DE/src/DE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Optimization via simple differential evolution\r\n",
    "The classic DE algorithm, shown in Algorithm 2 in our paper, is implemented in our own package [DifferentialEvolution](https://github.com/ShuhuaGao/DifferentialEvolution.jl). In this notebook, we demonstrate how to utilize the classic DE to estimate PV parameters for both SDM and DDM and the two datasets. Specifically, the `StdDE` used below refers to the simplest DE that implements \"DE/rand/1\" mutation and binomial crossover (please check Algorithm 2 in our paper).\r\n",
    "\r\n",
    "We mainly conducted the following tasks\r\n",
    "- Get the parameter values for all four cases obtained by DE in a typical run.\r\n",
    "- Visualize the I-V curve with the parameters obtained above.\r\n",
    "- Analyze the RMSE statistics acquired by DE for each case in 30 independent runs.\r\n",
    "- Measure the running time of DE in each case using a fine-grained benchmark tool called [BenchmarkTools](https://github.com/JuliaCI/BenchmarkTools.jl).\r\n",
    "\r\n",
    "Note that the language Julia uses a just-in-time (JIT) compiler. Thus, the *first* call of a function is generally slower due to precompilation and cannot reflect the true speed. [BenchmarkTools](https://github.com/JuliaCI/BenchmarkTools.jl) handles this situation and gives accurate runtime."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Import required packages and set up the environment"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "using Pkg\r\n",
    "Pkg.status()  # check current environment's status"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\u001b[32m\u001b[1m      Status\u001b[22m\u001b[39m `F:\\github\\rePVest\\Project.toml`\n",
      " \u001b[90m [6e4b80f9] \u001b[39mBenchmarkTools v1.1.4\n",
      " \u001b[90m [336ed68f] \u001b[39mCSV v0.9.1\n",
      " \u001b[90m [8f4d0f93] \u001b[39mConda v1.5.2\n",
      " \u001b[90m [a93c6f00] \u001b[39mDataFrames v1.2.2\n",
      " \u001b[90m [1e3681a4] \u001b[39mDifferentialEvolution v0.1.0 `https://github.com/ShuhuaGao/DifferentialEvolution.jl#bb8de3b`\n",
      " \u001b[90m [7073ff75] \u001b[39mIJulia v1.23.2\n",
      " \u001b[90m [eadc2687] \u001b[39mPandas v1.5.2\n",
      " \u001b[90m [91a5bcdd] \u001b[39mPlots v1.21.3\n",
      " \u001b[90m [d330b81b] \u001b[39mPyPlot v2.10.0\n",
      " \u001b[90m [d2ef9438] \u001b[39mSeaborn v1.0.0\n",
      " \u001b[90m [bd369af6] \u001b[39mTables v1.5.1\n",
      " \u001b[90m [8bb1440f] \u001b[39mDelimitedFiles\n",
      " \u001b[90m [de0858da] \u001b[39mPrintf\n",
      " \u001b[90m [9a3f8284] \u001b[39mRandom\n",
      " \u001b[90m [10745b16] \u001b[39mStatistics\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "using Plots\r\n",
    "using BenchmarkTools\r\n",
    "using Random, Printf\r\n",
    "using CSV, Tables\r\n",
    "using Statistics\r\n",
    "using DifferentialEvolution"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "# seed to reproduce our exact result\r\n",
    "# comment it and each run may generate a slightly different result\r\n",
    "Random.seed!(2);  "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "# directory to store images: change it to your own one\r\n",
    "const img_dir = \"./img\";"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Read data"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "const data_RT = CSV.File(\"data/RTFrance.csv\") |> Tables.matrix;\r\n",
    "const data_PW = CSV.File(\"data/Photowatt25.csv\") |> Tables.matrix\r\n",
    "@show size(data_RT)\r\n",
    "@show size(data_PW);"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "size(data_RT) = (26, 2)\n",
      "size(data_PW) = (25, 2)\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Set temperatures, search ranges, and import related functions"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "const T_RT = 33 + 273.15  # temperature in Kalvin of the RTC France case\r\n",
    "const T_PW = 45 + 273.15;  # temperature in Kalvin of the Photowatt case"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "# see Table 1 in our paper\r\n",
    "const bounds_RT_sdm = Float64[0 1; 0 1; 1 2; 0 0.5; 0 100];\r\n",
    "const bounds_RT_ddm = Float64[0 1; 0 1; 0 1; 1 2; 1 2; 0 0.5; 0 100]; \r\n",
    "const bounds_PW_sdm = Float64[0 2; 0 50; 1 50; 0 2; 0 2000]; \r\n",
    "const bounds_PW_ddm = Float64[0 2; 0 0.01; 0 50; 1 50; 1 50; 0 2; 0 2000];"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "include(\"models.jl\")  # import related functions"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "calculate_mae"
      ]
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Function to obtain the statistics of RMSE for DE\n",
    "Run the DE 30 times, and record the RMSE statistics"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "const ntrials = 30;"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "\"\"\"\r\n",
    "    measure_rmse_stats(model::Function, data, T, bounds, np, F, Cr, G)\r\n",
    "\r\n",
    "Measure the RMSE statistics in multiple runs of DE.\r\n",
    "\r\n",
    "- model: `model_sdm` or `model_ddm`\r\n",
    "- data: PV data\r\n",
    "- T: PV temperature in Kalvin\r\n",
    "- bounds: search range of parameters\r\n",
    "- np, F, Cr, G: DE control parameters\r\n",
    "\"\"\"\r\n",
    "function measure_rmse_stats(model::Function, data, T, bounds, np, F, Cr, G)\r\n",
    "    sse_evaluator(θ) = calculate_sse(data, (V, I) -> model(V, I, θ..., T))\r\n",
    "    records = zeros(ntrials)\r\n",
    "    for i = 1:ntrials\r\n",
    "        de = StdDE(np, bounds, StdOptions(F, Cr); senses=-1)\r\n",
    "        evolve!(de, sse_evaluator, G; stats=[])\r\n",
    "        rmse = sqrt(best_fitness(de) / size(data, 1))\r\n",
    "        records[i] = rmse\r\n",
    "    end\r\n",
    "    return Dict(\r\n",
    "        :min => minimum(records),\r\n",
    "        :mean => mean(records),\r\n",
    "        :max => maximum(records),\r\n",
    "        :std => std(records)\r\n",
    "    )\r\n",
    "end"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "measure_rmse_stats"
      ]
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## SDM results"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "const np = 50  # number of individuals\r\n",
    "const F = 0.6\r\n",
    "const Cr = 0.9\r\n",
    "const G_sdm = 800 # number of generations\r\n",
    "const G_ddm = 2000 # number of generations\r\n",
    ";"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### RTC France"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "# given a parameter vector θ, compute its SSE as the fitness in DE\r\n",
    "evaluator(θ) = calculate_sse(data_RT, (V, I) -> model_sdm(V, I, θ..., T_RT));"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- A typical run"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "# each run is new due to the involved randomness\r\n",
    "de = StdDE(np, bounds_RT_sdm, StdOptions(F, Cr); senses=-1)  # minimization\r\n",
    "evolve!(de, evaluator, G_sdm; stats=[:best, :std])  # show the best fitness and the standard deviation among population's fitness"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "gen  \tbest      \tstd       \t\n",
      "0    \t1.59938e+00\t1.18176e+08\t\n",
      "1    \t1.59938e+00\t1.00928e+07\t\n",
      "2    \t1.59938e+00\t9.07355e+05\t\n",
      "3    \t5.53470e-01\t1.13103e+03\t\n",
      "4    \t5.53470e-01\t2.36992e+02\t\n",
      "5    \t3.08822e-01\t2.30204e+00\t\n",
      "6    \t1.67475e-01\t1.79995e+00\t\n",
      "7    \t1.50249e-01\t6.93925e-01\t\n",
      "8    \t1.61642e-02\t6.56929e-01\t\n",
