, 20, 16, 26, 29, 1, 8, 12, 23, 7, 3, 28, 22, 2, 14, 27, 19, 30, 9, 11, 17, 25, 10, 18] <0>\n"
     ]
    },
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "best_solution.plot(show_conflicts=True)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "ga.plot_fitness()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Animation"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "anim = create_animation(ga.history)\n",
    "anim.save(f'imgs/{N}-queens-ga.gif', writer='imagemagick')\n",
    "clear_output()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "<img src=\"imgs/30-queens-ga.gif\" width=\"50%\">"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "anim = create_animation(ga.history, plot_objective=True)\n",
    "anim.save(f'imgs/{N}-queens-ga-with-objective.gif', writer='imagemagick')\n",
    "clear_output()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "<img src=\"imgs/30-queens-ga-with-objective.gif\">"
   ],
   "metadata": {}
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.9.6 64-bit ('venv': venv)"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  },
  "interpreter": {
   "hash": "db4280cfac26d1f17ba08bcc8b51b906ec3585d94092157597b7da58b570ab73"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}