Untitled.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import array\n",
    "from deap import base\n",
    "from deap import tools\n",
    "from deap import creator\n",
    "from deap import benchmarks\n",
    "import sympy\n",
    "from sympy.solvers import solve\n",
    "from sympy import Symbol\n",
    "from sympy import Eq\n",
    "from sympy import exp\n",
    "\n",
    "import networkx\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from mpmath import mp\n",
    "import math\n",
    "import numpy as np\n",
    "from itertools import chain\n",
    "\n",
    "##Define constants\n",
    "## number of individuals in the population\n",
    "NP = 30\n",
    "##coefficients from the datasheet of the PV panel\n",
    "IscTempcoeff = 0.059\n",
    "VocTempcoeff = - 0.32\n",
    "PeakPowTempcoeff = - 0.43\n",
    "Voc = 21.7\n",
    "Vmp = 17.4\n",
    "Isc = 3.45\n",
    "Imp = 3.15\n",
    "q = 1.60217646 *(10**(-19)) \n",
    "k = 1.3806503*(10**(-23))\n",
    "Scell = 36\n",
    "T = 298.15\n",
    "Vt = (Scell * k*T)/q\n",
    "x = []\n",
    "lengthy = []\n",
    "##amount of generations\n",
    "max = 100\n",
    "##lower and upper bounds of the variables to solve\n",
    "Xih = [2.0, 1.0 ,3000.0, 10**(-9), Isc]\n",
    "Xil = [1.0, 0.1, 100.0, 10**(-10), 0.000]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start to define the mutation,crossover, penalty and evaluation function from the paper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mutation:\n",
    "![title](Capture4.png)\n",
    "![title](Capture5.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#mutation function\n",
    "def mutateDE(mutant, a, b, c, f):\n",
    "    size = len(mutant)\n",
    "    for k in range(size):\n",
    "        mutant[k] = a[k] + f * (b[k] - c[k])\n",
    "    return mutant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Crossover and penalty function:\n",
    "![title](Capture3.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#crossover based on binomial\n",
    "def cxBinomial(x, mutant, cr):\n",
    "    size = len(x)\n",
    "    index = random.randrange(size)\n",
    "    for i in range(size):\n",
    "        if ((i == index) or (random.random() < cr)):\n",
    "            x[i] = mutant[i]\n",
    "    return x\n",
    "##OPTIONAL CROSSOVER TYPE THAT WAS TESTED\n",
    "def cxExponential(x, y, cr):\n",
    "    size = len(x)\n",
    "    index = random.randrange(size)\n",
    "    # Loop on the indices index -> end, then on 0 -> index\n",
    "    for i in chain(range(index, size), range(0, index)):\n",
    "        x[i] = y[i]\n",
    "        if random.random() < cr:\n",
    "            break\n",
    "    return x\n",
    "\n",
    "#Penalty function to ensure the parameters remain in acceptable range\n",
    "def cxPenalty(x):\n",
    "    z = random.uniform(0.0, 1.0)\n",
    "   \n",
    "    if (x[0] > Xih[0]):\n",
    "        x[0] = x[0] - (z * (Xih[0] - Xil[0]))\n",
    "    if (x[1] > Xih[1]):\n",
    "        x[1] = x[1] - (z * (Xih[1] - Xil[1]))\n",
    "    if (x[2] > Xih[2]):\n",
    "        x[2] = x[2] - (z * (Xih[2] - Xil[2]))\n",
    "    if (x[3] > Xih[3]):\n",
    "        x[3] = x[3] - (z * (Xih[3] - Xil[3]))\n",
    "    if (x[4] > Xih[4]):\n",
    "        x[4] = x[4] - (z * (Xih[4] - Xil[4]))\n",
    "        \n",
    "        \n",
    "    if (x[0] < Xil[0]):\n",
    "        x[0] = x[0] + (z * (Xih[0] - Xil[0]))\n",
    "    if (x[1] < Xil[1]): \n",
    "        x[1] = x[1] + (z * (Xih[1] - Xil[1]))\n",
    "    if (x[2] < Xil[2]):\n",
    "        x[2] = x[2] + (z * (Xih[2] - Xil[2]))\n",
    "    if (x[3] < Xil[3]):\n",
    "        x[3] = x[3] + (z * (Xih[3] - Xil[3]))\n",