      "9    \t1.61642e-02\t5.34309e-01\t\n",
      "10   \t1.61642e-02\t3.90601e-01\t\n",
      "11   \t1.61642e-02\t3.27953e-01\t\n",
      "12   \t1.61642e-02\t2.64659e-01\t\n",
      "13   \t6.87398e-03\t2.01966e-01\t\n",
      "14   \t6.87398e-03\t1.84509e-01\t\n",
      "15   \t6.87398e-03\t1.38278e-01\t\n",
      "16   \t6.87398e-03\t1.34176e-01\t\n",
      "17   \t6.87398e-03\t9.30110e-02\t\n",
      "18   \t6.87398e-03\t5.20098e-02\t\n",
      "19   \t6.27491e-03\t5.29589e-02\t\n",
      "20   \t6.27491e-03\t4.13384e-02\t\n",
      "21   \t4.41328e-03\t3.54865e-02\t\n",
      "22   \t4.41328e-03\t3.41310e-02\t\n",
      "23   \t4.41328e-03\t3.29712e-02\t\n",
      "24   \t4.41328e-03\t3.26569e-02\t\n",
      "25   \t4.41328e-03\t2.88623e-02\t\n",
      "26   \t4.41328e-03\t2.86430e-02\t\n",
      "27   \t4.41328e-03\t2.52793e-02\t\n",
      "28   \t4.41328e-03\t2.12367e-02\t\n",
      "29   \t1.07565e-03\t2.11221e-02\t\n",
      "30   \t1.07565e-03\t1.33419e-02\t\n",
      "31   \t1.07565e-03\t1.25308e-02\t\n",
      "32   \t3.82240e-04\t9.24094e-03\t\n",
      "33   \t3.82240e-04\t7.68639e-03\t\n",
      "34   \t3.82240e-04\t5.27738e-03\t\n",
      "35   \t3.82240e-04\t4.57180e-03\t\n",
      "36   \t3.82240e-04\t3.84134e-03\t\n",
      "37   \t3.82240e-04\t3.28480e-03\t\n",
      "38   \t3.29918e-04\t3.14954e-03\t\n",
      "39   \t3.29918e-04\t2.31122e-03\t\n",
      "40   \t3.29918e-04\t1.74014e-03\t\n",
      "41   \t3.29918e-04\t1.48253e-03\t\n",
      "42   \t9.31589e-05\t9.36464e-04\t\n",
      "43   \t6.08082e-05\t8.55712e-04\t\n",
      "44   \t6.08082e-05\t6.29898e-04\t\n",
      "45   \t6.08082e-05\t5.40120e-04\t\n",
      "46   \t6.08082e-05\t3.15716e-04\t\n",
      "47   \t6.08082e-05\t2.55675e-04\t\n",
      "48   \t6.08082e-05\t2.46891e-04\t\n",
      "49   \t6.08082e-05\t2.31417e-04\t\n",
      "50   \t6.08082e-05\t2.39390e-04\t\n",
      "51   \t6.08082e-05\t2.17319e-04\t\n",
      "52   \t6.08082e-05\t1.69544e-04\t\n",
      "53   \t6.08082e-05\t1.30390e-04\t\n",
      "54   \t4.84484e-05\t8.04909e-05\t\n",
      "55   \t4.84484e-05\t8.15996e-05\t\n",
      "56   \t4.84484e-05\t7.62845e-05\t\n",
      "57   \t4.84484e-05\t5.22673e-05\t\n",
      "58   \t4.78930e-05\t4.73426e-05\t\n",
      "59   \t4.78930e-05\t4.16811e-05\t\n",
      "60   \t4.78930e-05\t4.15412e-05\t\n",
      "61   \t4.50322e-05\t3.86602e-05\t\n",
      "62   \t3.65102e-05\t3.52999e-05\t\n",
      "63   \t3.65102e-05\t3.39054e-05\t\n",
      "64   \t3.65102e-05\t2.23040e-05\t\n",
      "65   \t3.65102e-05\t1.68310e-05\t\n",
      "66   \t3.65102e-05\t1.25544e-05\t\n",
      "67   \t3.65102e-05\t1.01708e-05\t\n",
      "68   \t3.65102e-05\t8.57035e-06\t\n",
      "69   \t3.65102e-05\t8.12491e-06\t\n",
      "70   \t3.65102e-05\t8.16239e-06\t\n",
      "71   \t3.65102e-05\t8.00930e-06\t\n",
      "72   \t3.65102e-05\t7.30265e-06\t\n",
      "73   \t3.54396e-05\t4.99181e-06\t\n",
      "74   \t3.54396e-05\t4.98706e-06\t\n",
      "75   \t3.54396e-05\t4.86190e-06\t\n",
      "76   \t3.51341e-05\t4.69899e-06\t\n",
      "77   \t3.51341e-05\t4.40969e-06\t\n",
      "78   \t3.51341e-05\t3.05077e-06\t\n",
      "79   \t3.51341e-05\t2.97990e-06\t\n",
      "80   \t3.51341e-05\t2.90229e-06\t\n",
      "81   \t3.51341e-05\t2.63783e-06\t\n",
      "82   \t3.49796e-05\t2.30460e-06\t\n",
      "83   \t3.37068e-05\t2.06094e-06\t\n",
      "84   \t3.37068e-05\t1.91939e-06\t\n",
      "85   \t3.37068e-05\t1.63763e-06\t\n",
      "86   \t3.34500e-05\t1.56518e-06\t\n",
      "87   \t3.34500e-05\t1.47147e-06\t\n",
      "88   \t3.34500e-05\t1.19300e-06\t\n",
      "89   \t3.29508e-05\t1.11062e-06\t\n",
      "90   \t3.26426e-05\t1.00168e-06\t\n",
      "91   \t3.16217e-05\t1.07715e-06\t\n",
      "92   \t3.16217e-05\t9.73237e-07\t\n",
      "93   \t3.16217e-05\t8.35119e-07\t\n",
      "94   \t3.16217e-05\t8.58168e-07\t\n",
      "95   \t3.16217e-05\t8.56131e-07\t\n",
      "96   \t3.16217e-05\t7.62363e-07\t\n",
      "97   \t3.13560e-05\t7.31964e-07\t\n",
      "98   \t3.12151e-05\t6.54460e-07\t\n",
      "99   \t3.03752e-05\t7.13946e-07\t\n",
      "100  \t3.03752e-05\t6.58835e-07\t\n",
      "101  \t3.03643e-05\t6.63233e-07\t\n",
      "102  \t3.03265e-05\t6.32264e-07\t\n",
      "103  \t3.03265e-05\t5.79792e-07\t\n",
      "104  \t2.99759e-05\t5.25892e-07\t\n",
      "105  \t2.96365e-05\t5.35896e-07\t\n",
      "106  \t2.93499e-05\t5.63567e-07\t\n",
      "107  \t2.93499e-05\t5.04676e-07\t\n",
      "108  \t2.92761e-05\t5.22736e-07\t\n",
      "109  \t2.92761e-05\t5.06606e-07\t\n",
      "110  \t2.91077e-05\t4.10030e-07\t\n",
      "111  \t2.91077e-05\t4.07571e-07\t\n",
      "112  \t2.88638e-05\t3.36508e-07\t\n",
      "113  \t2.83947e-05\t2.85143e-07\t\n",
      "114  \t2.83947e-05\t2.97779e-07\t\n",
      "115  \t2.83947e-05\t3.04488e-07\t\n",
      "116  \t2.83947e-05\t2.92146e-07\t\n",
      "117  \t2.77954e-05\t3.70331e-07\t\n",
      "118  \t2.77954e-05\t4.04447e-07\t\n",
      "119  \t2.77954e-05\t3.93316e-07\t\n",
      "120  \t2.77954e-05\t3.87681e-07\t\n",
      "121  \t2.77954e-05\t3.93927e-07\t\n",
      "122  \t2.76139e-05\t3.87604e-07\t\n",
      "123  \t2.76139e-05\t3.49222e-07\t\n",
      "124  \t2.76139e-05\t3.18638e-07\t\n",
      "125  \t2.76139e-05\t2.32490e-07\t\n",
      "126  \t2.74623e-05\t2.26526e-07\t\n",
      "127  \t2.73914e-05\t2.25817e-07\t\n",
      "128  \t2.73914e-05\t2.29523e-07\t\n",
      "129  \t2.72871e-05\t1.78636e-07\t\n",
      "130  \t2.71818e-05\t1.55862e-07\t\n",
      "131  \t2.71499e-05\t1.55992e-07\t\n",
      "132  \t2.71499e-05\t1.42414e-07\t\n",
      "133  \t2.70217e-05\t1.50230e-07\t\n",
      "134  \t2.70098e-05\t1.53725e-07\t\n",
      "135  \t2.70098e-05\t1.52414e-07\t\n",
      "136  \t2.70098e-05\t1.36270e-07\t\n",
      "137  \t2.69976e-05\t1.41635e-07\t\n",
      "138  \t2.68070e-05\t1.30864e-07\t\n",
      "139  \t2.68070e-05\t1.35727e-07\t\n",
      "140  \t2.68070e-05\t1.18874e-07\t\n",
      "141  \t2.66773e-05\t1.32862e-07\t\n",
      "142  \t2.66773e-05\t1.20363e-07\t\n",
      "143  \t2.66507e-05\t1.11966e-07\t\n",
      "144  \t2.66398e-05\t1.11727e-07\t\n",
      "145  \t2.66304e-05\t1.19833e-07\t\n",
      "146  \t2.65924e-05\t1.32183e-07\t\n",
      "147  \t2.65924e-05\t1.14684e-07\t\n",
      "148  \t2.65484e-05\t1.02497e-07\t\n",
      "149  \t2.64331e-05\t1.02059e-07\t\n",
      "150  \t2.64331e-05\t9.51836e-08\t\n",
      "151  \t2.64182e-05\t7.76785e-08\t\n",
      "152  \t2.64032e-05\t7.94856e-08\t\n",
      "153  \t2.63094e-05\t8.83564e-08\t\n",
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      "710  \t2.52782e-05\t2.21584e-18\t\n",
      "711  \t2.52782e-05\t2.21584e-18\t\n",
      "712  \t2.52782e-05\t2.21584e-18\t\n",
      "713  \t2.52782e-05\t2.21584e-18\t\n",
      "714  \t2.52782e-05\t2.21584e-18\t\n",
      "715  \t2.52782e-05\t2.21584e-18\t\n",
      "716  \t2.52782e-05\t2.21584e-18\t\n",
      "717  \t2.52782e-05\t2.24449e-18\t\n",
      "718  \t2.52782e-05\t2.24449e-18\t\n",
      "719  \t2.52782e-05\t2.24449e-18\t\n",
      "720  \t2.52782e-05\t2.24449e-18\t\n",
      "721  \t2.52782e-05\t2.24449e-18\t\n",
      "722  \t2.52782e-05\t2.24449e-18\t\n",
      "723  \t2.52782e-05\t2.24449e-18\t\n",
      "724  \t2.52782e-05\t2.24449e-18\t\n",
      "725  \t2.52782e-05\t2.24449e-18\t\n",
      "726  \t2.52782e-05\t2.21976e-18\t\n",
      "727  \t2.52782e-05\t2.21976e-18\t\n",
      "728  \t2.52782e-05\t2.21976e-18\t\n",
      "729  \t2.52782e-05\t2.21976e-18\t\n",
      "730  \t2.52782e-05\t2.21976e-18\t\n",
      "731  \t2.52782e-05\t2.21976e-18\t\n",
      "732  \t2.52782e-05\t2.20632e-18\t\n",
      "733  \t2.52782e-05\t2.20632e-18\t\n",
