set-cover.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright **`(c)`** 2024 Giovanni Squillero `<giovanni.squillero@polito.it>`  \n",
    "[`https://github.com/squillero/computational-intelligence`](https://github.com/squillero/computational-intelligence)  \n",
    "Free for personal or classroom use; see [`LICENSE.md`](https://github.com/squillero/computational-intelligence/blob/master/LICENSE.md) for details.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Set Cover problem\n",
    "\n",
    "See: https://en.wikipedia.org/wiki/Set_cover_problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import random, seed\n",
    "from itertools import accumulate\n",
    "from itertools import product\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from icecream import ic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = []\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reproducible Initialization\n",
    "\n",
    "If you want to get reproducible results, use `rng` (and restart the kernel); for non-reproducible ones, use `np.random`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {},
   "outputs": [],
   "source": [
    "UNIVERSE_SIZE = 10_000\n",
    "NUM_SETS = 1000\n",
    "DENSITY = 0.2\n",
    "\n",
    "MAX_STEPS = 10_000\n",
    "rng = np.random.Generator(np.random.PCG64([UNIVERSE_SIZE, NUM_SETS, int(10_000 * DENSITY)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DON'T EDIT THESE LINES!\n",
    "\n",
    "SETS = np.random.random((NUM_SETS, UNIVERSE_SIZE)) < DENSITY\n",
    "for s in range(UNIVERSE_SIZE):\n",
    "    if not np.any(SETS[:, s]):\n",
    "        SETS[np.random.randint(NUM_SETS), s] = True\n",
    "COSTS = np.pow(SETS.sum(axis=1), 1.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {},
   "outputs": [],
   "source": [
    "def valid(solution):\n",
    "    \"\"\"Checks wether solution is valid (ie. covers all universe)\"\"\"\n",
    "    return np.all(np.logical_or.reduce(SETS[solution]))\n",
    "\n",
    "\n",
    "def cost(solution):\n",
    "    \"\"\"Returns the cost of a solution (to be minimized)\"\"\"\n",
    "    return COSTS[solution].sum()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Have Fun!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.True_, np.float64(4276261.246112827))"
      ]
     },
     "execution_count": 454,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A dumb solution of \"all\" sets\n",
    "solution = np.full(NUM_SETS, True)\n",
    "valid(solution), cost(solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A random solution with random 50% of the sets\n",
    "#solution = rng.random(NUM_SETS) < .5\n",
    "#valid(solution), cost(solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitness(solution: np.ndarray):\n",
    "    return valid(solution), -cost(solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "metadata": {},
   "outputs": [],
   "source": [
    "#rng."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SIMPLE RHMC\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "metadata": {},
   "outputs": [],
   "source": [
    "def single_tweak(solution: np.ndarray) -> np.ndarray:\n",
    "    new_solution = solution.copy()\n",
    "\n",
    "    #pos = np.random.randint(NUM_SETS)\n",
    "    pos = rng.integers(0, NUM_SETS)\n",
    "    new_solution[pos] = not new_solution[pos]\n",
    "    \n",
    "    return new_solution\n",
    "\n",
    "def multi_tweak(solution: np.ndarray) -> np.ndarray:\n",
    "    mask = rng.random(NUM_SETS) < .01\n",
    "    new_solution = np.logical_xor(solution, mask)\n",
    "    \n",
    "    return new_solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 459,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| fitness_solution: (np.True_, np.float64(-2133867.089352033))\n",
      "ic| fitness_solution: (np.True_, np.float64(-530624.7189386132))\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1400x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "current_solution = rng.random(NUM_SETS) < 0.5\n",