    "    if (x[4] < Xil[4]):\n",
    "        x[4] = x[4] + (z * (Xih[4] - Xil[4]))\n",
    "        \n",
    "        \n",
    "    return x\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Objective function:\n",
    "\n",
    "![title](Capture.png)\n",
    "\n",
    "\n",
    "Parameter definitions:\n",
    "\n",
    "![title](Capture2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#evaluation and selection function\n",
    "def eval(a, Rs, Rp, Io):\n",
    "    r = (1 / (a * Vt))\n",
    "    Gp = (1 / Rp)\n",
    "    preex = (r*(Vmp + (Imp * Rs)))\n",
    "    expo = mp.exp(preex)\n",
    "    Jnum1 = (Io) * (r) * expo \n",
    "    Jnum = Jnum1 - (Gp)\n",
    "    Jden = 1 + ((Rs)*(Jnum1)) + (Gp * Rs)\n",
    "    J = -(Jnum / Jden) + (Imp/Vmp)\n",
    "    return abs(J)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Register the defined functions above to the deap framework and setup the statistics to keep track of the population progression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "    generation = 0\n",
    "    # DEAP framework definition\n",
    "    creator.create(\"Fitnessmin\", base.Fitness, weights=(-1.0,))\n",
    "    creator.create(\"Individual\", array.array, typecode='d', fitness=creator.Fitnessmin)\n",
    "    toolbox = base.Toolbox()\n",
    "    toolbox.register(\"attr_a\", random.uniform, 1.0, 2.0)\n",
    "    toolbox.register(\"attr_rs\", random.uniform, 0.1, 1.0)\n",
    "    toolbox.register(\"attr_rp\", random.uniform, 100.0, 3000.0)\n",
    "    toolbox.register(\"attr_io\", random.uniform, 10**(-10),10**(-9))\n",
    "    toolbox.register(\"attr_ipv\", random.uniform, 0.0, Isc)\n",
    "    \n",
    "    toolbox.register(\"individual\", tools.initCycle, creator.Individual,\n",
    "                     (toolbox.attr_a, toolbox.attr_rs, toolbox.attr_rp, toolbox.attr_io, toolbox.attr_ipv), 1)\n",
    "    toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)\n",
    "    toolbox.register(\"mutate\", mutateDE, f=0.4)\n",
    "    toolbox.register(\"select\", tools.selRandom, k=3)\n",
    "    toolbox.register(\"mate\", cxBinomial, cr=0.4)\n",
    "    toolbox.register(\"evaluate\", eval)\n",
    "      \n",
    "    # generate population\n",
    "    pop = toolbox.population(n=NP)\n",
    "    popfuture = pop\n",
    "    ## Hall of fame to save the best individual\n",
    "    hof = tools.HallOfFame(1)\n",
    "    \n",
    "    #Initialize stats\n",
    "    stats_fit = tools.Statistics(lambda agent: agent.fitness.values)\n",
    "    stats_size = tools.Statistics(key=len)\n",
    "    mstats = tools.MultiStatistics(fitness=stats_fit, size=stats_size)\n",
    "    mstats.register(\"avg\", np.mean)\n",
    "    mstats.register(\"std\", np.std)\n",
    "    mstats.register(\"min\", np.min)\n",
    "    mstats.register(\"max\", np.max)\n",
    "    \n",
    "\n",
    "    #store statistics for initial population\n",
    "    for agent in pop:\n",
    "        fit = toolbox.evaluate(agent[0], agent[1], agent[2], agent[3])\n",
    "        agent.fitness.values = fit,\n",
    "    record = mstats.compile(pop)\n",
    "    logbook = tools.Logbook()\n",
    "    logbook.record(gen=0, evals=len(pop), **record)\n",
    "    logbook.header = \"gen\", \"evals\", \"fitness\"\n",
    "    logbook.chapters[\"fitness\"].header = \"min\", \"avg\", \"max\"\n",
    "    generation = generation + 1 \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform the differential evolution algorithm searching for the global minimum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   \t     \t                             fitness                             \n",