      "734  \t2.52782e-05\t2.20632e-18\t\n",
      "735  \t2.52782e-05\t2.20632e-18\t\n",
      "736  \t2.52782e-05\t2.20632e-18\t\n",
      "737  \t2.52782e-05\t2.20632e-18\t\n",
      "738  \t2.52782e-05\t2.20632e-18\t\n",
      "739  \t2.52782e-05\t2.20632e-18\t\n",
      "740  \t2.52782e-05\t2.20632e-18\t\n",
      "741  \t2.52782e-05\t2.20632e-18\t\n",
      "742  \t2.52782e-05\t2.20632e-18\t\n",
      "743  \t2.52782e-05\t2.20632e-18\t\n",
      "744  \t2.52782e-05\t2.20632e-18\t\n",
      "745  \t2.52782e-05\t2.20632e-18\t\n",
      "746  \t2.52782e-05\t2.20632e-18\t\n",
      "747  \t2.52782e-05\t2.20632e-18\t\n",
      "748  \t2.52782e-05\t2.20632e-18\t\n",
      "749  \t2.52782e-05\t2.18112e-18\t\n",
      "750  \t2.52782e-05\t2.18112e-18\t\n",
      "751  \t2.52782e-05\t2.18112e-18\t\n",
      "752  \t2.52782e-05\t2.18112e-18\t\n",
      "753  \t2.52782e-05\t2.18112e-18\t\n",
      "754  \t2.52782e-05\t2.18112e-18\t\n",
      "755  \t2.52782e-05\t2.18112e-18\t\n",
      "756  \t2.52782e-05\t2.18112e-18\t\n",
      "757  \t2.52782e-05\t2.18112e-18\t\n",
      "758  \t2.52782e-05\t2.18112e-18\t\n",
      "759  \t2.52782e-05\t2.18112e-18\t\n",
      "760  \t2.52782e-05\t2.18112e-18\t\n",
      "761  \t2.52782e-05\t2.18112e-18\t\n",
      "762  \t2.52782e-05\t2.18112e-18\t\n",
      "763  \t2.52782e-05\t2.18112e-18\t\n",
      "764  \t2.52782e-05\t2.18112e-18\t\n",
      "765  \t2.52782e-05\t2.18112e-18\t\n",
      "766  \t2.52782e-05\t2.18112e-18\t\n",
      "767  \t2.52782e-05\t2.18112e-18\t\n",
      "768  \t2.52782e-05\t2.18112e-18\t\n",
      "769  \t2.52782e-05\t2.18112e-18\t\n",
      "770  \t2.52782e-05\t2.18122e-18\t\n",
      "771  \t2.52782e-05\t2.18122e-18\t\n",
      "772  \t2.52782e-05\t2.18122e-18\t\n",
      "773  \t2.52782e-05\t2.18122e-18\t\n",
      "774  \t2.52782e-05\t2.19074e-18\t\n",
      "775  \t2.52782e-05\t2.19074e-18\t\n",
      "776  \t2.52782e-05\t2.19074e-18\t\n",
      "777  \t2.52782e-05\t2.19074e-18\t\n",
      "778  \t2.52782e-05\t2.19074e-18\t\n",
      "779  \t2.52782e-05\t2.19074e-18\t\n",
      "780  \t2.52782e-05\t2.19074e-18\t\n",
      "781  \t2.52782e-05\t2.19074e-18\t\n",
      "782  \t2.52782e-05\t2.19074e-18\t\n",
      "783  \t2.52782e-05\t2.22044e-18\t\n",
      "784  \t2.52782e-05\t2.40233e-18\t\n",
      "785  \t2.52782e-05\t2.40233e-18\t\n",
      "786  \t2.52782e-05\t2.27026e-18\t\n",
      "787  \t2.52782e-05\t2.27026e-18\t\n",
      "788  \t2.52782e-05\t2.27026e-18\t\n",
      "789  \t2.52782e-05\t2.25483e-18\t\n",
      "790  \t2.52782e-05\t2.25483e-18\t\n",
      "791  \t2.52782e-05\t2.25483e-18\t\n",
      "792  \t2.52782e-05\t2.25483e-18\t\n",
      "793  \t2.52782e-05\t2.25483e-18\t\n",
      "794  \t2.52782e-05\t2.25483e-18\t\n",
      "795  \t2.52782e-05\t2.25483e-18\t\n",
      "796  \t2.52782e-05\t2.25483e-18\t\n",
      "797  \t2.52782e-05\t2.25483e-18\t\n",
      "798  \t2.52782e-05\t2.25469e-18\t\n",
      "799  \t2.52782e-05\t2.25469e-18\t\n",
      "800  \t2.52782e-05\t2.25469e-18\t\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0×0 Matrix{Float64}"
      ]
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "# note that the fitness refers to the SSE\r\n",
    "best_sse = best_fitness(de)\r\n",
    "best_rmse = sqrt(best_sse / size(data_RT, 1))\r\n",
    "@printf(\"Min RMSE (SDM + RTC France) = %.5e\", best_rmse)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Min RMSE (SDM + RTC France) = 9.86022e-04"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "println(\"Best parameter values (SDM + RTC France):\")\r\n",
    "best = best_individual(de)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Best parameter values (SDM + RTC France):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "5-element Vector{Float64}:\n",
       "  0.7607755305161579\n",
       "  0.3230208275156398\n",
       "  1.4811835955308978\n",
       "  0.036377092252018\n",
       " 53.71852336772324"
      ]
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "# error of estimation \r\n",
    "xstar = [0.760779120136, 0.322873926858, 1.48113747635, 0.0363792207867, 0.537009537057e2]\r\n",
    "δ = abs.(best .- xstar)\r\n",
    "δr = δ ./ xstar\r\n",
    "println(\"SDM + RT, error of estimation \")\r\n",
    "@show  δ δr;\r\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "SDM + RT, error of estimation \n",
      "δ = [3.5896198421481174e-6, 0.00014690065763983684, 4.6119180897807865e-5, 2.1285346819971407e-6, 0.017569662023241506]\n",
      "δr = [4.718346951354846e-6, 0.00045497838450251753, 3.113767738256167e-5, 5.85096281879495e-5, 0.0003271759775353227]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "## MBE and MAE\r\n",
    "mbe = calculate_mbe(data_RT, (V, I) -> model_sdm(V, I, best..., T_RT))\r\n",
    "mae = calculate_mae(data_RT, (V, I) -> model_sdm(V, I, best..., T_RT))\r\n",
    "@show mbe mae;"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "mbe = -1.1318042890449217e-10\n",
      "mae = 0.0008279564593450104\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Visualization"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "source": [
    "I_RT_SDM = [model_sdm(V, I, best..., T_RT) for (V, I) in eachrow(data_RT)];"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "source": [
    "p_RT = plot(size=(400, 300), labelfontsize=10)\r\n",
    "plot!(p_RT, data_RT[:, 1], data_RT[:, 2]; st=:scatter, label=\"Measurement\");\r\n",
    "plot!(p_RT, data_RT[:, 1], I_RT_SDM; label=\"SDM\");"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- RMSE statistics"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "source": [
    "println(\"RMSE statistics in $ntrials runs (SDM + RTC France):\")\r\n",
    "measure_rmse_stats(model_sdm, data_RT, T_RT, bounds_RT_sdm, np, F, Cr, G_sdm)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "RMSE statistics in 30 runs (SDM + RTC France):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Dict{Symbol, Float64} with 4 entries:\n",
       "  :max  => 0.000986022\n",
       "  :std  => 2.94647e-17\n",
       "  :mean => 0.000986022\n",
       "  :min  => 0.000986022"
      ]
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Measure average runtime"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "source": [
    "println(\"Measure the running time (SDM + RTC France):\")\r\n",
    "@benchmark begin\r\n",
    "    de = StdDE(np, bounds_RT_sdm, StdOptions(F, Cr); senses=-1)\r\n",
    "    evolve!(de, evaluator, G_sdm; stats=[])\r\n",
    "end evals=1 samples=ntrials seconds=1000"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Measure the running time (SDM + RTC France):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 30 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m262.998 ms\u001b[22m\u001b[39m … \u001b[35m373.785 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m6.06% … 4.41%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m269.467 ms               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m5.98%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m285.136 ms\u001b[22m\u001b[39m ± \u001b[32m 31.399 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m5.84% ± 0.63%\n",
       "\n",
       "  \u001b[39m \u001b[39m \u001b[39m█\u001b[34m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m▆\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[32m▁\u001b[39m\u001b[39m▄\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m \u001b[39m▁\n",
       "  263 ms\u001b[90m           Histogram: frequency by time\u001b[39m          374 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m176.55 MiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m10472561\u001b[39m."
