penlity_explaination.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I want to find 45 numbers with in range of [17, 99] that makes an average of 59.32\n",
    "\\begin{align}\n",
    "\\frac{1}{45} \\sum_{i=0}^{44}x_i = 59.32 \\\\\n",
    "17 \\leq x_i \\leq 99\n",
    "\\end{align}\n",
    "Find any combination of x_i that will make an average of 59.32"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this problem, I want to solve it with a genetic algorithm. Instead of using API ```gene_space = range(14, 99)``` nor initializing with ```init_range_low = 14```, ```init_range_high = 99```, I wanted to try to force the solutions into the range by implementing a penalty function. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "penlity function:\n",
    "\\begin{align}\n",
    "a \\neq b \\\\\n",
    "f(x) = \n",
    "\\begin{cases}\n",
    "    x & a \\leq x \\leq b \\\\\n",
    "    - 10^5 + x^3 & otherwise  \\\\\n",
    "\\end{cases}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This penlity function works, but I am unable to exmplain why the negative sign matters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pygad\n",
    "import numpy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "desired_output = 59.32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#penlity function\n",
    "#the more negative the number, the better the result. Up to -1E5, result of more negativity is negliable. \n",
    "def lgt(x, a=17, b=99):\n",
    "    greaterThan = numpy.where(x < a, 0, 1)\n",
    "    lessThan = numpy.where(x <= b, 1, 0)\n",
    "    return numpy.where(x * greaterThan * lessThan == 0, -1E5+(x**3), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "#GA wants to maximunize fitness. \n",
    "#The fitness function compares the desired to predict. \n",
    "def fitness_func(solution, solution_idx):\n",
    "    output = numpy.average(lgt(solution))\n",
    "    fitness = 1.0 / numpy.abs(output - desired_output)\n",
    "    return fitness"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hyper params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "fitness_function = fitness_func\n",
    "\n",
    "#number epochs.\n",
    "num_generations = 2000\n",
    "\n",
    "#number of genes in chromsome. We want 45 because we want a solution to be an array of 45\n",
    "num_genes = 45\n",
    "\n",
    "#number of solution within pupulation\n",
    "sol_per_pop = 41\n",
    "\n",
    "#Initial range\n",
    "#Set to [-50 to 50] to validate the effectiness of penlity function\n",
    "#If set to [17, 99], nothing much the GA need to do and will converage in a few cycles\n",
    "init_range_low = -50\n",
    "init_range_high = 50\n",
    "\n",
    "#parent selection method = Stochastic Universal Selection - SUS. \n",
    "#This selection method \"exhibits no bias and minimal spread\"\n",
    "parent_selection_type = \"sus\"\n",
    "keep_parents = 3\n",
    "\n",
    "#Set to high mutation rate to accerate convergion. \n",
    "crossover_type = \"single_point\"\n",
    "mutation_type = \"random\"\n",
    "mutation_percent_genes = 60\n",
    "num_parents_mating = 25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ga_instance = pygad.GA(num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=num_genes,\n",
    "                       init_range_low=init_range_low,\n",
    "                       init_range_high=init_range_high,\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_percent_genes=mutation_percent_genes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ga_instance.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It shows the penlity function is working. All elements are within [17, 99], and the predicted is very close to desired."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters of the best solution : [85.41931173 66.51627906 43.08436588 71.10861014 72.71008143 59.52646819\n",
      " 53.14073032 51.29883416 77.42584    45.7993689  48.58146195 81.59244905\n",
      " 48.86804363 64.38562125 53.06531501 41.27838483 55.99744961 73.63165326\n",
      " 54.2806442  43.07440527 47.09135739 51.25711701 75.44842554 52.7833863\n",
      " 42.75600667 46.07909066 42.33329718 54.82126266 46.4340347  79.81942868\n",
      " 76.31128252 77.59217825 64.86511865 57.1550478  52.15118582 64.84478735\n",
      " 36.78742282 72.25411071 49.65198908 62.70254746 41.34243786 60.8400411\n",
      " 76.77709565 81.89293685 64.62313905]\n",
      "Predicted output based on the best solution : 59.32000101312137\n"
     ]
    }
   ],
   "source": [
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Parameters of the best solution : {solution}\".format(solution=solution))\n",
    "prediction = numpy.average(solution)\n",
    "print(\"Predicted output based on the best solution : {prediction}\".format(prediction=prediction))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min value of array : 36.7874228182558\n",
      "max value of array : 85.41931173475018\n"
     ]
    }
   ],
   "source": [
    "print(\"min value of array : {min_num}\".format(min_num=min(solution)))\n",
    "print(\"max value of array : {max_num}\".format(max_num=max(solution)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ga_instance.plot_fitness()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 10 artists>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Solution distrubution\n",
    "a = numpy.array([])\n",
    "b = numpy.array([])\n",
    "i = int(min(solution))\n",