      "   \t     \t-----------------------------------------------------------------\n",
      "gen\tevals\tmin                \tavg              \tmax              \n",
      "0  \t30   \t0.0172704397875001 \t0.169364921260548\t0.187557040390997\n",
      "1  \t30   \t0.00170529677728751\t0.165159268197819\t0.185427111726179\n",
      "2  \t30   \t0.00170529677728751\t0.158968035092033\t0.185427111726179\n",
      "3  \t30   \t0.00170529677728751\t0.151931253445565\t0.185427111726179\n",
      "4  \t30   \t0.00170529677728751\t0.132028950579314\t0.181634972495005\n",
      "5  \t30   \t0.00170529677728751\t0.113714595433181\t0.181621596068017\n",
      "6  \t30   \t0.00170529677728751\t0.104445745288955\t0.181359720044154\n",
      "7  \t30   \t0.00170529677728751\t0.0931969662647172\t0.181346515697373\n",
      "8  \t30   \t0.00170529677728751\t0.0790788431076844\t0.181346515697373\n",
      "9  \t30   \t0.000956135276099696\t0.0728687611828068\t0.181346515697373\n",
      "10 \t30   \t0.000183225032812928\t0.0617549620152516\t0.146099513974257\n",
      "11 \t30   \t0.000183225032812928\t0.0558044556142599\t0.146099513974257\n",
      "12 \t30   \t0.000183225032812928\t0.0443481533785904\t0.140810560484169\n",
      "13 \t30   \t0.000183225032812928\t0.0396754788789583\t0.140358661040606\n",
      "14 \t30   \t0.000183225032812928\t0.0270022632974214\t0.103594547575524\n",
      "15 \t30   \t0.000183225032812928\t0.0241805733395757\t0.103594547575524\n",
      "16 \t30   \t0.000183225032812928\t0.0224812787734781\t0.100471903248289\n",
      "17 \t30   \t0.000183225032812928\t0.0195934763281973\t0.100471903248289\n",
      "18 \t30   \t0.000180465989477935\t0.0140691398800005\t0.100448359072589\n",
      "19 \t30   \t0.000180465989477935\t0.0111775145112759\t0.0580295098313373\n",
      "20 \t30   \t0.000180465989477935\t0.00900744482608562\t0.0420010528014196\n",
      "21 \t30   \t0.000180465989477935\t0.00809838840745962\t0.0420010528014196\n",
      "22 \t30   \t0.000180465989477935\t0.00704528398646859\t0.0316249938543262\n",
      "23 \t30   \t0.000180465989477935\t0.00417009100555639\t0.0173383988070946\n",
      "24 \t30   \t0.000180465989477935\t0.0035945343471622 \t0.0115908047297911\n",
      "25 \t30   \t0.000180465989477935\t0.00331769455742496\t0.0115908047297911\n",
      "26 \t30   \t0.000180465989477935\t0.00302756401251677\t0.0115908047297911\n",
      "27 \t30   \t0.000180465989477935\t0.00255304437203728\t0.0115908047297911\n",
      "28 \t30   \t3.981412263801e-5   \t0.00164809795129045\t0.0115908047297911\n",
      "29 \t30   \t9.37479446860845e-6 \t0.00151183785884372\t0.0115908047297911\n",
      "30 \t30   \t9.37479446860845e-6 \t0.00150842185986396\t0.0115908047297911\n",
      "31 \t30   \t3.4201793326083e-6  \t0.0014174605793729 \t0.0115908047297911\n",
      "32 \t30   \t3.4201793326083e-6  \t0.00139315220604605\t0.0115908047297911\n",
      "33 \t30   \t3.4201793326083e-6  \t0.00138825734936535\t0.0115908047297911\n",
      "34 \t30   \t3.4201793326083e-6  \t0.00132619833949623\t0.0115908047297911\n",
      "35 \t30   \t3.4201793326083e-6  \t0.00125314903591146\t0.0115908047297911\n",
      "36 \t30   \t3.4201793326083e-6  \t0.00121586872451489\t0.0110247434428284\n",
      "37 \t30   \t3.4201793326083e-6  \t0.000863776026709804\t0.00406805944695188\n",
      "38 \t30   \t3.4201793326083e-6  \t0.000848843693396954\t0.00406805944695188\n",
      "39 \t30   \t3.4201793326083e-6  \t0.000793806726222708\t0.00406805944695188\n",
      "40 \t30   \t3.4201793326083e-6  \t0.000663373669983117\t0.00406805944695188\n",
      "41 \t30   \t3.4201793326083e-6  \t0.00063822100452232 \t0.00406805944695188\n",
