medium_optimize.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn import tree\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from scipy.optimize import dual_annealing\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dataset creation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6 5]\n",
      " [1 5]\n",
      " [7 7]\n",
      " [5 9]\n",
      " [5 3]\n",
      " [9 8]\n",
      " [3 9]\n",
      " [9 6]\n",
      " [5 3]\n",
      " [3 2]\n",
      " [7 4]\n",
      " [4 3]\n",
      " [8 8]\n",
      " [8 8]\n",
      " [5 5]]\n",
      "[1.2        0.2        1.         0.55555556 1.66666667 1.125\n",
      " 0.33333333 1.5        1.66666667 1.5        1.75       1.33333333\n",
      " 1.         1.         1.        ]\n"
     ]
    }
   ],
   "source": [
    "nb_samples = 15\n",
    "\n",
    "np.random.seed(22)\n",
    "X = np.random.randint(1, high=10, size=(nb_samples, 2))\n",
    "print(X)\n",
    "\n",
    "y = X[:, 0] / X[:, 1]\n",
    "print(y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model creation and visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9343996768065437"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = DecisionTreeRegressor(max_depth=3)\n",
    "model.fit(X, y)\n",
    "model.score(X, y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 15))\n",
    "tree.plot_tree(model)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### SciPy Optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(v):\n",
    "\n",
    "\treturn model.predict(np.array([v]))[0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status: ['Maximum number of iteration reached']\n",
      "Total Evaluations: 410\n",
      "Minimum reached: 0.2\n",
      "Solution vector: [1.78224412 9.35220569]\n"
     ]
    }
   ],
   "source": [
    "bounds = [[1, 10], [1, 10]]\n",
    "\n",
    "result = dual_annealing(objective, bounds, maxiter=100)\n",
    "\n",
    "print(f\"Status: {result['message']}\")\n",
    "print(f\"Total Evaluations: {result['nfev']}\")\n",
    "print(f\"Minimum reached: {result['fun']}\")\n",
    "print(f\"Solution vector: {result['x']}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status: ['Maximum number of iteration reached']\n",
      "Total Evaluations: 404\n",
      "Minimum reached: 1.3333333333333333\n",
      "Solution vector: [4.32296802 1.87272909]\n"
     ]
    }
   ],
   "source": [
    "bounds = [[1, 10], [1, 4]]\n",
    "\n",
    "result = dual_annealing(objective, bounds, maxiter=100)\n",
    "\n",
    "print(f\"Status: {result['message']}\")\n",
    "print(f\"Total Evaluations: {result['nfev']}\")\n",
    "print(f\"Minimum reached: {result['fun']}\")\n",
    "print(f\"Solution vector: {result['x']}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Maximization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective_max(v):\n",
    "\n",
    "\treturn - model.predict(np.array([v]))[0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status: ['Maximum number of iteration reached']\n",
      "Total Evaluations: 410\n",
      "Maximum reached: 1.75\n",
      "Solution vector: [8.0829203 4.2638071]\n"
     ]
    }
   ],
   "source": [
    "bounds = [[1, 10], [1, 10]]\n",
    "\n",
    "result = dual_annealing(objective_max, bounds, maxiter=100)\n",
    "\n",
    "print(f\"Status: {result['message']}\")\n",
    "print(f\"Total Evaluations: {result['nfev']}\")\n",
    "print(f\"Maximum reached: {-result['fun']}\")\n",
    "print(f\"Solution vector: {result['x']}\")\n"
   ]
  }
 ],
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  "interpreter": {
   "hash": "2cc433850900f3f8369d2165de86f48230ddb438a74ebe063e2fe5118d266ca1"
  },
  "kernelspec": {
   "display_name": "datascience-beinheim-ecd",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
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