    "j = i+5\n",
    "while i <= max(solution):\n",
    "    a = numpy.append(a, numpy.count_nonzero((solution >= i) & (solution < j)))\n",
    "    b = numpy.append(b, j)\n",
    "    i = j\n",
    "    j += 5\n",
    "plt.bar(b,a, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This penlity function also works\n",
    "\\begin{align}\n",
    "a \\neq b \\\\\n",
    "f(x) = \n",
    "\\begin{cases}\n",
    "    x & a \\leq x \\leq b \\\\\n",
    "    - 10^5+x & otherwise  \\\\\n",
    "\\end{cases}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Without the x^3, the function works as well. Just takes longer to converage ~8000 epochs\n",
    "def lgt(x, a=17, b=99):\n",
    "    greaterThan = numpy.where(x < a, 0, 1)\n",
    "    lessThan = numpy.where(x <= b, 1, 0)\n",
    "    return numpy.where(x * greaterThan * lessThan == 0, -1E5+x, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitness_func(solution, solution_idx):\n",
    "    output = numpy.average(lgt(solution))\n",
    "    fitness = 1.0 / numpy.abs(output - desired_output)\n",
    "    return fitness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "fitness_function = fitness_func\n",
    "\n",
    "#number epochs -> 10000.\n",
    "num_generations = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "ga_instance = pygad.GA(num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=num_genes,\n",
    "                       init_range_low=init_range_low,\n",
    "                       init_range_high=init_range_high,\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_percent_genes=mutation_percent_genes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "ga_instance.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters of the best solution : [95.76811321 65.30069194 87.88861496 91.92895174 20.46564445 83.20392527\n",
      " 69.20315418 25.5080521  18.92425167 31.44847374 41.0826384  19.19826984\n",
      " 56.57074469 46.73416347 70.47900294 55.46831335 18.6142971  40.22329456\n",
      " 92.73160166 25.79354493 70.72300977 46.08858421 80.79554568 69.20260143\n",
      " 21.55271276 72.77527659 61.49797475 64.0900125  93.65341286 65.98202966\n",
      " 81.13026227 18.99341935 74.21357064 95.29434744 26.55793534 58.46503543\n",
      " 52.28581499 86.0880235  35.98573735 69.46953347 91.25604668 87.96584144\n",
      " 58.37693836 51.60968864 78.8108995 ]\n",
      "Predicted output based on the best solution : 59.31999997376553\n"
     ]
    }
   ],
   "source": [
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Parameters of the best solution : {solution}\".format(solution=solution))\n",
    "prediction = numpy.average(solution)\n",
    "print(\"Predicted output based on the best solution : {prediction}\".format(prediction=prediction))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min value of array : 18.614297098364432\n",
      "max value of array : 95.76811321167936\n"
     ]
    }
   ],
   "source": [
    "print(\"min value of array : {min_num}\".format(min_num=min(solution)))\n",
    "print(\"max value of array : {max_num}\".format(max_num=max(solution)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEbCAYAAADeeCN4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3de5wcVZ338c+XmAgCcjGjxAQISOTqcpsNIMqiwgqRFXhkFXRF8ZKFRRd1fVaB12pw113Xx9tC0BgRhSWCuiJkMagg8oAXLiGEawAjF4nJmhGEJNxC4Ld/nNOkutI9052ZqZ6Z/r5fr35NddXp6t/p6qlfn1OnqhQRmJmZ1WzS6QDMzGxkcWIwM7M6TgxmZlbHicHMzOo4MZiZWR0nBjMzq+PEYDZCSApJx3U6juEkaZakOzsdh/XPiWGUkfTtvAMJSc9Kul/SFyRt3uZ69pF0saTlkp6R9DtJCyQdK2mD74Wk+ZKek3R4g2WzCjGtk/SopF9JOl3SFoOpb+l9dpZ0nqSHcszLJf1c0nskTRiq9xlueRte0WDRJOC/q45nqJW+D8XHMcAXgL8olG32WVgHvajTAdhGuRp4NzAeeD1wHrA5cEorL5Z0FPAD4GfAScBSYFvgNcCZwM3AskL5ScCbgC8DHwCuarDae4FDAeV1vQ44HXifpNdHxP+0WcdyzL053iXAh4F7gJcAuwMfzHX45WDeY7AkTYiItRv7+sF+RiNM7ftQ9KeIeAZYU3041paI8GMUPYBvA1eU5n0DWEHaKS8FPl5aPg0IYD9SAukDLu3nPVR6fjopkewAPAW8rLR8FnBng/VMAh4BLhhknQXcBSwENhkoZmAycAnwp/z4ETCtHC9wPPBbYDVwGTCxtM6TgLuBp4H7gI8W3z9/pqcClwJPkH4NjwO+CTyQP6vfAP9Ye11+7yg9Di2s77jC+l9D+hHwFPBo3vZblb8LwGnA73NdvwW8pMlntAkp4X+4NP/V+b33zc//Ntf36fxd+Qnwoja2V8PvQ3lZs88CmJqn30b6EfJk3g6Hl9a1R962q4GVwMXAdqXP72fAqlzmNuANedl44GxgOfAM8DDwuU7/f4+Uh7uSxoangPGRvvHfBN5XWv4+YHFELAL+EpgIfL7ZyvJ6AJCk/PqLIuJ3wI2k1sqAImIFMA84plH3VBv2Ie0EvhARz/cXs6SXAD8n7dT+AjiIlDSvzstqpgLvAI4lfSb7Ap+tLZT0QeBfgU+RWiX/AHwC+LvSW38aWEDaCZ1L2vn+Hnh7ft2ZwBmkJAMpeXyPtMOflB+/Ktcnx/pj0q/r6TnO1wLnl4q+HtgLOKxQn9OafEbPk3ae7yotehdwd0Tcmltm5wJnAbvm9f640fqGwECfxWdJO++9Sa3YS2pdk7kVex0pwU/PcW4BzC98175D2vbTSdt3Ful7AfD3pM/qeNIPp3eQWjkGbjGMtgelFgPpS/9H4Lv5+XbAs8CB+fk40o7qQ/n5J0i/xrYprOM1pB1Q7fGuwrI3kH71T8jP3wfcUYppFs1/IZ6c3+/lg6jzOyj8os3ztirFfEYhvt9Q34IYl+vw9kK8T1P/6/tMYGnh+e+Ad5fi+AhpB1p7HsA5LcT/OeDqZtuwtL7j8vQHgceBLQvLD81ldims52EKv+ZJrcer+4nlz4rryPN+A5yep/9P+X03YnvNAp4rbZ+7Gn1XGn0WrG8x/G1h3uQ873X5+WeAn5Vet00uMz0/XwW8p0mMZ5NaE9qYOo71x5hoMUg6X9LKVkY7SPqypMX5cZ+kx6qIcYgdIWmNpKeBX5N+OX0YXuinvoL1rYYjgJeRfrk3cy/pV/k+pG6b8YVl7we+F+v7zv8LeJWkA1qMVflvw6s1Sror12WNpCtbXCekroFazMuB2sHn/YGdgNW19ZJ2dNsAryq8/qGIeLzwfDnw8hxTD7A98PVCbGtIO/jiOiB1b5XrdLKkhZL68us+SuqGa8fuwO0Rsbow71fA86TWU83dEbGuUT0aiYjbgTuAd+ZYDyDV6Tu5yFXAQ8ADkublA/tbthk7pC66fQqPGRuxjtsL08vz31rd9gcOKW2fh/Oy2jb6EnCepGsknSlpt8L6vp3juk/SuZLeMshW7ZgyVg4+fxuYDVw4UMGI+GhtWtKHSU3M0eY6YCapZbA8Ip4tLT8P+I6kj5ASxKUR8ae87L78dzdSUiHv9JdCGjJZW4mkrUn9vBNy10rNONJB6BtbiHUP0i+3R5osn8H6RPRUkzLFmG/NMT9fiLl4wHcTYDGpi6Ds0cJ0+TML1o/Sq/09mQbdPCVPFJ9IegfwFeDj+bWrSMchjh1gPWWiSTItze+vHs3MI30vPkPqRro+Ih4CiIjVkvYDDgEOJx1f+ldJfx4Ry5utsIG1EbG0jfKNvFC3iIjUq1m3jX5E+pzL/pBfM0vSPOBI