      "42 \t30   \t3.4201793326083e-6  \t0.000605136356226028\t0.00406805944695188\n",
      "43 \t30   \t3.4201793326083e-6  \t0.000605136356226028\t0.00406805944695188\n",
      "44 \t30   \t3.4201793326083e-6  \t0.000561496181326627\t0.00406805944695188\n",
      "45 \t30   \t3.4201793326083e-6  \t0.000561496181326627\t0.00406805944695188\n",
      "46 \t30   \t3.4201793326083e-6  \t0.000533265009346707\t0.00406805944695188\n",
      "47 \t30   \t3.4201793326083e-6  \t0.000530464901075513\t0.00406805944695188\n",
      "48 \t30   \t3.4201793326083e-6  \t0.000479414878788807\t0.00406805944695188\n",
      "49 \t30   \t3.4201793326083e-6  \t0.000402897493508927\t0.00177253788855547\n",
      "50 \t30   \t3.4201793326083e-6  \t0.000402897493508927\t0.00177253788855547\n",
      "51 \t30   \t3.4201793326083e-6  \t0.000379294692779333\t0.00177253788855547\n",
      "52 \t30   \t3.4201793326083e-6  \t0.000303534390184588\t0.00177253788855547\n",
      "53 \t30   \t2.60467226445571e-6 \t0.000255344750065654\t0.0012069099682816 \n",
      "54 \t30   \t2.60467226445571e-6 \t0.000246879002951526\t0.0012069099682816 \n",
      "55 \t30   \t2.60467226445571e-6 \t0.000235035978357628\t0.0012069099682816 \n",
      "56 \t30   \t2.60467226445571e-6 \t0.000235035978357628\t0.0012069099682816 \n",
      "57 \t30   \t2.60467226445571e-6 \t0.000235035978357628\t0.0012069099682816 \n",
      "58 \t30   \t2.60467226445571e-6 \t0.000193464869464853\t0.000675122164235681\n",
      "59 \t30   \t2.60467226445571e-6 \t0.000173233667991503\t0.000543123652798766\n",
      "60 \t30   \t2.60467226445571e-6 \t0.00017313503732166 \t0.000543123652798766\n",
      "61 \t30   \t2.60467226445571e-6 \t0.000164139344590921\t0.000543123652798766\n",
      "62 \t30   \t2.60467226445571e-6 \t0.000161937854851828\t0.000543123652798766\n",
      "63 \t30   \t2.60467226445571e-6 \t0.000161432767397196\t0.000543123652798766\n",
      "64 \t30   \t2.60467226445571e-6 \t0.000157930843015512\t0.000543123652798766\n",
      "65 \t30   \t2.60467226445571e-6 \t0.000157930843015512\t0.000543123652798766\n",
      "66 \t30   \t2.60467226445571e-6 \t0.000157930843015512\t0.000543123652798766\n",
      "67 \t30   \t2.60467226445571e-6 \t0.000157930843015512\t0.000543123652798766\n",
      "68 \t30   \t2.60467226445571e-6 \t0.000156673581290883\t0.000543123652798766\n",
      "69 \t30   \t2.60467226445571e-6 \t0.000151300608676265\t0.000543123652798766\n",
      "70 \t30   \t2.60467226445571e-6 \t0.000130044076273999\t0.000543123652798766\n",
      "71 \t30   \t2.60467226445571e-6 \t0.000121410122061072\t0.000543123652798766\n",
      "72 \t30   \t2.60467226445571e-6 \t0.000111128155745593\t0.000491333445722386\n",
      "73 \t30   \t2.60467226445571e-6 \t0.000104991828833522\t0.000491333445722386\n",
      "74 \t30   \t2.60467226445571e-6 \t0.000100207790186181\t0.000491333445722386\n",
      "75 \t30   \t2.60467226445571e-6 \t0.000100207790186181\t0.000491333445722386\n",
      "76 \t30   \t2.5513657470333e-6  \t9.94520676598193e-5 \t0.000491333445722386\n",
      "77 \t30   \t2.5513657470333e-6  \t9.75124785196457e-5 \t0.000491333445722386\n",
      "78 \t30   \t2.5513657470333e-6  \t9.72175798869666e-5 \t0.000491333445722386\n",
      "79 \t30   \t2.5513657470333e-6  \t9.22869376323114e-5 \t0.000491333445722386\n",
      "80 \t30   \t2.5513657470333e-6  \t9.0434444890299e-5  \t0.000491333445722386\n",
      "81 \t30   \t2.5513657470333e-6  \t8.42790527500877e-5 \t0.000395121526202608\n",
      "82 \t30   \t2.5513657470333e-6  \t8.17658077396403e-5 \t0.000395121526202608\n",
      "83 \t30   \t2.5513657470333e-6  \t7.97125187271143e-5 \t0.000395121526202608\n",