      ]
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Photowatt-PWP201"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "# given a parameter vector θ, compute its SSE as the fitness in DE\r\n",
    "# note that the temperature of the two datasets are different\r\n",
    "evaluator(θ) = calculate_sse(data_PW, (V, I) -> model_sdm(V, I, θ..., T_PW));"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- A typical run"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "source": [
    "# each run is new due to the involved randomness\r\n",
    "de = StdDE(np, bounds_PW_sdm, StdOptions(F, Cr); senses=-1)  # minimization\r\n",
    "evolve!(de, evaluator, G_sdm; stats=[:best, :std])"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "gen  \tbest      \tstd       \t\n",
      "0    \t2.07173e+02\tNaN       \t\n",
      "1    \t1.62832e+02\t8.77006e+26\t\n",
      "2    \t1.72391e+01\t7.64672e+26\t\n",
      "3    \t3.35293e-01\t5.17729e+06\t\n",
      "4    \t3.35293e-01\t2.88122e+04\t\n",
      "5    \t1.57794e-01\t9.44184e+03\t\n",
      "6    \t1.57794e-01\t1.80368e+02\t\n",
      "7    \t1.57794e-01\t1.13832e+02\t\n",
      "8    \t1.57794e-01\t7.43302e+01\t\n",
      "9    \t1.57794e-01\t2.96582e+01\t\n",
      "10   \t1.57794e-01\t1.42234e+01\t\n",
      "11   \t1.57794e-01\t6.93439e+00\t\n",
      "12   \t1.57794e-01\t2.54161e+00\t\n",
      "13   \t1.03621e-01\t2.24064e+00\t\n",
      "14   \t1.03621e-01\t1.55578e+00\t\n",
      "15   \t2.05777e-02\t1.01976e+00\t\n",
      "16   \t2.05777e-02\t7.69216e-01\t\n",
      "17   \t2.05777e-02\t5.74791e-01\t\n",
      "18   \t1.61285e-02\t5.52495e-01\t\n",
      "19   \t9.98181e-03\t2.89836e-01\t\n",
      "20   \t9.98181e-03\t2.04418e-01\t\n",
      "21   \t9.98181e-03\t2.05561e-01\t\n",
      "22   \t9.98181e-03\t6.23114e-02\t\n",
      "23   \t9.98181e-03\t5.67783e-02\t\n",
      "24   \t5.16940e-03\t4.33265e-02\t\n",
      "25   \t5.16940e-03\t4.05674e-02\t\n",
      "26   \t5.16940e-03\t3.39112e-02\t\n",
      "27   \t5.16940e-03\t2.78027e-02\t\n",
      "28   \t2.32141e-03\t2.74344e-02\t\n",
      "29   \t2.32141e-03\t2.21848e-02\t\n",
      "30   \t2.32141e-03\t2.01905e-02\t\n",
      "31   \t6.76745e-04\t1.93330e-02\t\n",
      "32   \t6.76745e-04\t1.93414e-02\t\n",
      "33   \t6.76745e-04\t1.84405e-02\t\n",
      "34   \t6.76745e-04\t1.62239e-02\t\n",
      "35   \t6.76745e-04\t1.62153e-02\t\n",
      "36   \t6.76745e-04\t1.35264e-02\t\n",
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      "592  \t1.47025e-04\t4.99626e-18\t\n",
      "593  \t1.47025e-04\t4.99626e-18\t\n",
      "594  \t1.47025e-04\t5.00724e-18\t\n",
      "595  \t1.47025e-04\t5.00724e-18\t\n",
      "596  \t1.47025e-04\t5.00724e-18\t\n",
      "597  \t1.47025e-04\t5.00724e-18\t\n",
      "598  \t1.47025e-04\t5.00724e-18\t\n",
      "599  \t1.47025e-04\t5.00724e-18\t\n",
      "600  \t1.47025e-04\t5.00724e-18\t\n",
      "601  \t1.47025e-04\t5.00724e-18\t\n",
      "602  \t1.47025e-04\t5.00724e-18\t\n",
      "603  \t1.47025e-04\t5.00724e-18\t\n",
      "604  \t1.47025e-04\t5.00724e-18\t\n",
      "605  \t1.47025e-04\t5.00724e-18\t\n",
      "606  \t1.47025e-04\t5.10519e-18\t\n",
      "607  \t1.47025e-04\t5.01160e-18\t\n",
      "608  \t1.47025e-04\t5.01160e-18\t\n",
      "609  \t1.47025e-04\t5.01160e-18\t\n",
      "610  \t1.47025e-04\t5.01160e-18\t\n",
      "611  \t1.47025e-04\t5.01160e-18\t\n",
      "612  \t1.47025e-04\t5.01160e-18\t\n",
      "613  \t1.47025e-04\t5.01160e-18\t\n",
      "614  \t1.47025e-04\t5.01160e-18\t\n",
      "615  \t1.47025e-04\t5.01160e-18\t\n",
      "616  \t1.47025e-04\t5.01160e-18\t\n",
      "617  \t1.47025e-04\t5.01160e-18\t\n",
      "618  \t1.47025e-04\t5.01160e-18\t\n",
      "619  \t1.47025e-04\t5.01160e-18\t\n",
      "620  \t1.47025e-04\t5.01160e-18\t\n",
      "621  \t1.47025e-04\t5.01160e-18\t\n",
      "622  \t1.47025e-04\t5.01160e-18\t\n",
      "623  \t1.47025e-04\t5.01160e-18\t\n",
      "624  \t1.47025e-04\t5.01160e-18\t\n",
      "625  \t1.47025e-04\t5.01160e-18\t\n",
      "626  \t1.47025e-04\t5.01160e-18\t\n",
      "627  \t1.47025e-04\t5.01160e-18\t\n",
      "628  \t1.47025e-04\t5.01160e-18\t\n",
      "629  \t1.47025e-04\t5.01160e-18\t\n",
      "630  \t1.47025e-04\t5.01160e-18\t\n",
      "631  \t1.47025e-04\t5.01160e-18\t\n",
      "632  \t1.47025e-04\t4.99890e-18\t\n",
      "633  \t1.47025e-04\t4.99890e-18\t\n",
      "634  \t1.47025e-04\t4.99890e-18\t\n",
      "635  \t1.47025e-04\t4.99890e-18\t\n",
      "636  \t1.47025e-04\t5.14670e-18\t\n",
      "637  \t1.47025e-04\t5.14449e-18\t\n",
      "638  \t1.47025e-04\t5.14449e-18\t\n",
      "639  \t1.47025e-04\t5.14449e-18\t\n",
      "640  \t1.47025e-04\t5.14449e-18\t\n",
      "641  \t1.47025e-04\t5.14449e-18\t\n",
      "642  \t1.47025e-04\t5.14449e-18\t\n",
      "643  \t1.47025e-04\t5.14449e-18\t\n",
      "644  \t1.47025e-04\t5.14449e-18\t\n",
      "645  \t1.47025e-04\t5.02345e-18\t\n",
      "646  \t1.47025e-04\t5.02345e-18\t\n",
      "647  \t1.47025e-04\t5.02345e-18\t\n",
      "648  \t1.47025e-04\t5.02345e-18\t\n",
      "649  \t1.47025e-04\t5.02345e-18\t\n",
      "650  \t1.47025e-04\t5.01887e-18\t\n",
      "651  \t1.47025e-04\t5.01887e-18\t\n",
      "652  \t1.47025e-04\t5.01887e-18\t\n",
      "653  \t1.47025e-04\t5.03839e-18\t\n",
      "654  \t1.47025e-04\t5.03839e-18\t\n",
      "655  \t1.47025e-04\t5.03839e-18\t\n",
      "656  \t1.47025e-04\t5.03839e-18\t\n",
      "657  \t1.47025e-04\t5.03839e-18\t\n",
      "658  \t1.47025e-04\t5.03839e-18\t\n",
      "659  \t1.47025e-04\t4.98784e-18\t\n",
      "660  \t1.47025e-04\t4.98784e-18\t\n",
      "661  \t1.47025e-04\t4.98784e-18\t\n",
      "662  \t1.47025e-04\t4.98784e-18\t\n",
      "663  \t1.47025e-04\t4.98784e-18\t\n",
      "664  \t1.47025e-04\t4.93818e-18\t\n",
      "665  \t1.47025e-04\t4.93818e-18\t\n",
      "666  \t1.47025e-04\t4.83210e-18\t\n",
      "667  \t1.47025e-04\t4.78685e-18\t\n",
      "668  \t1.47025e-04\t4.78685e-18\t\n",
      "669  \t1.47025e-04\t4.78685e-18\t\n",
      "670  \t1.47025e-04\t4.78685e-18\t\n",
      "671  \t1.47025e-04\t4.78685e-18\t\n",
      "672  \t1.47025e-04\t4.76532e-18\t\n",
      "673  \t1.47025e-04\t4.76532e-18\t\n",
      "674  \t1.47025e-04\t4.75973e-18\t\n",
      "675  \t1.47025e-04\t4.75879e-18\t\n",
      "676  \t1.47025e-04\t4.67108e-18\t\n",
      "677  \t1.47025e-04\t4.58256e-18\t\n",
      "678  \t1.47025e-04\t4.72396e-18\t\n",
      "679  \t1.47025e-04\t4.58103e-18\t\n",
      "680  \t1.47025e-04\t4.58103e-18\t\n",
      "681  \t1.47025e-04\t4.58103e-18\t\n",
      "682  \t1.47025e-04\t4.58103e-18\t\n",
      "683  \t1.47025e-04\t4.58103e-18\t\n",
      "684  \t1.47025e-04\t4.58103e-18\t\n",
      "685  \t1.47025e-04\t4.58103e-18\t\n",
      "686  \t1.47025e-04\t4.58103e-18\t\n",
      "687  \t1.47025e-04\t4.58103e-18\t\n",
      "688  \t1.47025e-04\t4.53276e-18\t\n",
      "689  \t1.47025e-04\t4.53334e-18\t\n",
      "690  \t1.47025e-04\t4.53334e-18\t\n",
      "691  \t1.47025e-04\t4.45146e-18\t\n",
      "692  \t1.47025e-04\t4.45146e-18\t\n",
      "693  \t1.47025e-04\t4.45146e-18\t\n",
      "694  \t1.47025e-04\t4.39292e-18\t\n",
      "695  \t1.47025e-04\t4.42629e-18\t\n",
      "696  \t1.47025e-04\t4.42629e-18\t\n",
      "697  \t1.47025e-04\t4.41521e-18\t\n",
      "698  \t1.47025e-04\t4.41521e-18\t\n",
      "699  \t1.47025e-04\t4.30634e-18\t\n",
      "700  \t1.47025e-04\t4.30634e-18\t\n",
      "701  \t1.47025e-04\t4.30634e-18\t\n",
      "702  \t1.47025e-04\t4.30400e-18\t\n",
      "703  \t1.47025e-04\t4.30400e-18\t\n",
      "704  \t1.47025e-04\t4.24947e-18\t\n",
      "705  \t1.47025e-04\t4.24947e-18\t\n",
      "706  \t1.47025e-04\t4.28183e-18\t\n",
      "707  \t1.47025e-04\t4.28183e-18\t\n",
      "708  \t1.47025e-04\t4.28183e-18\t\n",
      "709  \t1.47025e-04\t4.28183e-18\t\n",
      "710  \t1.47025e-04\t4.28183e-18\t\n",
      "711  \t1.47025e-04\t4.28183e-18\t\n",
      "712  \t1.47025e-04\t4.28183e-18\t\n",
      "713  \t1.47025e-04\t4.31512e-18\t\n",
      "714  \t1.47025e-04\t4.28311e-18\t\n",
      "715  \t1.47025e-04\t4.28311e-18\t\n",
      "716  \t1.47025e-04\t4.28276e-18\t\n",
      "717  \t1.47025e-04\t4.28276e-18\t\n",
      "718  \t1.47025e-04\t4.28276e-18\t\n",
      "719  \t1.47025e-04\t4.28276e-18\t\n",
      "720  \t1.47025e-04\t4.28276e-18\t\n",