4M3ApyWdHBHnR8QiSVNJP5zeCFwA3Cbp8GjSXdlNxkSGjIjrqP+nR9KrJP1Y0i2Sri/9Wqg5gdTnOto8GRFLI+KhBkkBUp/wKtKO7a+o75f+KWknfXoL7/Mu0sHHvan/9TcTeMdAQ2RzP/A7SYmp2bGBh3JdlkbE75usajFpNNI/Sho3QMyLgF2APxbWW3s8OsBrazH9gdT99qoG6xhoZ/c64MaImB0Ri3L5citjLSm59uduYO/Sr/XXkv5nl7RSj37MA3aRdCCpm+6i4sKIWBcR10TE6aSup82Bowb5ns208lk0sgjYk9TyK2+jF1pZEfGbiDg7It5COv72gcKy1RHx/Yg4BXgLKUHsMqjajBFjIjE0MZc0+mJ/0q+KrxYXStqR1OVwTQdiG1YR8RwpGfwbaQf3s8KyJ0jdQ0fkxHlETqKvkfQxYFNS/zC53H9FxJ3FB+nX1fOknUrNiyRtJ2mSpD0lzSS1SB6ltSTUX30CeC9pB/trSUdLerWk3SV9AJhSiHke6Rfj5ZL+QtJOkg6R9EVJ09p421mkRPRRSbtK2kvSiZIGqst9wH6SjpQ0TdI/URi3nz0I7JXXO1HS+A3WkurxBHBh3jaHAF8nJdlB/RKPiGWkVucc0rGa79eWSTpK0mmS9s3/I+8EtiQnI6XzXO6RNHkwMRQ8yMCfRSPn5ti/K+kApXNcDpM0V9KWkjbLXUSHSpqau8xeR0q4SPqYpBPyd2iXXM9VFIZpd7MxmRjyyIXXAt+XtJj0DzWpVOx40k7vufLrx4jzSf3u38o71hdExOXAgaS+92+Rzgm4ltTkPgmYl7sT9iUdU6D0+rXAfAq/vkgjWFaQ/rF+kdczF9gvhmB8fkTcRBpuewdwDmk0yg3Ae0gHjj+fyz1J6ga5n7TDu4eUyLYhDeds9f3OI3W3vJs0zPF6UkvpgQFe+nXSSJvvkEbSTAW+WCrzDdKOdiGpRXZwg/d/ktT98VLgJuByUqItjzjbWP9Jagn+KCKKx9keA44hjRS6h/Sj6gMRcX1evhVpW7e6Ax/IgJ9FI7lb62DSD5Qfk4Yzn0saevoM6YfCNqRtfy/wQ9Ln97G8itXA/yV9totILeEj8+fe9VTaZ4xaub/wiojYS9JLgXsjopwMiuVvBU6NiIH6kEel/Avpl8DOkYaZmpm1ZEy2GCJiFWlUxV9DGosvae/ackm7kn5N/LpDIQ4bSS/OTeN/AX7opGBm7ao8MUgaJ+lWNbg+St6Bny1pqaTbc3dGK+u8mLST31XSMknvJx04fb+k20jNzKMLLzkBuKTcxTJGnEBqOr+M9c1mM7OWVd6VlA9w9gIvjYijSstmkMbjzwAOAP4jIlodL29mZkOg0haDpCmkYWHnNSlyNHBhJDcAW+chj2ZmVpGqT3D7CumCYs3OpJzM+rMXIY1wmUwa7fKCPBRyJsDmm2++/267NTpFwczMmrnlllv+GBE9jZZVlhiULvW8MiJukXRos2IN5m3Q1xURc0lDIent7Y2FCze4KoGZmfVD0kPNllXZlXQw8FZJD5IuifxGSReVyiwjXaOmZgrrr5FiZmYVqCwxRMTpETElIqaSTi67JiL+plRsPnBiHp10IPB4pEs3m5lZRTp+ET1JJwNExBzSde1nkC6O9iTrr2FvZmYV6UhiiIhrSZdgqCWE2vzaHbHMzKxDxuSZz2ZmtvGcGMzMrE7HjzGYmVXp+edhycPw1NqBy44G014JW/V7Z5T2OTGYWVc5/Vtw3YA3AR49vjQTDtp9aNfpriQz6xrPrhtbSWG4uMVgZl2jfBmF/cfAjTxf+pKhX6cTg5l1pQkvgtkeHN+Qu5LMrGuMyTuwDAMnBjMzq+PEYGZmdZwYzKw7NbrIvwFODGbWRXyMoTVODGZmVseJwczM6jgxmFlX8iGG5pwYzMysjhODmZnVqSwxSNpU0k2SbpN0l6SzGpQ5VNLjkhbnx6eqis/MzJIqr5X0DPDGiFgjaTzwC0lXRsQNpXLXR8RRFcZlZl1IPsjQVGWJId/PeU1+Oj4/PKrYzCrj8xhaU+kxBknjJC0GVgJXRcSNDYodlLubrpS0Z5P1zJS0UNLCvr6+YY3ZzKzbVJoYIuK5iNgHmAJMl7RXqcgiYMeI2Bs4B7isyXrmRkRvRPT29PQMb9BmZl2mI6OSIuIx4FrgiNL8VRGxJk8vAMZLmlh9hGY2FhV7knyIobkqRyX1SNo6T28GHAbcUyqznZQOCUmanuN7pKoYzcys2lFJk4ALJI0j7fC/FxFXSDoZICLmAMcBp0haBzwFHJ8PWpuZWUWqHJV0O7Bvg/lzCtOzgdlVxWRm3cvDVZvzmc9m1jXc/9AaJwYzM6vjxGBmZnWcGMzMrI4Tg5mZ1XFiMDOzOk4MZmZWx4nBzLqSz2NozonBzLqGz2NojRODmZnVcWIwM7M6Tgxm1jV82e3WODGYmVkdJwYzM6vjxGBmZnWcGMysaxSHq/o8huacGMzMrE6V93zeVNJNkm6TdJeksxqUkaSzJS2VdLuk/aqKz8zMkirv+fwM8MaIWCNpPPALSVdGxA2FMkcC0/LjAOBr+a+Z2dByV1JTlbUYIlmTn47Pj/IJ6kcDF+ayNwBbS5pUVYxmNrb5khitqfQYg6RxkhYDK4GrIuLGUpHJwMOF58vyvPJ6ZkpaKGlhX1/f8AVsZtaFKk0MEfFcROwDTAGmS9qrVKRR426DHB8RcyOiNyJ6e3p6hiNUM7Ou1ZFRSRHxGHAtcERp0TJg+8LzKcDyisIysy7iQwzNVTkqqUfS1nl6M+Aw4J5SsfnAiXl00oHA4xGxoqoYzcys2lFJk4ALJI0jJaTvRcQVkk4GiIg5wAJgBrAUeBI4qcL4zMyMChNDRNwO7Ntg/pzCdACnVhWTmZltyGc+m1nX8CUxWuPEYGZmdZwYzMysjhODmZnVcWIws67hW3u2xonBzMzqODGYmVkdJwYzM6vjxGBmXcPnMbTGicHMzOo4MZiZWR0nBjMzq+PEYGZmdZwYzMysjhODmZnVcWIws67h4aqtcWIwM7M6Vd7zeXtJP5e0RNJdkk5rUOZQSY9LWpwfn6oqPjMzS6q85/M64B8iYpGkLYFbJF0VEXeXyl0fEUdVGJeZmRVU1mKIiBURsShPrwaWAJOren8zs7pjDJ0LY8TryDEGSVOBfYEbGyw+SNJtkq6UtGeT18+UtFDSwr6+vmGM1Mys+1SeGCRtAfwA+EhErCotXgTsGBF7A+cAlzVaR0TMjYjeiOjt6ekZ3oDNzLpMpYlB0nhSUpgXEZeWl0fEqohYk6cXAOMlTawyRjOzblflqCQB3wSWRMSXmpTZLpdD0vQc3yNVxWhmY1vdrT19kKGpKkclHQy8G7hD0uI87wxgB4CImAMcB5wiaR3wFHB8RPFwkZmZDbfKEkNE/IIBBgJExGxgdjURmZlZIz7z2czM6jgxmFnXqOuY9jGGppwYzMysjhODmZnVGXRiyOcmmJnZGNFWYpD095LeVnj+TeApSfdK2nXIozMzGyY+xNBcuy2Gvwf6ACQdArwdeCewGPji0IZmZmad0O55DJOBB/P0XwHfj4jvSboDuH4oAzMzs85ot8WwCqhdte5w4Gd5+llg06EKysxsOPjWnq1pt8XwU+Abkm4FdgGuzPP3BB4YysDMzKwz2m0xnAr8EpgIHBcRj+b5+wEXD2VgZmbWGW21GPL9Ez7cYP6nhywiMzPrqHaHq+5RHJYq6XBJF0k6XdK4oQ/PzGzo+IoYrWm3K+mbpFtyImkKcDmwLamL6V+GNjQzM+uEdhPD7qTbbwL8NXBjRMwg3WfhhKEMzMzMOqPdxDAOWJun3wQsyNO/BV4xVEGZmVnntJsY7iTdYe31pMTw4zx/MvDHoQzMzGyo+TyG1rSbGD4BfBC4Frg4Iu7I898K3NTfCyVtL+nnkpZIukvSaQ3KSNLZkpZKul3Sfm3GZ2Zmg9TucNXrJPUAL42IPxUWfR14coCXrwP+ISIWSdoSuEXSVRFxd6HMkcC0/DgA+Fr+a2ZmFWn7stsR8RwwTtIBkl6c5z0YESsHeN2KiFiUp1cDS0hdUEVHAxdGcgOwtaRJ7cZoZmYbr93zGLaU9H1gJfAr8o5d0hxJs9pYz1TSsNcbS4smAw8Xni9jw+SBpJmSFkpa2NfX104VzMxsAO22GP4deCXpEhhPFeZfARzbygokbQH8APhIPpO6bnGDl8QGMyLmRkRvRPT29PQ0eImZmW2sdi+i91bg2IhYLKm4w14C7DzQi/Pd3n4AzIuISxsUWQZsX3g+BVjeZoxmZjYI7bYYtgEeaTB/S+C5/l4oSaQzp5dExJeaFJsPnJhHJx0IPB4RK9qM0cysodig/8EaabfFcDOp1fCV/Lz2Mf8t6ZhDfw4mnSF9h6TFed4ZwA4AETGHdMLcDGApaZTTSW3GZ2bWEp/H0Fy7ieEM4CeS9syv/Vieng4c0t8LI+IXDHDdqogI0nWXzMysQ9rqSoqIXwGvBSaQLoPxJtIxgINqQ1HNzGx0a7fFQD7b+T3DEIuZ2bCquyRG58IY8dpODACSXgm8nFKLw60GM7PRr63EIGlf4CJgNzZMuEG6+qqZmY1i7bYY5pLOTP4g6diCB3+ZmY0x7SaGPYB9I+K+4QjGzGw41d3a0wcZmmr3BLc7gO2GIxAzMxsZ2k0MZwCfl3SYpFdI2rb4GI4AzcysWu12JV2d//6UUqsMH3w2sxHOl8RoTbuJ4Q3DEoWZWdV8jKGpdhPDA8DD+dIVL8gXyNu+8UvMzGw0afcYwwNAoxsgbJuXmZnZKNduYqgdSyjbAnh68OGYmVmntdSVJOnsPBnAv0l6srB4HOnqqos3eKGZ2QjlQwzNtXqM4TX5r4DdgbWFZWuBRcAXhjAuMzPrkJYSQ0S8AUDSt4DTGtyr2czMxoi2RiVFhO+oZmajls9jaM2AiUHSfOBvImJVnm4qIt7az3rOB44CVkbEXg2WHwpczvrRTZdGxGcGis/MbGP4WknNtdJieAT4M0m/ztMb69vAbODCfspcHxFHDeI9zMxskAZMDBFxkqTngEm1riRJPwI+EBErWn2jiLhO0tSNDdTMzKrR6nkM5UbX64HNhjgWgIMk3SbpSkl7Ng1GmilpoaSFfX19wxCGmY1FPsTQmnZPcKsZjt65RcCOEbE3cA5wWbOCETE3Inojorenp9GJ2GZm/fMhhuZaTQzBhsl2SJNvRKyKiDV5egEwXtLEoXwPMzMbWKvDVQVcJOmZ/HxT4BulM6D7HZU04BtI2wF/iIiQNJ2UtAZzsNvMrI6Hq7am1cRwQen5Re2+kaSLgUOBiZKWAZ8GxgNExBzgOOAUSeuAp4Djy1dxNTMbMu5LaqrVM58HfWJbRJwwwPLZpOGsZmbWQRt78NnMzMYoJwYzM6vjxGBmXcmHGJpzYjAzszpODGZmVseJwcy6hgfAt8aJwcy6ki+73ZwTg5mZ1XFiMDOzOk4MZtY1fIyhNU4MZtaVfIihOScGMzOr48RgZl3DPUmtcWIwM7M6Tgxm1pV8HkNzTgxmZlbHicHMuoaHq7amssQg6XxJKyXd2WS5JJ0taamk2yXtV1VsZtaF3JXUVJUthm8DR/Sz/EhgWn7MBL5WQUxmZlZSWWKIiOuAR/spcjRwYSQ3AFtLmlRNdGZmVjOSjjFMBh4uPF+W521A0kxJCyUt7OvrqyQ4M7NuMZISQ6Mev4aHiiJibkT0RkRvT0/PMIdlZmORDzE0N5ISwzJg+8LzKcDyDsViZta1RlJimA+cmEcnHQg8HhErOh2UmY0dHq7amhdV9UaSLgYOBSZKWgZ8GhgPEBFzgAXADGAp8CRwUlWxmZnZepUlhog4YYDlAZxaUThm1uV8SYzmRlJXkpmZjQBODGbWNXyIoTVODGZmVseJwcy6kg8xNOfEYGZmdZwYzKxr+DyG1jgxmJlZHScGM+tOPsjQlBODmZnVcWIws+7hYwwtcWIwM7M6Tgxm1pV8iKE5JwYz6xruSWqNE4OZmdVxYjCzruTLbjfnxGBmZnWcGMysa/iSGK2pNDFIOkLSvZKWSvpkg+WHSnpc0uL8+FSV8ZmZWbX3fB4HnAscDiwDbpY0PyLuLhW9PiKOqiouM+tOPsTQXJUthunA0oi4PyLWApcAR1f4/mZm1oIqE8Nk4OHC82V5XtlBkm6TdKWkPRutSNJMSQslLezr6xuOWM1sDPIhhtZUmRgatdzK22kRsGNE7A2cA1zWaEURMTcieiOit6enZ4jDNDPrblUmhmXA9oXnU4DlxQIRsSoi1uTpBcB4SROrC9HMuoXPY2iuysRwMzBN0k6SJgDHA/OLBSRtJ6XNJWl6ju+RCmM0M+t6lY1Kioh1kj4E/AQYB5wfEXdJOjkvnwMcB5wiaR3wFHB8hEcem9nQ8N6kNZUlBnihe2hBad6cwvRsYHaVMZmZWT2f+Wxm3cnHGJpyYjAzszpODGZmVseJwczM6jgxmFlX8iGG5pwYzKxreLhqa5wYzMysjhODmXUlXxKjOScGMzOr48RgZl3Dhxha48RgZmZ1nBjMrCv5EENzTgxmZlbHicHMuobPY2iNE4OZmdVxYjCz7uSDDE1VeqMeM+vf88/DH1d1Ooqx67E1nY5gdKg0MUg6AvgP0q09z4uIz5WWKy+fATwJvDciFlUZo1mn/GkNvP/LsOLRTkdi3a6yxCBpHHAucDiwDLhZ0vyIuLtQ7EhgWn4cAHwt/x1STzwNX72i/zKtHKRqqUwrAQ1QqJV1DFUsQ3Fwrls/u1YK9Vfk6ltbeRMbKlu9pNMRjFxVthimA0sj4n4ASZcARwPFxHA0cGFEBHCDpK0lTYqIFUMZyNp1cOkvh3KNZkNv4ladjmDs6tkK3nt4p6MYuapMDJOBhwvPl7Fha6BRmclAXWKQNBOYCbDDDjsMeaBmnTRuE5j3Cdjx5Z2OxLpVlYmh0RiAcsu6lTJExFxgLkBvb2/bnR+bTYCPv23gckN19cVW1jNQkZbWMcribUU3fnZ7TYVJ2w5FNGYbp8rEsAzYvvB8CrB8I8oM2qYT4G2vG+q1mpmNDVWex3AzME3STpImAMcD80tl5gMnKjkQeHyojy+YmVn/KmsxRMQ6SR8CfkIarnp+RNwl6eS8fA6wgDRUdSlpuOpJVcVnZmZJpecxRMQC0s6/OG9OYTqAU6uMyczM6vmSGGZmVseJwczM6jgxmJlZHScGMzOroxjld66Q1Ac8tJEvnwj8cQjD6STXZWQaK3UZK/UA16Vmx4joabRg1CeGwZC0MCJ6Ox3HUHBdRqaxUpexUg9wXVrhriQzM6vjxGBmZnW6PTHM7XQAQ8h1GZnGSl3GSj3AdRlQVx9jMDOzDXV7i8HMzEqcGMzMrE7XJgZJR0i6V9JSSZ/sdDwDkfSgpDskLZa0MM/bVtJVkn6T/25TKH96rtu9kt7cuchB0vmSVkq6szCv7dgl7Z8/g6WSzpaG6vY6g67LLEm/z9tmsaQZI70ukraX9HNJSyTdJem0PH/UbZd+6jIat8umkm6SdFuuy1l5frXbJSK67kG67PdvgZ2BCcBtwB6djmuAmB8EJpbmfR74ZJ7+JPDveXqPXKcXAzvluo7rYOyHAPsBdw4mduAm4CDSTdCuBI4cIXWZBXy8QdkRWxdgErBfnt4SuC/HO+q2Sz91GY3bRcAWeXo8cCNwYNXbpVtbDNOBpRFxf0SsBS4Bju5wTBvjaOCCPH0BcExh/iUR8UxEPEC6v8X0DsQHQERcBzxamt1W7JImAS+NiF9H+tZfWHhNZZrUpZkRW5eIWBERi/L0amAJ6f7qo2679FOXZkZyXSIi1uSn4/MjqHi7dGtimAw8XHi+jP6/SCNBAD+VdIukmXneKyLf4S7/rd0+fjTUr93YJ+fp8vyR4kOSbs9dTbVm/qioi6SpwL6kX6ejeruU6gKjcLtIGidpMbASuCoiKt8u3ZoYGvW1jfRxuwdHxH7AkcCpkg7pp+xorF9Ns9hHcp2+BrwK2AdYAXwxzx/xdZG0BfAD4CMRsaq/og3mjfS6jMrtEhHPRcQ+pHveT5e0Vz/Fh6Uu3ZoYlgHbF55PAZZ3KJaWRMTy/Hcl8ENS19AfcpOR/HdlLj4a6tdu7MvydHl+x0XEH/I/8/PAN1jfbTei6yJpPGlHOi8iLs2zR+V2aVSX0bpdaiLiMeBa4Agq3i7dmhhuBqZJ2knSBOB4YH6HY2pK0uaStqxNA38J3EmK+T252HuAy/P0fOB4SS+WtBMwjXQgaiRpK/bcfF4t6cA8uuLEwms6qvYPmx1L2jYwguuS3/ebwJKI+FJh0ajbLs3qMkq3S4+krfP0ZsBhwD1UvV2qPOI+kh7ADNLohd8CZ3Y6ngFi3Zk08uA24K5avMDLgJ8Bv8l/ty285sxct3vpwOidUvwXk5ryz5J+ybx/Y2IHekn/3L8FZpPP3B8BdflP4A7g9vyPOmmk1wV4Halr4XZgcX7MGI3bpZ+6jMbt8mfArTnmO4FP5fmVbhdfEsPMzOp0a1eSmZk14cRgZmZ1nBjMzKyOE4OZmdVxYjAzszpODGajgNLVdT/e6TisOzgx2Jgh6RWSvpwvTfy00uWxfyXpw/lyCSNevlT0nQ0W/Tnw1arjse70ok4HYDYU8sXTfgmsAv6JdILQJsCrSWd9PgJ8p0PhIWlCpCv5boL1aZMAAAOrSURBVJSI6BvKeMz64xaDjRVfA54HeiPikoi4OyLujIhLI+IY0hnLSNpK0tzcmlgt6f9L6q2tRNJ7Ja2R9CZJd0p6QukmMDsV30zSX+Ur3T4t6QFJn82XV6ktfzD/+j9f0mPAvDz/c/mGKk/lMp+XtGntvYFPA3tKivx4b2F9Hy+sfwdJP8x1WC3pUklTCstn5fiPl/TbXOYySROH+oO3sceJwUY9SdsCbwbOjYgnGpWJiMjXjPkR6fLDR5Euz3wdcE3pujovBk4H3ke60cnWwJzC+72ZtKOfDeyZyx0H/GvpbT9Gus5NL3BGnvdELr878Hek63SdmZd9l3QF0HtJN5+ZlOeV6yvgMuAVwBuBNwCvBC7Ly2qmAu8gXSfoL3N9P9vo8zGrU+V1QPzwYzgewAGka+UcW5q/DFiTH3NIO9E1wGalcouBf8zT783r2rWw/F3AWmCT/Pw64J9K6zgmr7t2mZkHgf9uIfaTSTeNqj2fReHucIX5D5LvRgYcDjwHTC0s35nUYjqssJ6nga0KZc4svpcffjR7+BiDjWWvJ93GdS6wKbA/8BKgr/6HNZuSrttf80xE3Ft4vpx0J62tSXdv2590nfxPFMpsAmwGbEe6yB7AwnJAko4DPgLsAmyR4xvXZr12B5ZHxIO1GRFxv6TlpFs9Xp1nPxQRj5fq8XLMBuDEYGPBUtKv/N2KMyPd6hBJT+ZZmwB/ICWMsuJNataVltWuNLlJ4e9ZwPcbrKd4kLiuW0vSgaTbyJ4FfBR4DHgr8IUG6+mPaH7TleL8Zxssc/exDciJwUa9iHhE0k9Jt3E8J9bfM7dsEalf/vmIuH8Qb7kI2C0ilrb5uoOB30fEP9dmSNqxVGYtA7cg7gYmS5paazVI2pl0nOHuNmMy24B/PdhY8Xek7/Mtkk6QtIekV0s6Adib1Cd/NWlI6+WSjlS6UdNBks6S1KgV0cxngHdK+oykvSTtJuk4SZ8f4HX3kXbo75K0s6RTgBNKZR4EdpS0n6SJkl7cYD1Xk+7NMU/S/nlU1TxSwrqmjXqYNeTEYGNCbgHsC/wY+GfSzU4WkUYGfZV0H+Ag3cDlGtKtHu8FvgfsShu3PYyInwBvIY0Guik/Pgn8boDX/Tfw/4CvkM6zOBz4VKnYD4AFpJux9LFh4iDX45i8/Frg58D/AMfkZWaD4hv1mJlZHbcYzMysjhODmZnVcWIwM7M6TgxmZlbHicHMzOo4MZiZWR0nBjMzq+PEYGZmdf4X5fW7bGJMxJoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ga_instance.plot_fitness()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 16 artists>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Solution distrubution\n",
    "a = numpy.array([])\n",
    "b = numpy.array([])\n",
    "i = int(min(solution))\n",
    "j = i+5\n",
    "while i <= max(solution):\n",
    "    a = numpy.append(a, numpy.count_nonzero((solution >= i) & (solution < j)))\n",
    "    b = numpy.append(b, j)\n",
    "    i = j\n",
    "    j += 5\n",
    "plt.bar(b,a, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, if the constant is changed to positve number, the range regulation won't work. Why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# -1E5 -> 1E5\n",
    "def lgt(x, a=17, b=99):\n",
    "    greaterThan = numpy.where(x < a, 0, 1)\n",
    "    lessThan = numpy.where(x <= b, 1, 0)\n",
    "    return numpy.where(x * greaterThan * lessThan == 0, 1E5+x, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitness_func(solution, solution_idx):\n",