      "84 \t30   \t2.5513657470333e-6  \t6.33268836455943e-5 \t0.000370870505246673\n",
      "85 \t30   \t2.5513657470333e-6  \t6.33268836455943e-5 \t0.000370870505246673\n",
      "86 \t30   \t2.5513657470333e-6  \t6.00288108743741e-5 \t0.000370870505246673\n",
      "87 \t30   \t2.5513657470333e-6  \t6.00288108743741e-5 \t0.000370870505246673\n",
      "88 \t30   \t2.5513657470333e-6  \t6.00288108743741e-5 \t0.000370870505246673\n",
      "89 \t30   \t2.5513657470333e-6  \t5.96600987578031e-5 \t0.000370870505246673\n",
      "90 \t30   \t2.5513657470333e-6  \t5.85705342278485e-5 \t0.000370870505246673\n",
      "91 \t30   \t2.5513657470333e-6  \t5.85705342278485e-5 \t0.000370870505246673\n",
      "92 \t30   \t2.5513657470333e-6  \t5.64167758686581e-5 \t0.000370870505246673\n",
      "93 \t30   \t2.5513657470333e-6  \t5.43373116870092e-5 \t0.000370870505246673\n",
      "94 \t30   \t2.5513657470333e-6  \t5.43373116870092e-5 \t0.000370870505246673\n",
      "95 \t30   \t2.5513657470333e-6  \t4.99428850890225e-5 \t0.000370870505246673\n",
      "96 \t30   \t2.5513657470333e-6  \t4.99428850890225e-5 \t0.000370870505246673\n",
      "97 \t30   \t2.5513657470333e-6  \t3.78156957246967e-5 \t0.000231274331202624\n",
      "98 \t30   \t2.12791976225701e-6 \t3.72758795552671e-5 \t0.000231274331202624\n",
      "99 \t30   \t2.12791976225701e-6 \t3.49854608244438e-5 \t0.000231274331202624\n"
     ]
    }
   ],
   "source": [
    "while (generation < max):\n",
    "        for i, agent in enumerate(pop):\n",
    "            # Mutation\n",
    "            unique_idx = np.random.choice(np.random.permutation(len(pop)), 3)\n",
    "            a,b,c = [toolbox.clone(pop[i]) for i in unique_idx]\n",
    "            mutant1 = toolbox.clone(agent)\n",
    "            mutant = toolbox.clone(agent)\n",
    "            mutant = toolbox.mutate(mutant, a, b, c)\n",
    "            trialvec = toolbox.mate(mutant1, mutant)\n",
    "            trialvec = cxPenalty(trialvec)\n",
    "            trialeval = (toolbox.evaluate(trialvec[0], trialvec[1], trialvec[2], trialvec[3]))\n",
    "            curreval = (toolbox.evaluate(agent[0], agent[1], agent[2], agent[3]))\n",
    "            popfuture[i].fitness.values = curreval, \n",
    "            if ((trialeval < curreval)):\n",
    "                #selection -> trialvector is better than original vector\n",
    "                popfuture[i] = trialvec\n",
    "                popfuture[i].fitness.values = trialeval,\n",
    "        pop = popfuture\n",
    "        hof.update(pop)\n",
    "        record = mstats.compile(pop)\n",
    "        logbook.record(gen=generation, evals=len(pop), **record)\n",
    "        print(logbook.stream)\n",
    "        x.append(logbook.chapters[\"fitness\"].select(\"min\"))\n",
    "        lengthy.append(generation)\n",
    "        generation = generation + 1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fitness = (mpf('2.1279197622570134e-6'),)\n",
      "io = 8.430917433017934e-10\n",
      "Rs = 0.7233506329170805\n",
      "Rp =  1626.5476671092133\n",
      "a = 1.0997366390031305\n",
      "Vt = 0.9249338197129674\n",
      "r = 0.9831066780674615\n",
      "solving start:\n",
      "Imp = 3.22519195294008\n",
      "0.0\n",
      "[3.44846640528024]\n",
      "0.5\n",
      "[3.44815913617697]\n",
      "1.0\n",
      "[3.44785186313308]\n",
      "1.5\n",
      "[3.44754458364825]\n",
      "2.0\n",
      "[3.44723729363573]\n",
      "2.5\n",
      "[3.44692998641572]\n",
      "3.0\n",
      "[3.44662265107016]\n",
      "3.5\n",
      "[3.44631526975347]\n",
      "4.0\n",
      "[3.44600781329717]\n",