    "fitness_solution = fitness(current_solution)\n",
    "history = [float(fitness_solution[1])]\n",
    "ic(fitness_solution)\n",
    "\n",
    "steps =  0\n",
    "\n",
    "#tweak = single_tweak\n",
    "tweak = multi_tweak\n",
    "for steps in range(MAX_STEPS):\n",
    "    \n",
    "\n",
    "    #tweak  \n",
    "    new_solution = tweak(current_solution)   \n",
    "    f = fitness(new_solution)\n",
    "    history.append(float(f[1]))\n",
    "    if(f> fitness_solution):\n",
    "       # ic(steps, cost(current_solution), cost(new_solution))\n",
    "        fitness_solution = fitness(new_solution)\n",
    "        current_solution = new_solution\n",
    "   \n",
    "\n",
    "plt.figure(figsize=(14, 8))\n",
    "plt.plot(\n",
    "    range(len(history)),\n",
    "    list(accumulate(history, max)),\n",
    "    color=\"red\",\n",
    ")\n",
    "_ = plt.scatter(range(len(history)), history, marker=\".\")\n",
    "\n",
    "\n",
    "ic(fitness_solution)\n",
    "\n",
    "results.append((1,fitness_solution[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## improved RHMC with Stength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "metadata": {},
   "outputs": [],
   "source": [
    "def multi_tweak_strength(solution: np.ndarray, strength: float = 0.3) -> np.ndarray:\n",
    "    mask = rng.random(NUM_SETS) < strength\n",
    "    if (not np.any(mask)): #if all false add 1 true\n",
    "        mask[np.random.randint(NUM_SETS)] = True\n",
    "\n",
    "    new_solution = np.logical_xor(solution, mask)\n",
    "    \n",
    "    return new_solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| fitness_solution: (np.True_, np.float64(-2147642.3261499954))\n",
      "ic| history.index(max(history)): 8858\n",
      "ic| fitness_solution: (np.True_, np.float64(-123356.13330952077))\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BUFFER_SIZE = 50 #rule 1/5\n",
    "\n",
    "current_solution = rng.random(NUM_SETS) < 0.5\n",
    "fitness_solution = fitness(current_solution)\n",
    "history = [float(fitness_solution[1])]\n",
    "ic(fitness_solution)\n",
    "\n",
    "strength = 0.5\n",
    "buffer  = list()\n",
    "\n",
    "\n",
    "for steps in range(MAX_STEPS):\n",
    "    #SEELF ADAPTIVE\n",
    "#    if steps % 1000:\n",
    "#       strength /= 2\n",
    "\n",
    "    #tweak  \n",
    "    new_solution = multi_tweak_strength(current_solution, strength)   \n",
    "    f = fitness(new_solution)\n",
    "    history.append(float(f[1]))\n",
    "    buffer.append(f > fitness_solution)\n",
    "    #take only the last BUFFER_SIZE elements\n",
    "    buffer = buffer[-BUFFER_SIZE:]\n",
    "    #if the fitness increased by 12% increase strength\n",
    "    if (sum(buffer) > 10):\n",
    "        strength *= 1.2\n",
    "    elif (sum(buffer) < 10 ):\n",
    "        strength /= 1.2\n",
    "\n",
    "    if(f> fitness_solution):\n",
    "       # ic(steps, cost(current_solution), cost(new_solution))\n",
    "        fitness_solution = fitness(new_solution)\n",
    "        current_solution = new_solution\n",
    "   \n",
    "\n",
    "plt.figure(figsize=(14, 8))\n",
    "plt.plot(\n",
    "    range(len(history)),\n",
    "    list(accumulate(history, max)),\n",
    "    color=\"red\",\n",
    ")\n",
    "_ = plt.scatter(range(len(history)), history, marker=\".\")\n",
    "\n",
    "ic(history.index(max(history)))\n",
    "ic(fitness_solution)\n",
    "\n",
    "results.append((2,fitness_solution[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## my RHMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "metadata": {},
   "outputs": [],
   "source": [
    "#multi mutation tweak with probability of 20%\n",
    "def tweak(solution):\n",
    "    new_solution = solution.copy()\n",
    "    index = None\n",
    "    while index is None or np.random.random() < 0.2:\n",
    "        index = np.random.randint(0, NUM_SETS)\n",
    "        new_solution[index] = not new_solution[index]\n",