    "    output = numpy.average(lgt(solution))\n",
    "    fitness = 1.0 / numpy.abs(output - desired_output)\n",
    "    return fitness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "fitness_function = fitness_func\n",
    "num_generations = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "ga_instance = pygad.GA(num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=num_genes,\n",
    "                       init_range_low=init_range_low,\n",
    "                       init_range_high=init_range_high,\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_percent_genes=mutation_percent_genes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "ga_instance.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters of the best solution : [ 17.71377722  17.31299344  17.65591079  17.33169855  17.02969603\n",
      "  19.28740284  18.31314551  17.94636189 -53.76151574  17.26081627\n",
      "  17.13600466 -33.84011644  18.72591586  18.16741919 -93.52622424\n",
      "  19.06251392 -53.60713305 -80.44971866  17.21316588 -67.75766744\n",
      "  17.28328394  17.97291968  21.01078983  18.58933444  18.21278229\n",
      "  17.71336441  19.3185958   18.15640235 -68.17831801  18.47370494\n",
      "  18.66649041  18.95779831  20.85166765 -47.92106588  17.06442898\n",
      " -62.77696097 -78.3906316   17.08322265 -49.75222773  17.96676183\n",
      "  17.24879443  18.96849874  17.10683244  17.84113711  17.52621844]\n",
      "Predicted output based on the best solution : -1.6398162009054051\n"
     ]
    }
   ],
   "source": [
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Parameters of the best solution : {solution}\".format(solution=solution))\n",
    "prediction = numpy.average(solution)\n",
    "print(\"Predicted output based on the best solution : {prediction}\".format(prediction=prediction))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min value of array : -93.52622423940862\n",
      "max value of array : 21.01078982579159\n"
     ]
    }
   ],
   "source": [
    "print(\"min value of array : {min_num}\".format(min_num=min(solution)))\n",
    "print(\"max value of array : {max_num}\".format(max_num=max(solution)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ga_instance.plot_fitness()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 23 artists>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Solution distrubution\n",
    "a = numpy.array([])\n",
    "b = numpy.array([])\n",
    "i = int(min(solution))\n",
    "j = i+5\n",
    "while i <= max(solution):\n",
    "    a = numpy.append(a, numpy.count_nonzero((solution >= i) & (solution < j)))\n",
    "    b = numpy.append(b, j)\n",
    "    i = j\n",
    "    j += 5\n",
    "plt.bar(b,a, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Why this works"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with the ```x**3``` of the funtion. ```x**3``` retains the sign of x while making the values not in the range easier to elimate. For values moving to the desired direction will receive an explanically better fitness, it'll make the GA converge faster. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = numpy.arange(-15,16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7faf7ff25df0>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, t**3, label='x^3')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the problem with this method is that it also wants to converge to 0, where the effect is minimized and therefore have no negative impact on fitness. Hence, the more offline have two choices: converge to zero; converge to within the range. To solve that problem, we can make x + some constant. So that even at 0, it still has a negative impact on the fitness"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function ```10000-x^3``` works about the same as ```x^3-10000```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7faf80029e50>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, t**3, label='x^3')\n",
    "plt.plot(t, 1000-(t**3), label='10000-x^3')\n",
    "plt.plot(t, -1000+(t**3), label='x^3-10000')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## x^3 + constant "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lgt(x, func, a=17, b=99):\n",
    "    greaterThan = numpy.where(x < a, 0, 1)\n",
    "    lessThan = numpy.where(x <= b, 1, 0)\n",
    "    return numpy.where(x * greaterThan * lessThan == 0, func, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7faf800e9250>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, t, label='t')\n",
    "plt.plot(t, lgt(t, t**3, 4,10), label='t^3')\n",
    "plt.plot(t, lgt(t, -500+t**3, 4,10), label='-500+t^3')\n",
    "plt.plot(t, lgt(t, 500+t**3, 4,10), label='500+t^3')\n",
    "plt.plot(t, lgt(t, 10000+t**3, 4,10), label='10000+t^3')\n",