      "721  \t1.47025e-04\t4.07164e-18\t\n",
      "722  \t1.47025e-04\t4.07164e-18\t\n",
      "723  \t1.47025e-04\t4.07164e-18\t\n",
      "724  \t1.47025e-04\t3.90548e-18\t\n",
      "725  \t1.47025e-04\t3.90548e-18\t\n",
      "726  \t1.47025e-04\t3.90548e-18\t\n",
      "727  \t1.47025e-04\t3.90548e-18\t\n",
      "728  \t1.47025e-04\t3.85313e-18\t\n",
      "729  \t1.47025e-04\t3.87669e-18\t\n",
      "730  \t1.47025e-04\t3.87669e-18\t\n",
      "731  \t1.47025e-04\t3.87669e-18\t\n",
      "732  \t1.47025e-04\t3.87669e-18\t\n",
      "733  \t1.47025e-04\t3.87669e-18\t\n",
      "734  \t1.47025e-04\t3.87669e-18\t\n",
      "735  \t1.47025e-04\t3.85856e-18\t\n",
      "736  \t1.47025e-04\t3.85856e-18\t\n",
      "737  \t1.47025e-04\t3.85856e-18\t\n",
      "738  \t1.47025e-04\t3.85856e-18\t\n",
      "739  \t1.47025e-04\t3.85856e-18\t\n",
      "740  \t1.47025e-04\t3.85856e-18\t\n",
      "741  \t1.47025e-04\t3.85856e-18\t\n",
      "742  \t1.47025e-04\t3.85856e-18\t\n",
      "743  \t1.47025e-04\t3.85856e-18\t\n",
      "744  \t1.47025e-04\t3.87412e-18\t\n",
      "745  \t1.47025e-04\t3.84878e-18\t\n",
      "746  \t1.47025e-04\t3.80435e-18\t\n",
      "747  \t1.47025e-04\t3.80435e-18\t\n",
      "748  \t1.47025e-04\t3.78118e-18\t\n",
      "749  \t1.47025e-04\t3.84163e-18\t\n",
      "750  \t1.47025e-04\t3.84163e-18\t\n",
      "751  \t1.47025e-04\t3.84163e-18\t\n",
      "752  \t1.47025e-04\t3.81813e-18\t\n",
      "753  \t1.47025e-04\t3.65437e-18\t\n",
      "754  \t1.47025e-04\t3.65437e-18\t\n",
      "755  \t1.47025e-04\t3.65437e-18\t\n",
      "756  \t1.47025e-04\t3.65437e-18\t\n",
      "757  \t1.47025e-04\t3.65437e-18\t\n",
      "758  \t1.47025e-04\t3.65068e-18\t\n",
      "759  \t1.47025e-04\t3.65068e-18\t\n",
      "760  \t1.47025e-04\t3.41079e-18\t\n",
      "761  \t1.47025e-04\t3.27498e-18\t\n",
      "762  \t1.47025e-04\t3.27498e-18\t\n",
      "763  \t1.47025e-04\t3.27498e-18\t\n",
      "764  \t1.47025e-04\t3.21774e-18\t\n",
      "765  \t1.47025e-04\t3.27312e-18\t\n",
      "766  \t1.47025e-04\t3.27312e-18\t\n",
      "767  \t1.47025e-04\t3.28826e-18\t\n",
      "768  \t1.47025e-04\t3.11407e-18\t\n",
      "769  \t1.47025e-04\t3.11407e-18\t\n",
      "770  \t1.47025e-04\t3.00682e-18\t\n",
      "771  \t1.47025e-04\t3.07549e-18\t\n",
      "772  \t1.47025e-04\t3.08303e-18\t\n",
      "773  \t1.47025e-04\t3.08303e-18\t\n",
      "774  \t1.47025e-04\t3.08303e-18\t\n",
      "775  \t1.47025e-04\t3.10431e-18\t\n",
      "776  \t1.47025e-04\t3.10431e-18\t\n",
      "777  \t1.47025e-04\t3.09962e-18\t\n",
      "778  \t1.47025e-04\t3.09962e-18\t\n",
      "779  \t1.47025e-04\t3.09962e-18\t\n",
      "780  \t1.47025e-04\t3.12124e-18\t\n",
      "781  \t1.47025e-04\t3.12124e-18\t\n",
      "782  \t1.47025e-04\t3.12661e-18\t\n",
      "783  \t1.47025e-04\t3.12661e-18\t\n",
      "784  \t1.47025e-04\t3.12661e-18\t\n",
      "785  \t1.47025e-04\t3.12661e-18\t\n",
      "786  \t1.47025e-04\t3.18561e-18\t\n",
      "787  \t1.47025e-04\t3.18561e-18\t\n",
      "788  \t1.47025e-04\t3.18561e-18\t\n",
      "789  \t1.47025e-04\t3.19150e-18\t\n",
      "790  \t1.47025e-04\t3.19150e-18\t\n",
      "791  \t1.47025e-04\t3.22810e-18\t\n",
      "792  \t1.47025e-04\t3.24931e-18\t\n",
      "793  \t1.47025e-04\t3.25292e-18\t\n",
      "794  \t1.47025e-04\t3.30483e-18\t\n",
      "795  \t1.47025e-04\t3.17307e-18\t\n",
      "796  \t1.47025e-04\t3.17307e-18\t\n",
      "797  \t1.47025e-04\t3.21714e-18\t\n",
      "798  \t1.47025e-04\t3.20782e-18\t\n",
      "799  \t1.47025e-04\t3.34941e-18\t\n",
      "800  \t1.47025e-04\t3.47168e-18\t\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0×0 Matrix{Float64}"
      ]
     },
     "metadata": {},
     "execution_count": 23
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "source": [
    "# note that the fitness refers to the SSE\r\n",
    "best_sse = best_fitness(de)\r\n",
    "best_rmse = sqrt(best_sse / size(data_PW, 1))\r\n",
    "@printf(\"Min RMSE (SDM + Photowatt-PWP201) = %.5e\", best_rmse)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Min RMSE (SDM + Photowatt-PWP201) = 2.42507e-03"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "source": [
    "println(\"Best parameter values (SDM + Photowatt-PWP201):\")\r\n",
    "best = best_individual(de)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Best parameter values (SDM + Photowatt-PWP201):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "5-element Vector{Float64}:\n",
       "   1.0305143001507115\n",
       "   3.4822624854718685\n",
       "  48.64283439534843\n",
       "   1.2012710195270726\n",
       " 981.982083729755"
      ]
     },
     "metadata": {},
     "execution_count": 25
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "source": [
    "# error of estimation \r\n",
    "xstar = [1.03052020484, 3.48287904343, 48.6435574734, 1.20123680201, 9.8126369078e2]\r\n",
    "δ = abs.(best .- xstar)\r\n",
    "δr = δ ./ xstar\r\n",
    "println(\"SDM + PW, error of estimation\")\r\n",
    "@show δ δr;"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "SDM + PW, error of estimation\n",
      "δ = [5.904689288405152e-6, 0.0006165579581316472, 0.0007230780515712354, 3.4217517072665515e-5, 0.718392949754957]\n",
      "δr = [5.729814185760601e-6, 0.00017702537195332803, 1.4864826692962162e-5, 2.8485238726794073e-5, 0.0007321099888898479]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Visualization"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "source": [
    "I_PW_SDM = [model_sdm(V, I, best..., T_PW) for (V, I) in eachrow(data_PW)]\r\n",
    "p_PW = plot(data_PW[:, 1], data_PW[:, 2]; st=:scatter, label=\"Measurement\", size=(400, 300))\r\n",
    "plot!(p_PW, data_PW[:, 1], I_PW_SDM; label=\"SDM\");"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- RMSE statistics"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "source": [
    "println(\"RMSE statistics in $ntrials runs (SDM + Photowatt-PWP201):\")\r\n",
    "measure_rmse_stats(model_sdm, data_PW, T_PW, bounds_PW_sdm, np, F, Cr, G_sdm)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "RMSE statistics in 30 runs (SDM + Photowatt-PWP201):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Dict{Symbol, Float64} with 4 entries:\n",
       "  :max  => 0.00242507\n",
       "  :std  => 1.75467e-17\n",
       "  :mean => 0.00242507\n",
       "  :min  => 0.00242507"
      ]
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Measure average runtime"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "source": [
    "println(\"Measure the running time (SDM + Photowatt-PWP201):\")\r\n",
    "@benchmark begin\r\n",
    "    de = StdDE(np, bounds_PW_sdm, StdOptions(F, Cr); senses=-1)  # minimization\r\n",
    "    evolve!(de, evaluator, G_sdm; stats=[])\r\n",
    "end evals=1 samples=ntrials seconds=1000"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Measure the running time (SDM + Photowatt-PWP201):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 30 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m258.240 ms\u001b[22m\u001b[39m … \u001b[35m421.655 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m6.31% … 7.01%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m323.612 ms               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m5.58%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m326.866 ms\u001b[22m\u001b[39m ± \u001b[32m 50.843 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m6.00% ± 1.14%\n",
       "\n",
       "  \u001b[39m█\u001b[39m▃\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[34m▃\u001b[39m\u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▃\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▁\u001b[39m▇\u001b[39m▁\u001b[39m▇\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▇\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▁\u001b[34m█\u001b[39m\u001b[39m▁\u001b[32m▇\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▁\u001b[39m▇\u001b[39m▇\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▇\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m \u001b[39m▁\n",
       "  258 ms\u001b[90m           Histogram: frequency by time\u001b[39m          422 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m169.80 MiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m10071311\u001b[39m."