    "    return new_solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| solution_fiteness: (np.True_, np.float64(-2135892.9236099413))\n",
      "ic| fitness(current_solution): (np.True_, np.float64(-126475.06774977251))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "current_solution = rng.random(NUM_SETS) < 0.5\n",
    "solution_fiteness = fitness(current_solution)\n",
    "history = [float(solution_fiteness[1])]\n",
    "ic(solution_fiteness)\n",
    "\n",
    "\n",
    "for steps in range(MAX_STEPS):\n",
    "    \n",
    "    #tweak\n",
    "    new_solution = tweak(current_solution)   \n",
    "    f = fitness(new_solution)\n",
    "    if(f > solution_fiteness):\n",
    "        #ic(steps, cost(current_solution), cost(new_solution))\n",
    "        current_solution = new_solution\n",
    "        solution_fiteness = f\n",
    "    history.append(float(f[1]))\n",
    "\n",
    "plt.figure(figsize=(14, 8))\n",
    "plt.plot(\n",
    "    range(len(history)),\n",
    "    list(accumulate(history, max)),\n",
    "    color=\"red\",\n",
    ")\n",
    "_ = plt.scatter(range(len(history)), history, marker=\".\")\n",
    "\n",
    "ic(fitness(current_solution))\n",
    "\n",
    "results.append((3,solution_fiteness[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## simulated annealing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulated_annealing(solution_fitness, new_solution_fitness, temp):\n",
    "    accepting_probability = np.exp(-(solution_fitness[1] - new_solution_fitness[1]) / temp)\n",
    "    #ic(solution_fitness[1] - new_solution_fitness[1])\n",
    "    #ic(accepting_probability)\n",
    "    return np.random.random() < accepting_probability\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| solution_fiteness: (np.True_, np.float64(-2204421.602773117))\n",
      "ic| fitness(current_solution): (np.True_, np.float64(-123865.81834122408))\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "current_solution = rng.random(NUM_SETS) < 0.5\n",
    "solution_fiteness = fitness(current_solution)\n",
    "history = [solution_fiteness[1]]\n",
    "ic(solution_fiteness)\n",
    "\n",
    "\n",
    "\n",
    "temp = 1565\n",
    "for steps in range(MAX_STEPS):\n",
    "    #tweak \n",
    "    new_solution = single_tweak(current_solution)   \n",
    "    f = fitness(new_solution)\n",
    "    if(f > solution_fiteness or (f[0]  and simulated_annealing(solution_fiteness, f, temp))):\n",
    "        #ic(steps, cost(current_solution), cost(new_solution))\n",
    "        current_solution = new_solution\n",
    "        solution_fiteness = f\n",
    "    history.append(float(f[1]))\n",
    "    temp*=0.99\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "plt.figure(figsize=(14, 8))\n",
    "plt.plot(\n",
    "    range(len(history)),\n",
    "    list(accumulate(history, max)),\n",
    "    color=\"red\",\n",
    ")\n",
    "_ = plt.scatter(range(len(history)), history, marker=\".\")\n",
    "\n",
    "ic(fitness(current_solution))\n",
    "\n",
    "\n",
    "results.append((4,solution_fiteness[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 469,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| sorted_results: [(2, np.float64(-123356.13330952077)),\n",
      "                     (4, np.float64(-123865.81834122408)),\n",
      "                     (3, np.float64(-126475.06774977251)),\n",
      "                     (1, np.float64(-530624.7189386132))]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[(2, np.float64(-123356.13330952077)),\n",
       " (4, np.float64(-123865.81834122408)),\n",
       " (3, np.float64(-126475.06774977251)),\n",
       " (1, np.float64(-530624.7189386132))]"
      ]
     },
     "execution_count": 469,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sort results, array of tuples, where the first element is the algorithm and the second is the fitness\n",
    "\n",
    "sorted_results = sorted(results, key=lambda x: x[1], reverse = True)\n",
    "ic(sorted_results)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}