    "plt.plot(t, lgt(t, -10000+t**3, 4,10), label='-10000+t^3')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we see, the greater number of the constant helps better distanish the elements that have a negative impact on the fitness. The ```x**3``` also provides a sense of direction to better converge to the range"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So then, when positive constant doesn't work but negative constant works? The function ```x-10000``` works perfectly fine but just takes longer to converge without ```x**3```."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constant "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7faf80203f10>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEDCAYAAAA4FgP0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3de3zcdZ3v8ddnZnJpkl5om0lbSqWy7UJBiRhARLEuIoWjW1BcqRylKFZOYdfds4uU5TzqyvG4YcFV0VK2IFv2HCsqCnSlKyBaAQWkaIW23ApyiS1NKaSXNE1mMp/zx8yk03SSzC2ZZH7v5+Mxj8z8LjOfyWU++X6/v8/3a+6OiIgEV6jcAYiISHkpEYiIBJwSgYhIwCkRiIgEnBKBiEjAKRGIiATcmE0EZnabmbWb2aYcj/8rM9tiZpvNbM1wxyciMlbYWK0jMLMzgH3Af7j7CUMcOwf4IfAX7v6WmUXdvX0k4hQRGe3GbIvA3R8C3szcZmbHmNnPzOxJM3vYzI5N7fo8sMLd30qdqyQgIpIyZhPBAFYBf+3u7wb+AbgptX0uMNfMfm1mj5nZgrJFKCIyykTKHUCpmFkD8F7gR2aW3lyT+hoB5gDzgZnAw2Z2grt3jHScIiKjTcUkApKtmw53b86yrw14zN1jwB/N7DmSieGJkQxQRGQ0qpiuIXffQ/JD/hMAlnRiavfdwAdT26eS7Cp6qSyBioiMMmM2EZjZ94FHgT83szYz+xxwEfA5M/sDsBlYmDr8PmCXmW0Bfglc6e67yhG3iMhoM2YvHxURkdIYsy0CEREpjTE5WDx16lQ/+uijyx2GiMiY8uSTT77h7o39t4/JRHD00UezYcOGcochIjKmmNkr2bara0hEJOCUCEREAk6JQEQk4MbkGIGICEAsFqOtrY0DBw6UO5RRpba2lpkzZ1JVVZXT8UoEIjJmtbW1MX78eI4++mgy5hgLNHdn165dtLW1MXv27JzOKUnX0FCLxKSme7jRzLaa2VNmdlLGvgVm9lxq37JSxCMiwXDgwAGmTJmiJJDBzJgyZUperaRSjRGsBgab2vkckpO8zQGWACsBzCwMrEjtnwcsMrN5JYpJRAJASeBw+X5PStI15O4PmdnRgxyykORKYg48ZmaTzGw6cDSw1d1fAjCzO1LHbilFXP3t/eUvOfB0TitbiowtoRATF/4l1UcdVe5IxqzefftIdHaWO4whhSdNIlRTM/SBeRipMYIjgdcyHreltmXbfmq2JzCzJSRbE8yaNaugIDoffpi31ny/oHNFRrvE3j00XX11ucMYs+Lbt5Po7s7rnI49e/jBunV84cILhymqw4Xq6mCMJoJs7RQfZPvhG91XkVyBjJaWloJmypu2fDnTli8v5FSRUe3Fc/8bsdd3lDuMMc1jcSKTJ1M1Y0bO5+x4+WVuvftu/varXx3GyIbfSNURtAGZbdaZwLZBtotIHiLRKPF2LcVdKO/txRO9kOPllmnLli3jxRdfpLm5mSuvvHKYoht+I9UiWAtckRoDOBXY7e7bzWwnMMfMZgN/Ai4EPjVCMYlUjEi0ka4nf1fuMMrqK/+5mS3b9hR2sidI7O/Cat7CIlv7Ns+bMYEvf/T4AU9rbW1l06ZNbNy4sbDXHSVKkghSi8TMB6aaWRvwZaAKwN1vBtYB5wJbgf3AJal9cTO7guTCMWHgNnffXIqYRIKkKhplb3s77q6raAqRWpclqN+7Ul01tGiI/Q5cPsC+dSQThYgUKBJtwmMxejs6iBxxRLnDKYvB/nMfSryjg1hbGzV/9meEamtLGNXYoLmGRCpAJBoF0DhBoeJxACzPMYLx48ezd+/e4YhoRCkRiFQAJYLieCwGFoJQfh+JU6ZM4fTTT+eEE07QYLGIlFdVUyoR7NAlpIXweByrihQ0RrBmzZphiGhkqUUgUgHCjcnVB2NqERTEYzEsEtz/i5UIRCpAqLqa8BFHqGuoQMkWQX7jA5VEiUCkQiSLynaWO4wxx93xWByLKBGIyBgXaYpqjKAQvb3gCaxKXUMiMsZpmonCeOrSUTRGICJjXVU0SnzXroMfbJITL7CGoJIoEYhUiEi0CRIJ4rt2lTuUMcVjMYCirxp69tlnOe2006ipqeGGG244ZF84HKa5ubnv1traCsDixYuZPXt23/Zc5yzq6OjgpptuKireTMFtC4lUmMyisqqmpjJHM3Z4rDQtgsmTJ3PjjTdy9913H7Zv3LhxA37IX3/99VxwwQUDPu/ixYtZvHgx8+fP79uWTgRLly4tKuY0tQhEKoSqiwsUj2HhMJZnVXF/0WiUk08+maoR6GIq9fTXahGIVIhINFlUFthE8F/L4PWn8z4t3H2AcCIBj9UdvnPaO+Cc1qJD6+rqorm5ue/x1VdfzSc/+UkArrnmGq699lrOPPNMWltbqclh9bFST3+tRCBSISJTpkA4TEyXkObHPTnP0DAaqGvon//5n5k2bRo9PT0sWbKE6667juXLl3Pfffdx1VVXAfDqq6/yyCOP0NDQQE1NDY8//njJ41MiEKkQFg4TmTo1uEVlBf7n3vPcc4Tq66meOTPvc1esWMEtt9wCwLp165iRxzKXANOnTwegpqaGSy65pG+Q+eyzz+bss88Gso8RlJrGCEQqiGoJ8lNsVfHll1/Oxo0b2bhxY95JAGD79u19cdx9992ccMIJOZ1X6umvS7VC2QLgWyRXGbvV3Vv77b8SuCjjNY8DGt39TTN7GdgL9AJxd28pRUwiQRRpihJ75dVyhzF2xOOAl6Sq+PXXX6elpYU9e/YQCoX45je/yZYtW5gwYcJhYwQLFiygtbWViy66iJ07d+LuNDc3c/PNN+f0WpnTX59zzjlcf/31RcVe9Ls3szCwAjiL5GL0T5jZWnffkj7G3a8Hrk8d/1Hg79z9zYyn+aC7v1FsLCJBVxWN0vXEhnKHMWaUsphs2rRptLW1Zd3X29ubdfsvfvGLIZ939erVWbeXcvrrUnQNnQJsdfeX3L0HuANYOMjxi4Dvl+B1RaSfSDRK7+7dJLq7yx3KmFCqYrKxrhSJ4EjgtYzHbalthzGzOmAB8OOMzQ7cb2ZPmtmSgV7EzJaY2QYz27BzZ0AHw0SGEGlM1RLobyQnmmcoqRSJINuSPj7AsR8Fft2vW+h0dz8JOAe43MzOyHaiu69y9xZ3b2lMLcIhIoeKpCqKNQtpbvqqipUIitYGHJXxeCawbYBjL6Rft5C7b0t9bQfuItnVJCIFCHxRWZ48nlyZrNiq4rGuFO/+CWCOmc02s2qSH/Zr+x9kZhOBDwD3ZGyrN7Px6fvAh4FNJYhJJJCqNM1EXjweD3xrAEpw1ZC7x83sCuA+kpeP3ubum83sstT+9PVQ5wP3u3tnxulNwF2pBaMjwBp3/1mxMYkEVWjiRKymhtgOJYKcxGKBnn46rSTtIXdf5+5z3f0Yd/8/qW03ZyQB3H21u1/Y77yX3P3E1O349LkiUhgzU1FZHjwWL3qg+LOf/SzRaPSQYrD+00u/973vBWD9+vVMnDixb/u1116b8+usXr2abdsG6nUvTrA7xkQqkBJBbjyRwHuLX7R+8eLF/Oxnh3dkXH/99X1Vx7/5zW/6tr///e/v2758+fLDzlu/fj2LFy8+bLsSgYjkLBJtVCLIQV8xWZEtgjPOOIPJkyeXIqQB3XnnnWzYsIGLLrqI5uZmurq6Svr8GiURqTBV0Sb2/eoh3J3U+FsgXPfb63j2zWdzPyGRINHVhb1Si4XDWQ85dvKxXHXKVQXFc+WVV/LVr34VgOOPP57vfe97ADz66KOceOKJzJgxgxtuuIHjjz9+yOe64IIL+M53vsMNN9xAS0vpZ+FRIhCpMJFoFN+/n0RnJ+GGhnKHM2p5IgEwbMky28pjJ510Eq+88goNDQ2sW7eO8847jxdeeAGAU089le7ubvbt28ebb77ZNzfRdddd1zcT6XBRIhCpMJkrlQUpEeT7n3t81y5i27dTe+yxI3YJ6YQJE/run3vuuSxdupQ33niDqVOn9q0zsH79elavXj3gHEPDQWMEIhUm0pRKBKouHpTHYmAGA3QLDYfXX38d9+TEC7/97W9JJBJMmTIlp3NLPfV0JrUIRCqMispyky4mK7ZraNGiRaxfv5433niDmTNn8pWvfAU4dIwAkh/8d955JytXriQSiTBu3DjuuOOOnF9/8eLFXHbZZYwbN45HH32UcePGFRV3Jktnp7GkpaXFN2zQVLsi2SQ6O3nu3S00/v3/ZOrnP1/ucIbVM888w3HHHVfQud1//CMkEtQcc0yJoxodsn1vzOzJbGu+qGtIpMKE6usJNTQEd8nKHHm8+BqCSqFEIFKBIk1NGiMYShFLVFYaJQKRCqSissF5by+e6IUSLFFZCZQIRCpQlaaZGFSpqoorhRKBSAWKRJuI7dzZVzQlhyrlWsWVQIlApAJFolGIxejt6Ch3KKOS1io+lBKBSAWKqJZgcLHStQjymYYakpXDzc3NHH/88XzgAx/I+XU0+6iI5EVLVg7O4zEIhZK3IuUzDXVHRwdLly5l7dq1bN68mR/96EeHnTdmp6E2swVm9pyZbTWzZVn2zzez3Wa2MXVbnuu5IpK/qtQi9jFdQppVqaqKIb9pqNesWcPHPvYxZs2aBUA01XIbyqifhtrMwsAK4CySC9k/YWZr3X1Lv0MfdvePFHiuiOQhMnUqEKwWwetf+xrdz+Q2DXXiwAEAQrW1gx5Xc9yxTPvHfywonmzTUD///PPEYjHmz5/P3r17+eIXv8hnPvOZIZ9rLExDfQqw1d1fAjCzO4CFQC4f5sWcKyIDsOpqwpMnq7p4IO4l6RYaTLZpqOPxOE8++SQPPvggXV1dnHbaabznPe9h7ty5Y34a6iOB1zIetwGnZjnuNDP7A7AN+Ad335zHuZjZEmAJ0NesEpGBRaLRQFUX5/qfu7tzYMsWIlOmUDVt2jBHdaiZM2cydepU6uvrqa+v54wzzuAPf/gDc+fOHfPTUGfrZOs/k93vgLe5+4nAt4G78zg3udF9lbu3uHtLY2NjwcGKBEWkSUVlWfX2gntZLh1duHAhDz/8MPF4nP379/P444/nPGnecE5DXYpE0AYclfF4Jsn/+vu4+x5335e6vw6oMrOpuZwrIoWpikaJ7VQi6K/UxWSLFi3itNNO47nnnmPmzJl897vfBZJjBOnLR5ubm+np6eG4445jwYIFvPOd7+SUU07h0ksvPeSy08Gkp6EejsHioqehNrMI8DxwJvAn4AngU6mun/Qx04Ad7u5mdgpwJ/A2IDzUudloGmqRoe288du8sXIlxz79VMUWThUyDXXv3n30vPIy1bNnE66vH6bIyi+faaiL/u1w97iZXQHcR/KD/TZ332xml6X23wxcAPwPM4sDXcCFnsxAWc8tNiYRSc5AijvxN94Y8b7w0czjqapiTS/RpyT/JqS6e9b123Zzxv3vAN/J9VwRKV5mUZkSwUEe04Rz/amyWKRCaZqJAcRjWDiMDfPlo2OJvhMiFSq9drGqiw+VriqWg5QIRCpUeMoUCIdVVNaPx