      ]
     },
     "metadata": {},
     "execution_count": 29
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## DDM results"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### RTC France"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "source": [
    "# given a parameter vector θ, compute its SSE as the fitness in DE\r\n",
    "evaluator(θ) = calculate_sse(data_RT, (V, I) -> model_ddm(V, I, θ..., T_RT));"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- A typical run"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "source": [
    "# each run is new due to the involved randomness\r\n",
    "de = StdDE(np, bounds_RT_ddm, StdOptions(F, Cr); senses=-1)  # minimization\r\n",
    "evolve!(de, evaluator, G_ddm; stats=[:best, :std])"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "gen  \tbest      \tstd       \t\n",
      "0    \t2.16794e-01\t2.58457e+11\t\n",
      "1    \t2.16794e-01\t3.88180e+08\t\n",
      "2    \t1.66889e-01\t5.12271e+05\t\n",
      "3    \t1.66889e-01\t9.70769e+03\t\n",
      "4    \t6.36873e-02\t2.47138e+01\t\n",
      "5    \t6.36873e-02\t3.54909e+00\t\n",
      "6    \t6.36873e-02\t8.86091e-01\t\n",
      "7    \t5.65772e-03\t7.94582e-01\t\n",
      "8    \t5.65772e-03\t6.56352e-01\t\n",
      "9    \t5.65772e-03\t5.29985e-01\t\n",
      "10   \t5.65772e-03\t3.91530e-01\t\n",
      "11   \t5.65772e-03\t3.44762e-01\t\n",
      "12   \t5.65772e-03\t2.09823e-01\t\n",
      "13   \t5.65772e-03\t1.92130e-01\t\n",
      "14   \t5.65772e-03\t1.55744e-01\t\n",
      "15   \t5.65772e-03\t1.35864e-01\t\n",
      "16   \t5.65772e-03\t1.26236e-01\t\n",
      "17   \t5.65772e-03\t8.56700e-02\t\n",
      "18   \t4.82172e-03\t6.95267e-02\t\n",
      "19   \t4.82172e-03\t6.67474e-02\t\n",
      "20   \t4.82172e-03\t6.46679e-02\t\n",
      "21   \t4.82172e-03\t6.45206e-02\t\n",
      "22   \t4.82172e-03\t5.33356e-02\t\n",
      "23   \t3.20442e-03\t4.76911e-02\t\n",
      "24   \t3.20442e-03\t4.17093e-02\t\n",
      "25   \t3.20442e-03\t3.91403e-02\t\n",
      "26   \t1.18719e-03\t3.40184e-02\t\n",
      "27   \t1.18719e-03\t2.70708e-02\t\n",
      "28   \t1.18719e-03\t2.64255e-02\t\n",
      "29   \t1.18719e-03\t2.69168e-02\t\n",
      "30   \t1.18719e-03\t2.55473e-02\t\n",
      "31   \t1.18719e-03\t2.34475e-02\t\n",
      "32   \t1.18719e-03\t2.13468e-02\t\n",
      "33   \t1.18719e-03\t2.15276e-02\t\n",
      "34   \t1.18719e-03\t1.89601e-02\t\n",
      "35   \t1.18719e-03\t1.51102e-02\t\n",
      "36   \t1.18719e-03\t1.54184e-02\t\n",
      "37   \t1.18719e-03\t1.51583e-02\t\n",
      "38   \t1.18719e-03\t1.17359e-02\t\n",
      "39   \t1.18719e-03\t1.12517e-02\t\n",
      "40   \t1.18719e-03\t1.09851e-02\t\n",
      "41   \t1.18719e-03\t1.09851e-02\t\n",
      "42   \t1.18719e-03\t1.09973e-02\t\n",
      "43   \t1.18719e-03\t1.10842e-02\t\n",
      "44   \t1.18719e-03\t1.09287e-02\t\n",
      "45   \t1.18719e-03\t1.07555e-02\t\n",
      "46   \t1.18719e-03\t1.00560e-02\t\n",
      "47   \t1.18719e-03\t9.37884e-03\t\n",
      "48   \t1.18719e-03\t9.27458e-03\t\n",
      "49   \t1.18719e-03\t9.16365e-03\t\n",
      "50   \t1.18719e-03\t8.95442e-03\t\n",
      "51   \t1.18719e-03\t8.95442e-03\t\n",
      "52   \t1.18719e-03\t6.68548e-03\t\n",
      "53   \t1.06316e-03\t4.55896e-03\t\n",
      "54   \t8.40621e-04\t4.39232e-03\t\n",
      "55   \t8.40621e-04\t4.41362e-03\t\n",
      "56   \t8.40621e-04\t4.41362e-03\t\n",
      "57   \t8.40621e-04\t4.03686e-03\t\n",
      "58   \t8.40621e-04\t3.79934e-03\t\n",
      "59   \t8.40621e-04\t3.53294e-03\t\n",
      "60   \t8.40621e-04\t3.46005e-03\t\n",
      "61   \t4.92933e-04\t3.52633e-03\t\n",
      "62   \t4.92933e-04\t3.12370e-03\t\n",
      "63   \t4.92933e-04\t3.08295e-03\t\n",
      "64   \t4.92933e-04\t2.78416e-03\t\n",
      "65   \t4.92933e-04\t1.30623e-03\t\n",
      "66   \t4.92933e-04\t9.02419e-04\t\n",
      "67   \t4.92933e-04\t8.92192e-04\t\n",
      "68   \t4.92933e-04\t8.85604e-04\t\n",
      "69   \t2.73214e-04\t9.00518e-04\t\n",
      "70   \t2.73214e-04\t8.78666e-04\t\n",
      "71   \t2.73214e-04\t8.05507e-04\t\n",
      "72   \t2.73214e-04\t6.93303e-04\t\n",
      "73   \t2.73214e-04\t6.91184e-04\t\n",
      "74   \t2.73214e-04\t6.53228e-04\t\n",
      "75   \t2.73214e-04\t5.47329e-04\t\n",
      "76   \t2.73214e-04\t5.02308e-04\t\n",
      "77   \t2.73214e-04\t5.07837e-04\t\n",
      "78   \t2.73214e-04\t5.05688e-04\t\n",
      "79   \t2.73214e-04\t4.98506e-04\t\n",
      "80   \t2.73214e-04\t5.03304e-04\t\n",
      "81   \t1.48859e-04\t4.22158e-04\t\n",
      "82   \t1.48859e-04\t3.95196e-04\t\n",
      "83   \t1.48859e-04\t3.72069e-04\t\n",
      "84   \t1.48859e-04\t3.39718e-04\t\n",
      "85   \t1.48859e-04\t2.97702e-04\t\n",
      "86   \t1.48859e-04\t2.98865e-04\t\n",
      "87   \t1.48859e-04\t2.98865e-04\t\n",
      "88   \t1.48859e-04\t2.80774e-04\t\n",
      "89   \t1.48859e-04\t2.65668e-04\t\n",
      "90   \t1.48859e-04\t2.34070e-04\t\n",
      "91   \t1.48859e-04\t2.10147e-04\t\n",
      "92   \t1.48859e-04\t1.88045e-04\t\n",
      "93   \t1.48859e-04\t1.87312e-04\t\n",
      "94   \t1.48859e-04\t1.87790e-04\t\n",
      "95   \t1.48859e-04\t1.85659e-04\t\n",
      "96   \t1.48859e-04\t1.89014e-04\t\n",
      "97   \t1.48859e-04\t1.89014e-04\t\n",
      "98   \t1.48859e-04\t1.89182e-04\t\n",
      "99   \t1.48859e-04\t1.41943e-04\t\n",
      "100  \t1.48859e-04\t1.40644e-04\t\n",
      "101  \t1.48859e-04\t1.37661e-04\t\n",
      "102  \t1.48859e-04\t1.39345e-04\t\n",
      "103  \t1.48859e-04\t1.32941e-04\t\n",
      "104  \t1.48859e-04\t1.33154e-04\t\n",
      "105  \t1.48859e-04\t1.33042e-04\t\n",
      "106  \t1.48859e-04\t1.32507e-04\t\n",
      "107  \t1.48859e-04\t1.31402e-04\t\n",
      "108  \t1.48859e-04\t1.30926e-04\t\n",
      "109  \t1.48859e-04\t1.16657e-04\t\n",
      "110  \t1.48859e-04\t7.96686e-05\t\n",
      "111  \t1.48859e-04\t7.91248e-05\t\n",
      "112  \t1.48859e-04\t8.09472e-05\t\n",
      "113  \t1.48859e-04\t7.93298e-05\t\n",
      "114  \t1.48859e-04\t7.82223e-05\t\n",
      "115  \t1.48859e-04\t7.39677e-05\t\n",
      "116  \t1.48859e-04\t6.77508e-05\t\n",
      "117  \t1.48859e-04\t6.76072e-05\t\n",
      "118  \t1.48859e-04\t6.83187e-05\t\n",
      "119  \t1.48859e-04\t7.06720e-05\t\n",
      "120  \t1.48859e-04\t7.06642e-05\t\n",
      "121  \t1.48859e-04\t6.97370e-05\t\n",
      "122  \t1.48859e-04\t7.02517e-05\t\n",
      "123  \t1.44179e-04\t7.01595e-05\t\n",
      "124  \t1.44179e-04\t6.60687e-05\t\n",
      "125  \t1.44179e-04\t6.56777e-05\t\n",
      "126  \t1.44179e-04\t6.37904e-05\t\n",
      "127  \t1.26680e-04\t6.02145e-05\t\n",
      "128  \t1.26680e-04\t5.83224e-05\t\n",
      "129  \t1.26680e-04\t5.83224e-05\t\n",
      "130  \t1.26680e-04\t5.83224e-05\t\n",
      "131  \t1.26680e-04\t5.83224e-05\t\n",
      "132  \t1.26680e-04\t5.09621e-05\t\n",
      "133  \t1.26680e-04\t4.77276e-05\t\n",
      "134  \t1.26680e-04\t4.70413e-05\t\n",
      "135  \t1.26680e-04\t4.82200e-05\t\n",
      "136  \t1.26680e-04\t4.88014e-05\t\n",
      "137  \t1.26680e-04\t4.82032e-05\t\n",
      "138  \t1.26680e-04\t4.68463e-05\t\n",
      "139  \t1.26680e-04\t4.64099e-05\t\n",
      "140  \t1.26680e-04\t4.45945e-05\t\n",
      "141  \t1.26680e-04\t4.50120e-05\t\n",
      "142  \t1.26680e-04\t3.93249e-05\t\n",
      "143  \t1.26680e-04\t3.81381e-05\t\n",
      "144  \t1.21988e-04\t3.92183e-05\t\n",
      "145  \t1.21988e-04\t3.76182e-05\t\n",
      "146  \t1.21988e-04\t3.82432e-05\t\n",
      "147  \t1.21483e-04\t3.87173e-05\t\n",
      "148  \t1.21483e-04\t3.87173e-05\t\n",
      "149  \t1.06301e-04\t3.89889e-05\t\n",
      "150  \t1.06301e-04\t3.84871e-05\t\n",
      "151  \t8.44918e-05\t3.55445e-05\t\n",
      "152  \t8.44918e-05\t3.07136e-05\t\n",
      "153  \t7.84668e-05\t3.23531e-05\t\n",
      "154  \t7.84668e-05\t2.88719e-05\t\n",
      "155  \t7.84668e-05\t2.69965e-05\t\n",
      "156  \t7.84668e-05\t2.69201e-05\t\n",
      "157  \t7.84668e-05\t2.74990e-05\t\n",
      "158  \t7.84668e-05\t2.64290e-05\t\n",
      "159  \t7.84668e-05\t2.57436e-05\t\n",
      "160  \t7.84668e-05\t2.43725e-05\t\n",
      "161  \t7.84668e-05\t2.44689e-05\t\n",