      "4.5\n",
      "[3.44570023402549]\n",
      "5.0\n",
      "[3.44539245401271]\n",
      "5.5\n",
      "[3.44508434588980]\n",
      "6.0\n",
      "[3.44477570147338]\n",
      "6.5\n",
      "[3.44446618049072]\n",
      "7.0\n",
      "[3.44415522677335]\n",
      "7.5\n",
      "[3.44384193128213]\n",
      "8.0\n",
      "[3.44352480823938]\n",
      "8.5\n",
      "[3.44320142926311]\n",
      "9.0\n",
      "[3.44286782548272]\n",
      "9.5\n",
      "[3.44251751062448]\n",
      "10.0\n",
      "[3.44213988511763]\n",
      "10.5\n",
      "[3.44171762993232]\n",
      "11.0\n",
      "[3.44122245301223]\n",
      "11.5\n",
      "[3.44060815336010]\n",
      "12.0\n",
      "[3.43979932835394]\n",
      "12.5\n",
      "[3.43867303309209]\n",
      "13.0\n",
      "[3.43702911371599]\n",
      "13.5\n",
      "[3.43454253951406]\n",
      "14.0\n",
      "[3.43068764844912]\n",
      "14.5\n",
      "[3.42461993165282]\n",
      "15.0\n",
      "[3.41499710634452]\n",
      "15.5\n",
      "[3.39972208004318]\n",
      "16.0\n",
      "[3.37560656774756]\n",
      "16.5\n",
      "[3.33800486972359]\n",
      "17.0\n",
      "[3.28057159663885]\n",
      "17.5\n",
      "[3.19543045717880]\n",
      "18.0\n",
      "[3.07406238624290]\n",
      "18.5\n",
      "[2.90890892967051]\n",
      "19.0\n",
      "[2.69508592148116]\n",
      "19.5\n",
      "[2.43130416089387]\n",
      "20.0\n",
      "[2.11958491592609]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "##extract best individual from the hall of fame\n",
    "bestid = hof[0]\n",
    "fit = hof[0].fitness\n",
    "print(\"fitness =\",fit)\n",
    "##extract parameters from individual\n",
    "a = ((bestid[0]))\n",
    "Rs = ((bestid[1]))\n",
    "Rp = ((bestid[2]))\n",
    "io = ((bestid[3]))\n",
    "print(\"io =\",io)\n",
    "print(\"Rs =\",Rs)\n",
    "print(\"Rp = \",Rp)\n",
    "print(\"a =\",a)\n",
    "#print(\"evaluation function =\",toolbox.evaluate(a, Rs, Rp, io))\n",
    "r = (1.0 / (a * Vt)) \n",
    "print(\"Vt =\",Vt)\n",
    "print(\"r =\",r)\n",
    "#Solve to ensure that Imp is retrieved when Vmp is provided\n",
    "print(\"solving start:\")\n",
    "exp1 = (Vmp +(Imp*Rs))*r\n",
    "s1= mp.exp(exp1) -1\n",
    "s1a = io*s1\n",
    "s2 = (Vmp + (Imp*Rs))/(Rp)\n",
    "s3 = Isc - s1a - s2\n",
    "t =[]\n",
    "v = []\n",
    "p = []\n",
    "print(\"Imp =\",s3)\n",
    "for z in range(44):\n",
    "    V = z*0.5\n",
    "    if(z == 43):\n",
    "        print(\"appended\")\n",
    "        v.append(Voc)\n",
    "    else:\n",
    "        v.append(V)\n",
    "    I = sympy.Symbol('I')\n",
    "    eqn = Eq(-I + Isc-io*(exp(r*(V + I * Rs)) - 1)-((V+I*Rs)/Rp),0)\n",
    "    t.append(solve(eqn,I,rational=False,real=True))\n",
    "    print(v[z])\n",
    "    print(t[z])\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(v)\n",
    "print(t)\n",
    "plt.plot(v,t)\n",
    "plt.ylabel(\"Current\")\n",
    "plt.xlabel(\"Voltage\")\n",
    "plt.savefig(\"IV.png\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "gen = logbook.select(\"gen\")\n",
    "fit_mins = logbook.chapters[\"fitness\"].select(\"min\")\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "line1 = ax1.plot(gen, fit_mins, \"b-\", label=\"Minimum Fitness\")\n",
    "ax1.set_xlabel(\"Generation\")\n",
    "ax1.set_ylabel(\"Fitness\", color=\"b\")\n",
    "for tl in ax1.get_yticklabels():\n",
    "    tl.set_color(\"b\")\n",
    "\n",
    "lns = line1\n",
    "labs = [l.get_label() for l in lns]\n",
    "ax1.legend(lns, labs, loc=\"center right\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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