2Kg8YFDKBGIVCgLhYg0aqWy/tQiOJwSgUgFi2ilskO4Ox4bnkXrn332WU477TRqamq44YYbDtkXDocPqSlobW3ti+eaa65h7ty5HHfccdx44405vVZHRwc33XRTyWJXWhSpYFVNUXpefrncYYwe8TgwPFXFkydP5sYbb+Tuu+8+bN+4cePYuHHjYdtXr17Na6+9xrPPPksoFKI9S9JevHgxixcvZv78+X3b0olg6dKlJYldLQKRChZpjBLTGEGf4VyiMhqNcvLJJ1OVx3OvXLmS5cuXE0pdwZTrtNTLli3jxRdfpLm5mSuvvLKgeDOpRSBSwSLRKIndu0kcODDklMtj3cM/fJ43Xts36DHeG8cPdBMa1wWh8JDPOfWoBt7/V3OLjq2rq6tvNlGAq6++mk9+8pO8+OKL/OAHP+Cuu+6isbGRG2+8kTlz5gz5fK2trWzatClrK6MQSgQiFSyzlqBas/Ymp58GsJHtDBmoa6i7u5va2lo2bNjAT37yEz772c/y8MMPc99993HVVVcB8Oqrr/LII4/Q0NBATU1N3yylpaREIFLBIk3BSQS5/Oce27GD+M6d1B5/fElWJ1uxYgW33HILAOvWrWPGjBl5nT9z5kw+/vGPA3D++edzySWXAHD22Wf3rUGQbYyg1DRGIFLBqlRdfIhSLlEJcPnll/etS5xvEgA477zz+MUvfgHAr371K+bOza0bqtRTUqtFIFLB0l1DMSUCIFlMNlw1BK+//jotLS3s2bOHUCjEN7/5TbZs2cKECRMOGyNYsGABra2tLFu2jIsuuohvfOMbNDQ0cOutt+b0WlOmTOH000/nhBNO4JxzzuH6668vKnYlApEKFpowAautJb5DiQCA+PDUEABMmzaNtra2rPt6e3uzbp80aRL33nvvoM870Epla9asySu+wahrSKSCmZmKyjJ4LA4RTS/RnxKBSIWLRDXNBIAnEnhvHKtSR0h/JUkEZrbAzJ4zs61mtizL/ovM7KnU7TdmdmLGvpfN7Gkz22hmWnZMpMSqolFi7ZU7A2muqyz2FZMFYJ6hfFeeLDoRmFkYWAGcA8wDFpnZvH6H/RH4gLu/E/jfwKp++z/o7s3ZllATkeJEok3E23fm/eEwFtTW1rJr166c3ttwVhWPJu7Orl27qM2jgLAUqfEUYKu7vwRgZncAC4EtGYH9JuP4x0guUi8iIyASjeJdXST27SM8fny5wympmTNn0tbWxs6dQ0+jkejqovett4gkEhWfDGpra5k5M/eP2VIkgiOB1zIetwGnDnL854D/ynjswP1m5sC/uXv/1gIAZrYEWAIwq8ILY0RKKbO6uNISQVVVFbNnz87p2Df/4/+y42tfY85vfk1k8uRhjmxsKcUYQbbKjKztNDP7IMlEcFXG5tPd/SSSXUuXm9kZ2c5191Xu3uLuLY2NjcXGLBIYVenq4oCvVBbf2Q5VVYSPOKLcoYw6pUgEbcBRGY9nAtv6H2Rm7wRuBRa6+670dnfflvraDtxFsqtJREpERWVJ8fZ2qhobS1ZVXElKkQieAOaY2WwzqwYuBNZmHmBms4CfAJ929+cztteb2fj0feDDwKYSxCQiKZFUCzroS1bG2tv7kqIcqugxAnePm9kVwH1AGLjN3Teb2WWp/TcDy4EpwE2pbBxPXSHUBNyV2hYB1rj7z4qNSUQOCtXVERo/PvC1BPEd7dT82Z+VO4xRqSQX1Lr7OmBdv203Z9y/FLg0y3kvASf23y4ipRVpimqMoL2d+tNPL3cYo5Iqi0UCoCrg00wkOjtJ7NtHJKoLTbJRIhAJgEhjlNjO4CaC9EB5lcYIslIiEAmASFOqujiRKHcoZZEeKI80NZU5ktFJiUAkACLRKMTj9L71VrlDKYt0t5iuGspOiUAkANJ940EdJ1AiGJwSgUgABH3Jynj7DqyujlB9fblDGZWUCEQCIN03HgvoJaSx9naqolFVFQ9AiUAkACJTpwLBrS6Ot+9Ut9AgKn+FhgwPvPIAG9s3ljuMUcuzzxUoY0CIEB855iMcO/nYrPutqorwlCkB7hpqZ9yJg9euPvDKA/y+/fcjFFHhLph7AW+f+PaSPmegEsHv23/Pj5//cbnDGNXUdB6benp7uPOFO1n5oZW8K/qurMcEtbrY3Ynv2EGkaeAWwe2bb+eGDTdQG64lHAqPYHT5e9+R71MiKMaXTv4SXzr5S+UOQ6TkdnTu4NL7L+ULD3yBFWeu4ORpJx92TFVAi8oSu3fjPT0DFpPd+vStfOt33+LDb/swrWe0UhWq7EVrstEYgUgFaKpv4t8X/Dsz6mew9OdLeXTbo4cdE4lGAzlGEBvg0lF3Z+UfVvKt332Lc2efy3VnXBfIJABKBCIVY+q4qdy24DZmTZjFFQ9ewUNtDx2yPxKN0rtrFx6LlSnC8ojvODwRuDvf/v23uWnjTSw8ZiFfe9/XiIQC1UFyCCUCkQoyuXYy3/3wdzlm0jF88Zdf5Bev/qJvX6QpCu7E33ijjBGOvL5istQltO7O1zd8nVuevoUL5l7AtadfO+rHBYabEoFIhZlUO4lbz76V4yYfx9+v/3vuf/l+4NC1i4MknhoXiTQ24u60/raV27fczqJjF7H8PcsJmT4G9R0QqUATqiew6qxVvKPxHXzpoS9x70v39g2WBm3Jynh7O+GJE6G6imsfu5Y1z67hM/M+w9WnXK2r5FJKkgjMbIGZPWdmW81sWZb9ZmY3pvY/ZWYn5XquiBSmobqBmz90Myc1ncTVD1/Nz/cnr5FP95kHRWxHO+GmKMt/vZw7n7+TS99xKf/Q8g9KAhmKTgRmFgZWAOcA84BFZjav32HnAHNStyXAyjzOFZEC1VXVseLMFZw6/VSu2dSKh0OB6xqKte/gj1W7uefFe1h64lL+5l1/oyTQTymGyU8BtqaWncTM7gAWAlsyjlkI/Ie7O/CYmU0ys+nA0TmcWzJf+c/NbNm2ZzieWmRUS/Bp6qr28fysOn7/eIIDn/nXcoc0Yur9VHbV/JLG2Bmsf7yZ9Y8/Vu6QijJvxgS+/NHjS/qcpUgERwKvZTxuA07N4ZgjczwXADNbQrI1waxZs4qLWCRgQh7hmjdCtB31YdzrqYp1lDukEbNrcpT68F4+uq+Ox8aVO5rRqRSJIFsbq/+kNQMdk8u5yY3uq4BVAC0tLQVNilPqLCoyJiQScO/f4dt/yr9FFnPimUfz3o/PKXdUI+YHX32M+r0zWbz7S/AXb4d3fqLcIY06pRgsbgOOyng8E9iW4zG5nCsihUr0wtor4MnVdL/nKnoTYeon1ZY7qhFVf8Q4Ose/A952Ovzk8/D775U7pFGnFIngCWCOmc02s2rgQmBtv2PWAp9JXT30HmC3u2/P8VwRKURvHO76Amz8Hsz/Rzrf8dcA1E+qKXNgI6t+Ug2de+LwqR/C2+fDPUthw7+XO6xRpehE4O5x4ArgPuAZ4IfuvtnMLjOzy1KHrQNeArYCtwBLBzu32JhEAq83Bj/+HDz9IzjzyzD/Kjp39wBQP7G6zMGNrPqJNXTt7aE3XAuL7oA5Z8NP/xYeX1Xu0EaNkkyu4e7rSH7YZ267OeO+A5fneq6IFCHeDT+6BJ67F87+GpyW/NPr3N0NBLBFMLEaHPbv7mH85Fr45P+DOy+B/7oServhvX9d7hDLTpXFIpUkdgB+8N+TSeDcG/qSAEBnR7JFUBe0FkEq8aUTIZFq+MRqmHce3P+/4OGvly+4USK40+2JVJqe/XDHp+Cl9fDRb8G7Fx+yu7Ojm9r6KiJVwZpgrS8RdHQf3Biugo9/F8LV8OC1ya60D1wFAS00UyIQqQTd++D7F8LLj8DCFfCuiw47pHN3N/WTgtUagOQYARxsEfUJR+D8m5NJYf0/J7vUzlweyGQQrETw62/BlnvKHYVI6e3bCXv+BB+7ZcDr5Ds7uvs+FINkXEMVoZAd7BrKFArDX34nmQwe+Vd4/j6IjPLv0TnXwVGnlPQpg5UIqupg3BHljkKk9OqmJD8gjj13wEM6O7qZcmTDCAY1OljIqJtYzf6OLIkAIBSCj3wTJs6EVx8f2eAKMQwL6AQrEZzy+eRNJGASCWf/np7AXTGUVj+phn0DJQJIdgedceXIBTTK6KohkQDo2tuDe/BqCNLqJ9X01VHI4ZQIRAIgfcVMXQDHCCA5YLw/2xiBAEoEIoGQTgQNRwQ0EUyqpnt/nFhPb7lDGZWUCEQC4OD0EkFNBFlqCaSPEoFIAHR2dGMG48ZXlTuUskgnQHUPZadEIBIAnR3d1E2oJhQO5p/8gEVlAigRiARCsqo4mN1CAPWpsZFBLyENMCUCkQDo7OgJ7BVDANW1YSLVoezVxaJEIBIEQW8RmFnyElK1CLJSIhCpcL2xBAf2xWgI4IRzmVRUNrCiEoGZTTazB8zshdTXwybyMbOjzOyXZvaMmW02sy9m7PsnM/uTmW1M3QaeKEVECpLuDgly1xDkMM1EgBXbIlgGPOjuc4AHU4/7iwN/7+7HAe8BLjezeRn7v+HuzambVioTKbG+GoIAdw1BcnqN/R3dJBdMlEzFJoKFwO2p+7cD5/U/wN23u/vvUvf3klyb+MgiX1dEctRXVRz0RDCphngsQU9XvNyhjDrFJoImd98OyQ98IDrYwWZ2NPAuIHOu1yvM7Ckzuy1b11LGuUvMbIOZbdi5c2eRYYsERzoRBLWqOC3dIlL30OGGTARm9nMz25TltjCfFzKzBuDHwN+6+57U5pXAMUAzsB0YcPFQd1/l7i3u3tLY2JjPS4sEWufubkIRo6Y+WLPO99dXXayissMM+Zvh7h8aaJ+Z7TCz6e6+3cymA+0DHFdFMgl8z91/kvHcOzKOuQX4aT7Bi8jQOncnVyazAC7BmCm9TKdqCQ5XbNfQWuDi1P2LgcPWgbTkb993gWfc/V/77Zue8fB8YFOR8YhIP50d3YEfH4CMaSaUCA5TbCJoBc4ysxeAs1KPMbMZZpa+Auh04NPAX2S5TPRfzOxpM3sK+CDwd0XGIyL9BL2qOC1SHaamLkLnW0oE/RXVaejuu4Azs2zfBpybuv8IkLVN6u6fLub1RWRonbu7mXX85HKHMSqoqCw7VRaLVLCeA3FiB3oDf8VQWv3EanUNZaFEIFLB+i4d1RgBkBwn0OI0h1MiEKlgqio+VP2kGvbv7sETqi7OpEQgUsEOFpMFe8K5tPpJNSQSTte+WLlDGVWUCEQqmLqGDnVwpTJ1D2VSIhCpYJ27u6mqDVNdG+yq4jQtYp+dEoFIBevs6NEVQxlUXZydEoFIBdu/u7vvw09g3IRqMLUI+lMiEKlg+zqCvURlf+FwiHHjq1VU1o8SgUiFcve+CefkoIZJqiXoT4lApEJ1d8ZJxF2JoB9VFx9OiUCkQu3TpaNZ1alFcBglApEKlf6vV4ngUPUTa+jaG6O3N1HuUEYNJQKRCqWq4uzSazPs14BxHyUCkQq1f7fWKs6mLpUY1T10UFGJwMwmm9kDZvZC6mvWxefN7OXUAjQbzWxDvueLSP72dfRQ21BFuEr/72Xqqy7WgHGfYn9DlgEPuvsc4EKCi98AAAs4SURBVMHU44F80N2b3b2lwPNFJA+dHbp0NJsGTTNxmGITwULg9tT924HzRvh8ERmAqoqzq62vIhQ2Ojs0RpBWbCJocvftAKmv0QGOc+B+M3vSzJYUcD5mtsTMNpjZhp07dxYZtkjlU1VxdhYy6lRLcIghpyQ0s58D07LsuiaP1znd3beZWRR4wMyedfeH8jgfd18FrAJoaWnRqhIig0j0JujaownnBqKVyg41ZCJw9w8NtM/MdpjZdHffbmbTgfYBnmNb6mu7md0FnAI8BOR0vojkp2tvDHfVEAykYVINb27vLHcYo0axXUNrgYtT9y8G7ul/gJnVm9n49H3gw8CmXM8Xkfz1FZOphiCrukk1mnguQ7GJoBU4y8xeAM5KPcbMZpjZutQxTcAjZvYH4LfAve7+s8HOF5Hi7HtLVcWDqZ9YTU9XnFh3b7lDGRWKWrbI3XcBZ2bZvg04N3X/JeDEfM4XkeLs1/QSg8qsJZgUrStzNOWnShORCtS5uwcLGePGq2soGy1ZeSglApEKtK+jm7oJ1YRCVu5QRqW+Rex1CSmgRCBSkfZ3dGugeBAHWwQaMAYlApGK1LlbxWSDqa4NE6kJq2soRYlApAJ1dqiYbDBmppXKMigRiFSYeKyXA50xtQiGoOrig5QIRCpMesEVTTg3uHoVlfVRIhCpMAdXJlOLYDD1qbWL3TV1mRKBSIXRovW5qZ9YTW8sQff+eLlDKTslApEKc7BrSIlgMFqp7CAlApEK09nRTTgSoqauqBlkKl6662y/agmUCEQqTWdqZTIzVRUPJt0i2Kcrh5QIRCpNp1Ymy0m68lpdQ0oEIhWnc7eKyXIRqQ5TUxdhv1oESgQilaazo1uJIEf1k2rUNYQSgUhFSS+2oq6h3KioLKmoRGBmk83sATN7IfX1iCzH/LmZbcy47TGzv03t+ycz+1PGvnOLiUck6PqWqFRVcU7qJ1b3LeITZMW2CJYBD7r7HODB1ONDuPtz7t7s7s3Au4H9wF0Zh3wjvd/d1/U/X0Ryp6ri/NRPTLYIPBHs6uJiE8FC4PbU/duB84Y4/kzgRXd/pcjXFZEsOlVMlpf6STV4wtm/N9jdQ8UmgiZ33w6Q+hod4vgLge/323aFmT1lZrdl61pKM7MlZrbBzDbs3LmzuKhFKlS6RVCnRWlykk6Y+wM+TjBkIjCzn5vZpiy3hfm8kJlVA38J/Chj80rgGKAZ2A58faDz3X2Vu7e4e0tjY2M+Ly0SGJ0d3VTXhqmuVVVxLvqWrAz4lUND/ra4+4cG2mdmO8xsurtvN7PpQPsgT3UO8Dt335Hx3H33zewW4Ke5hS0i2WhlsvykB9WDXlRWbNfQWuDi1P2LgXsGOXYR/bqFUskj7XxgU5HxiARaZ0c3dRoozlndhGowTTNRbCJoBc4ysxeAs1KPMbMZZtZ3BZCZ1aX2/6Tf+f9iZk+b2VPAB4G/KzIekUDr7OihQS2CnIXCIerGVwe+uriojkR330XySqD+27cB52Y83g9MyXLcp4t5fRE5yN37JpyT3KmoTJXFIhXjQGeMRK+rayhPmmZCiUCkYqSvfFHXUH5UXaxEIFIxOjtUTFaI+kk1dO2N0RtPlDuUslEiEKkQ6UsgVUyWn76VyvYEd5xAiUCkQmieocL0rV0c4HECJQKRCtHZ0c248VWEI/qzzkdfUZkSgYiMdZ27e3TFUAH6ppkI8ICxEoFIhdDKZIWpra8iFLa+wfYgUiIQqRCdHd00qJgsbxay5LoE6hoSkbEs0Ztg/94e6nTpaEHqJ1Wra0hExrb9e2LgumKoUGoRiMiYd3CtYiWCQtRPUiIQkTFO00sUp35SDT0Heuk5EC93KGWhRCBSAbREZXHqU9+3oC5ZqUQgUgE6d3djIWPceCWCQqQH2YM6YKxEIFIBkjUE1YRCVu5QxqSGgE8zUVQiMLNPmNlmM0uYWcsgxy0ws+fMbKuZLcvYPtnMHjCzF1JfjygmHpGgUlVxcQ4uYq+uoUJsAj4GPDTQAWYWBlaQXLx+HrDIzOaldi8DHnT3OcCDqccikqd0i0AKU1UbJlITDmzXULFLVT4DYDZoc/QUYKu7v5Q69g5gIbAl9XV+6rjbgfXAVcXENJgN6/7I80+0D9fTD869PK8rgdDR3sWMOZPKHcaYZWbUT6zmmd9s59XNu8odzqDmX3RsyX/WRSWCHB0JvJbxuA04NXW/yd23A7j7djOLDvQkZrYEWAIwa9asggKpm1DD5Ol1BZ1bGuq/leExZWYDx75nernDGNPeveBoXtk0upMAJFsvpTZkIjCznwPTsuy6xt3vyeE1sn365f3vsbuvAlYBtLS0FPTv9bz3zWDe+2YUcqqIVLjj3jud494bzGQ6ZCJw9w8V+RptwFEZj2cC21L3d5jZ9FRrYDpQpn4bEZHgGonLR58A5pjZbDOrBi4E1qb2rQUuTt2/GMilhSEiIiVU7OWj55tZG3AacK+Z3ZfaPsPM1gG4exy4ArgPeAb4obtvTj1FK3CWmb0AnJV6LCIiI8h8DF7N0tLS4hs2bCh3GCIiY4qZPenuh9V8qbJYRCTglAhERAJOiUBEJOCUCEREAm5MDhab2U7glQJPnwq8UcJwyknvZfSplPcBei+jVTHv5W3u3th/45hMBMUwsw3ZRs3HIr2X0adS3gfovYxWw/Fe1DUkIhJwSgQiIgEXxESwqtwBlJDey+hTKe8D9F5Gq5K/l8CNEYiIyKGC2CIQEZEMSgQiIgEXmERgZp8ws81mljCzloztR5tZl5ltTN1uLmecQxnofaT2XW1mW83sOTM7u1wxFsLM/snM/pTxczi33DHly8wWpL73W81sTK+/bWYvm9nTqZ/FmJrh0cxuM7N2M9uUsW2ymT1gZi+kvh5RzhhzMcD7GJa/k8AkAmAT8DHgoSz7XnT35tTtshGOK19Z34eZzSO51sPxwALgJjMr/Zp2w+sbGT+HdeUOJh+p7/UK4BxgHrAo9TMZyz6Y+lmMtevvV5P8G8i0DHjQ3ecAD6Yej3arOfx9wDD8nQQmEbj7M+7+XLnjKNYg72MhcIe7d7v7H4GtwCkjG12gnQJsdfeX3L0HuIPkz0RGmLs/BLzZb/NC4PbU/duB80Y0qAIM8D6GRWASwRBmm9nvzexXZvb+cgdToCOB1zIet6W2jSVXmNlTqSbxqG+691MJ3/9MDtxvZk+a2ZJyB1MCTe6+HSD1NVrmeIpR8r+TikoEZvZzM9uU5TbYf2bbgVnu/i7gfwJrzGzCyEScXYHvw7JsG1XXBg/xvlYCxwDNJH8mXy9rsPkb9d//PJ3u7ieR7Oq63MzOKHdAAgzT38mQi9ePJe7+oQLO6Qa6U/efNLMXgblA2QbICnkfJP8DPSrj8UxgW2kiKo1c35eZ3QL8dJjDKbVR//3Ph7tvS31tN7O7SHZ9ZRtfGyt2mNl0d99uZtOB9nIHVAh335G+X8q/k4pqERTCzBrTg6pm9nZgDvBSeaMqyFrgQjOrMbPZJN/Hb8scU85Sf5xp55McFB9LngDmmNlsM6smOXC/tswxFcTM6s1sfPo+8GHG3s+jv7XAxan7FwP3lDGWgg3X30lFtQgGY2bnA98GGoF7zWyju58NnAFca2ZxoBe4zN1HZICmEAO9D3ffbGY/BLYAceByd+8tZ6x5+hczaybZnfIy8IXyhpMfd4+b2RXAfUAYuM3dN5c5rEI1AXeZGSQ/I9a4+8/KG1LuzOz7wHxgqpm1AV8GWoEfmtnngFeBT5QvwtwM8D7mD8ffiaaYEBEJuMB3DYmIBJ0SgYhIwCkRiIgEnBKBiEjAKRGIiAScEoGISMApEYiIBNz/B+JKwOiKylsSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, t, label='t')\n",
    "plt.plot(t, lgt(t, -1E5+t, 4,10), label='-1E5+t')\n",
    "plt.plot(t, lgt(t, 1E5+t, 4,10), label='1E5+t')\n",
    "plt.plot(t, lgt(t, 1E6+t, 4,10), label='1E6+t')\n",
    "plt.plot(t, lgt(t, -1E6+t, 4,10), label='-1E6+t')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At some point, -1E5 has the same meaning as -1E6. As long as constant << min(solution), -1E5 is the same as -1E6. This explains why more negativity doesn't help accurates the converage after -1E5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average of nagative number const: -7741.935483870968\n",
      "average of positive number const: 7741.935483870968\n"
     ]
    }
   ],
   "source": [
    "neg_avg=numpy.average(lgt(t, -10000+t, 4,10))\n",
    "pos_avg=numpy.average(lgt(t, 10000+t, 4,10))\n",
    "print(\"average of nagative number const: {neg_avg}\".format(neg_avg=neg_avg))\n",
    "print(\"average of positive number const: {pos_avg}\".format(pos_avg=pos_avg))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem isn't the way fitness is calculated either. If fitness is the issue here, change ```fitness = 1.0 / numpy.abs(output - desired_output)``` to ```fitness = 1.0 / numpy.abs(output + desired_output)``` should work for positve numbers. However, it doesn't."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```-10000+x``` should work the same as ```10000+x```. Yet, the experimental result showed only negative constant works. Why?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}