      "162  \t7.84668e-05\t2.22861e-05\t\n",
      "163  \t7.84668e-05\t2.19787e-05\t\n",
      "164  \t7.84668e-05\t2.24432e-05\t\n",
      "165  \t7.84668e-05\t2.06606e-05\t\n",
      "166  \t7.84668e-05\t1.84274e-05\t\n",
      "167  \t7.84668e-05\t1.86753e-05\t\n",
      "168  \t7.49490e-05\t1.83631e-05\t\n",
      "169  \t7.32129e-05\t1.64415e-05\t\n",
      "170  \t6.94170e-05\t1.67899e-05\t\n",
      "171  \t6.94170e-05\t1.60971e-05\t\n",
      "172  \t5.89607e-05\t1.59923e-05\t\n",
      "173  \t5.89607e-05\t1.64001e-05\t\n",
      "174  \t5.89607e-05\t1.67718e-05\t\n",
      "175  \t5.89607e-05\t1.23894e-05\t\n",
      "176  \t5.89607e-05\t1.12127e-05\t\n",
      "177  \t5.89607e-05\t1.19030e-05\t\n",
      "178  \t5.89607e-05\t1.15031e-05\t\n",
      "179  \t5.89607e-05\t1.11034e-05\t\n",
      "180  \t5.45141e-05\t1.15277e-05\t\n",
      "181  \t5.45141e-05\t1.14473e-05\t\n",
      "182  \t5.45141e-05\t1.08000e-05\t\n",
      "183  \t4.91739e-05\t1.18176e-05\t\n",
      "184  \t4.91739e-05\t1.06542e-05\t\n",
      "185  \t4.91739e-05\t9.33211e-06\t\n",
      "186  \t4.91739e-05\t7.45908e-06\t\n",
      "187  \t4.91739e-05\t7.25576e-06\t\n",
      "188  \t4.91739e-05\t7.52784e-06\t\n",
      "189  \t4.91739e-05\t7.80700e-06\t\n",
      "190  \t4.91739e-05\t6.48370e-06\t\n",
      "191  \t4.91739e-05\t6.25019e-06\t\n",
      "192  \t4.91739e-05\t6.00438e-06\t\n",
      "193  \t4.72079e-05\t5.79074e-06\t\n",
      "194  \t4.72079e-05\t5.59668e-06\t\n",
      "195  \t4.72079e-05\t5.53525e-06\t\n",
      "196  \t4.72079e-05\t5.44902e-06\t\n",
      "197  \t4.72079e-05\t5.12849e-06\t\n",
      "198  \t4.72079e-05\t4.81865e-06\t\n",
      "199  \t4.58606e-05\t4.97187e-06\t\n",
      "200  \t4.58606e-05\t4.91292e-06\t\n",
      "201  \t4.58606e-05\t4.65556e-06\t\n",
      "202  \t4.51353e-05\t4.50047e-06\t\n",
      "203  \t4.51353e-05\t4.13301e-06\t\n",
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      "1874 \t2.50972e-05\t2.25075e-18\t\n",
      "1875 \t2.50972e-05\t2.25075e-18\t\n",
      "1876 \t2.50972e-05\t2.25075e-18\t\n",
      "1877 \t2.50972e-05\t2.25075e-18\t\n",
      "1878 \t2.50972e-05\t2.25075e-18\t\n",
      "1879 \t2.50972e-05\t2.25075e-18\t\n",
      "1880 \t2.50972e-05\t2.25075e-18\t\n",
      "1881 \t2.50972e-05\t2.25075e-18\t\n",
      "1882 \t2.50972e-05\t2.25075e-18\t\n",
      "1883 \t2.50972e-05\t2.25075e-18\t\n",
      "1884 \t2.50972e-05\t2.25075e-18\t\n",
      "1885 \t2.50972e-05\t2.25075e-18\t\n",
      "1886 \t2.50972e-05\t2.25075e-18\t\n",
      "1887 \t2.50972e-05\t2.25075e-18\t\n",
      "1888 \t2.50972e-05\t2.25075e-18\t\n",
      "1889 \t2.50972e-05\t2.25075e-18\t\n",
      "1890 \t2.50972e-05\t2.25075e-18\t\n",
      "1891 \t2.50972e-05\t2.25075e-18\t\n",
      "1892 \t2.50972e-05\t2.25075e-18\t\n",
      "1893 \t2.50972e-05\t2.25075e-18\t\n",
      "1894 \t2.50972e-05\t2.25075e-18\t\n",
      "1895 \t2.50972e-05\t2.25075e-18\t\n",
      "1896 \t2.50972e-05\t2.25003e-18\t\n",
      "1897 \t2.50972e-05\t2.25003e-18\t\n",
      "1898 \t2.50972e-05\t2.20423e-18\t\n",
      "1899 \t2.50972e-05\t2.20423e-18\t\n",
      "1900 \t2.50972e-05\t2.20423e-18\t\n",
      "1901 \t2.50972e-05\t2.20423e-18\t\n",
      "1902 \t2.50972e-05\t2.20423e-18\t\n",
      "1903 \t2.50972e-05\t2.20423e-18\t\n",
      "1904 \t2.50972e-05\t2.20423e-18\t\n",
      "1905 \t2.50972e-05\t2.20423e-18\t\n",
      "1906 \t2.50972e-05\t2.20423e-18\t\n",
      "1907 \t2.50972e-05\t2.20144e-18\t\n",
      "1908 \t2.50972e-05\t2.20144e-18\t\n",
      "1909 \t2.50972e-05\t2.20144e-18\t\n",
      "1910 \t2.50972e-05\t2.20144e-18\t\n",
      "1911 \t2.50972e-05\t2.20144e-18\t\n",
      "1912 \t2.50972e-05\t2.20144e-18\t\n",
      "1913 \t2.50972e-05\t2.20144e-18\t\n",
      "1914 \t2.50972e-05\t2.20144e-18\t\n",
      "1915 \t2.50972e-05\t2.20144e-18\t\n",
      "1916 \t2.50972e-05\t2.20144e-18\t\n",
      "1917 \t2.50972e-05\t2.20144e-18\t\n",
      "1918 \t2.50972e-05\t2.20144e-18\t\n",
      "1919 \t2.50972e-05\t2.20144e-18\t\n",
      "1920 \t2.50972e-05\t2.20144e-18\t\n",
      "1921 \t2.50972e-05\t2.20144e-18\t\n",
      "1922 \t2.50972e-05\t2.20144e-18\t\n",
      "1923 \t2.50972e-05\t2.20144e-18\t\n",
      "1924 \t2.50972e-05\t2.20144e-18\t\n",
      "1925 \t2.50972e-05\t2.20144e-18\t\n",
      "1926 \t2.50972e-05\t2.20144e-18\t\n",
      "1927 \t2.50972e-05\t2.20144e-18\t\n",
      "1928 \t2.50972e-05\t2.20144e-18\t\n",
      "1929 \t2.50972e-05\t2.20144e-18\t\n",
      "1930 \t2.50972e-05\t2.17187e-18\t\n",
      "1931 \t2.50972e-05\t2.17187e-18\t\n",
      "1932 \t2.50972e-05\t2.17187e-18\t\n",
      "1933 \t2.50972e-05\t2.17187e-18\t\n",
      "1934 \t2.50972e-05\t2.18043e-18\t\n",
      "1935 \t2.50972e-05\t2.17318e-18\t\n",
      "1936 \t2.50972e-05\t2.17318e-18\t\n",
      "1937 \t2.50972e-05\t2.17318e-18\t\n",
      "1938 \t2.50972e-05\t2.17318e-18\t\n",
      "1939 \t2.50972e-05\t2.17318e-18\t\n",
      "1940 \t2.50972e-05\t2.17318e-18\t\n",
      "1941 \t2.50972e-05\t2.17318e-18\t\n",
      "1942 \t2.50972e-05\t2.17318e-18\t\n",
      "1943 \t2.50972e-05\t2.16370e-18\t\n",
      "1944 \t2.50972e-05\t2.16370e-18\t\n",
      "1945 \t2.50972e-05\t2.08878e-18\t\n",
      "1946 \t2.50972e-05\t2.08628e-18\t\n",
      "1947 \t2.50972e-05\t2.08628e-18\t\n",
      "1948 \t2.50972e-05\t2.08628e-18\t\n",
      "1949 \t2.50972e-05\t2.08628e-18\t\n",
      "1950 \t2.50972e-05\t2.08628e-18\t\n",
      "1951 \t2.50972e-05\t2.08628e-18\t\n",
      "1952 \t2.50972e-05\t2.08628e-18\t\n",
      "1953 \t2.50972e-05\t2.08628e-18\t\n",
      "1954 \t2.50972e-05\t2.08707e-18\t\n",
      "1955 \t2.50972e-05\t2.08707e-18\t\n",
      "1956 \t2.50972e-05\t2.08707e-18\t\n",
      "1957 \t2.50972e-05\t2.04665e-18\t\n",
      "1958 \t2.50972e-05\t2.04665e-18\t\n",
      "1959 \t2.50972e-05\t2.02478e-18\t\n",
      "1960 \t2.50972e-05\t2.02478e-18\t\n",
      "1961 \t2.50972e-05\t2.02478e-18\t\n",
      "1962 \t2.50972e-05\t2.02478e-18\t\n",
      "1963 \t2.50972e-05\t2.02478e-18\t\n",
      "1964 \t2.50972e-05\t2.02478e-18\t\n",
      "1965 \t2.50972e-05\t2.02478e-18\t\n",
      "1966 \t2.50972e-05\t2.02478e-18\t\n",
      "1967 \t2.50972e-05\t2.02478e-18\t\n",
      "1968 \t2.50972e-05\t2.02478e-18\t\n",
      "1969 \t2.50972e-05\t2.02478e-18\t\n",
      "1970 \t2.50972e-05\t2.03531e-18\t\n",
      "1971 \t2.50972e-05\t2.03531e-18\t\n",
      "1972 \t2.50972e-05\t2.03583e-18\t\n",
      "1973 \t2.50972e-05\t2.03583e-18\t\n",
      "1974 \t2.50972e-05\t2.03583e-18\t\n",
      "1975 \t2.50972e-05\t2.01000e-18\t\n",
      "1976 \t2.50972e-05\t2.01000e-18\t\n",
      "1977 \t2.50972e-05\t2.01000e-18\t\n",
      "1978 \t2.50972e-05\t2.01000e-18\t\n",
      "1979 \t2.50972e-05\t2.01345e-18\t\n",
      "1980 \t2.50972e-05\t2.01345e-18\t\n",
      "1981 \t2.50972e-05\t2.01345e-18\t\n",
      "1982 \t2.50972e-05\t2.01345e-18\t\n",
      "1983 \t2.50972e-05\t2.01345e-18\t\n",
      "1984 \t2.50972e-05\t2.01345e-18\t\n",
      "1985 \t2.50972e-05\t2.02049e-18\t\n",
      "1986 \t2.50972e-05\t2.02049e-18\t\n",
      "1987 \t2.50972e-05\t2.02049e-18\t\n",
      "1988 \t2.50972e-05\t2.02865e-18\t\n",
      "1989 \t2.50972e-05\t2.02865e-18\t\n",
      "1990 \t2.50972e-05\t2.02865e-18\t\n",
      "1991 \t2.50972e-05\t2.02865e-18\t\n",
      "1992 \t2.50972e-05\t2.02865e-18\t\n",
      "1993 \t2.50972e-05\t2.02865e-18\t\n",
      "1994 \t2.50972e-05\t2.02865e-18\t\n",
      "1995 \t2.50972e-05\t2.02865e-18\t\n",
      "1996 \t2.50972e-05\t2.02865e-18\t\n",
      "1997 \t2.50972e-05\t2.02865e-18\t\n",
      "1998 \t2.50972e-05\t2.02865e-18\t\n",
      "1999 \t2.50972e-05\t2.02865e-18\t\n",
      "2000 \t2.50972e-05\t2.02865e-18\t\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0×0 Matrix{Float64}"
      ]
     },
     "metadata": {},
     "execution_count": 31
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "source": [
    "# note that the fitness refers to the SSE\r\n",
    "best_sse = best_fitness(de)\r\n",
    "best_rmse = sqrt(best_sse / size(data_RT, 1))\r\n",
    "@printf(\"Min RMSE (DDM + RTC France) = %.5e\", best_rmse)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Min RMSE (DDM + RTC France) = 9.82485e-04"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "source": [
    "println(\"Best parameter values (DDM + RTC France):\")\r\n",
    "best = best_individual(de)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Best parameter values (DDM + RTC France):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "7-element Vector{Float64}:\n",
       "  0.7607810794094393\n",
       "  0.7493471988378033\n",
       "  0.2259743226066568\n",
       "  1.9999999999996494\n",
       "  1.4510167876774782\n",
       "  0.03674042959602902\n",
       " 55.485439055084655"
      ]
     },
     "metadata": {},
     "execution_count": 33
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Visualization"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "source": [
    "I_RT_DDM = [model_ddm(V, I, best..., T_RT) for (V, I) in eachrow(data_RT)];"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "source": [
    "# continue the plot `p_RT`\r\n",
    "plot!(p_RT, data_RT[:, 1], I_RT_DDM; label=\"DDM\", linestyle=:dash, linecolor=:green)\r\n",
    "plot!(p_RT; legend=:bottomleft, xlabel=\"Voltage(V)\", ylabel=\"Current(A)\", framestyle=:box)\r\n",
    "lens!(p_RT, [0.35, 0.48], [0.65, 0.75], inset=(1, bbox(0.15, 0.15, 0.5, 0.3)), framestyle=:box)\r\n",
    "savefig(p_RT, joinpath(img_dir, \"DE_RT.pdf\"))\r\n",
    "p_RT  # display it here"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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     },
     "metadata": {},
     "execution_count": 35
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- RMSE statistics"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "source": [
    "println(\"RMSE statistics in $ntrials runs (DDM + RTC France):\")\r\n",
    "measure_rmse_stats(model_ddm, data_RT, T_RT, bounds_RT_ddm, np, F, Cr, G_ddm)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "RMSE statistics in 30 runs (DDM + RTC France):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Dict{Symbol, Float64} with 4 entries:\n",
       "  :max  => 0.000986022\n",
       "  :std  => 8.963e-7\n",
       "  :mean => 0.000982727\n",
       "  :min  => 0.000982485"
      ]
     },
     "metadata": {},
     "execution_count": 36
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Measure average runtime"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "source": [
    "println(\"Measure the running time (DDM + RTC France):\")\r\n",
    "@benchmark begin\r\n",
    "    de = StdDE(np, bounds_RT_ddm, StdOptions(F, Cr); senses=-1)\r\n",
    "    evolve!(de, evaluator, G_ddm; stats=[])\r\n",
    "end evals=1 samples=ntrials seconds=1000"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Measure the running time (DDM + RTC France):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 30 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m814.105 ms\u001b[22m\u001b[39m … \u001b[35m   1.216 s\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m5.36% … 4.46%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m889.930 ms               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m5.51%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m919.281 ms\u001b[22m\u001b[39m ± \u001b[32m116.029 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m5.72% ± 0.55%\n",
       "\n",
       "  \u001b[39m█\u001b[39m▄\u001b[39m▁\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[34m▁\u001b[39m\u001b[39m \u001b[39m▄\u001b[39m \u001b[39m \u001b[32m▁\u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[34m█\u001b[39m\u001b[39m▁\u001b[39m█\u001b[39m▆\u001b[39m▆\u001b[32m█\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[39m \u001b[39m▁\n",
       "  814 ms\u001b[90m           Histogram: frequency by time\u001b[39m          1.22 s \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m519.77 MiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m31340365\u001b[39m."
      ]
     },
     "metadata": {},
     "execution_count": 37
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Photowatt-PWP201"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "source": [
    "# given a parameter vector θ, compute its SSE as the fitness in DE\r\n",
    "evaluator(θ) = calculate_sse(data_PW, (V, I) -> model_ddm(V, I, θ..., T_PW));"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- A typical run"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "source": [
    "# each run is new due to the involved randomness\r\n",
    "de = StdDE(np, bounds_PW_ddm, StdOptions(F, Cr); senses=-1)  # minimization\r\n",
    "evolve!(de, evaluator, G_ddm; stats=[:best, :std])"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "gen  \tbest      \tstd       \t\n",
      "0    \t2.30041e+02\tInf       \t\n",
      "1    \t1.34378e+01\t3.19873e+52\t\n",
      "2    \t1.16159e+01\t3.19873e+52\t\n",
      "3    \t1.35936e+00\t2.47734e+33\t\n",
      "4    \t1.35936e+00\t2.14108e+08\t\n",
      "5    \t1.35936e+00\t1.78306e+07\t\n",
      "6    \t5.60660e-01\t3.42742e+05\t\n",
      "7    \t5.60660e-01\t2.09124e+02\t\n",
      "8    \t2.41067e-01\t6.11527e+01\t\n",
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      "1682 \t1.47025e-04\t4.61144e-19\t\n",
      "1683 \t1.47025e-04\t4.61144e-19\t\n",
      "1684 \t1.47025e-04\t4.61144e-19\t\n",
      "1685 \t1.47025e-04\t4.59907e-19\t\n",
      "1686 \t1.47025e-04\t4.61404e-19\t\n",
      "1687 \t1.47025e-04\t4.61404e-19\t\n",
      "1688 \t1.47025e-04\t4.61485e-19\t\n",
      "1689 \t1.47025e-04\t4.60460e-19\t\n",
      "1690 \t1.47025e-04\t4.60460e-19\t\n",
      "1691 \t1.47025e-04\t4.60460e-19\t\n",
      "1692 \t1.47025e-04\t4.60460e-19\t\n",
      "1693 \t1.47025e-04\t4.60460e-19\t\n",
      "1694 \t1.47025e-04\t4.84034e-19\t\n",
      "1695 \t1.47025e-04\t4.84034e-19\t\n",
      "1696 \t1.47025e-04\t4.82794e-19\t\n",
      "1697 \t1.47025e-04\t4.82794e-19\t\n",
      "1698 \t1.47025e-04\t4.82794e-19\t\n",
      "1699 \t1.47025e-04\t5.02396e-19\t\n",
      "1700 \t1.47025e-04\t5.20685e-19\t\n",
      "1701 \t1.47025e-04\t5.19287e-19\t\n",
      "1702 \t1.47025e-04\t5.19287e-19\t\n",
      "1703 \t1.47025e-04\t5.19287e-19\t\n",
      "1704 \t1.47025e-04\t5.08831e-19\t\n",
      "1705 \t1.47025e-04\t5.08831e-19\t\n",
      "1706 \t1.47025e-04\t5.08831e-19\t\n",
      "1707 \t1.47025e-04\t5.07414e-19\t\n",
      "1708 \t1.47025e-04\t5.08182e-19\t\n",
      "1709 \t1.47025e-04\t5.05208e-19\t\n",
      "1710 \t1.47025e-04\t4.66735e-19\t\n",
      "1711 \t1.47025e-04\t4.66735e-19\t\n",
      "1712 \t1.47025e-04\t4.66735e-19\t\n",
      "1713 \t1.47025e-04\t4.71926e-19\t\n",
      "1714 \t1.47025e-04\t4.71735e-19\t\n",
      "1715 \t1.47025e-04\t4.71735e-19\t\n",
      "1716 \t1.47025e-04\t4.68482e-19\t\n",
      "1717 \t1.47025e-04\t4.69505e-19\t\n",
      "1718 \t1.47025e-04\t4.65400e-19\t\n",
      "1719 \t1.47025e-04\t4.66654e-19\t\n",
      "1720 \t1.47025e-04\t4.66654e-19\t\n",
      "1721 \t1.47025e-04\t4.66654e-19\t\n",
      "1722 \t1.47025e-04\t4.66654e-19\t\n",
      "1723 \t1.47025e-04\t4.48518e-19\t\n",
      "1724 \t1.47025e-04\t4.46827e-19\t\n",
      "1725 \t1.47025e-04\t4.46827e-19\t\n",
      "1726 \t1.47025e-04\t4.45112e-19\t\n",
      "1727 \t1.47025e-04\t4.45112e-19\t\n",
      "1728 \t1.47025e-04\t4.45112e-19\t\n",
      "1729 \t1.47025e-04\t4.26658e-19\t\n",
      "1730 \t1.47025e-04\t3.93686e-19\t\n",
      "1731 \t1.47025e-04\t3.93686e-19\t\n",
      "1732 \t1.47025e-04\t3.91413e-19\t\n",
      "1733 \t1.47025e-04\t3.55142e-19\t\n",
      "1734 \t1.47025e-04\t3.63054e-19\t\n",
      "1735 \t1.47025e-04\t3.14193e-19\t\n",
      "1736 \t1.47025e-04\t3.12399e-19\t\n",
      "1737 \t1.47025e-04\t3.12998e-19\t\n",
      "1738 \t1.47025e-04\t3.12998e-19\t\n",
      "1739 \t1.47025e-04\t3.13166e-19\t\n",
      "1740 \t1.47025e-04\t3.13166e-19\t\n",
      "1741 \t1.47025e-04\t3.12471e-19\t\n",
      "1742 \t1.47025e-04\t3.16334e-19\t\n",
      "1743 \t1.47025e-04\t3.17847e-19\t\n",
      "1744 \t1.47025e-04\t3.11510e-19\t\n",
      "1745 \t1.47025e-04\t3.16405e-19\t\n",
      "1746 \t1.47025e-04\t3.24892e-19\t\n",
      "1747 \t1.47025e-04\t3.24892e-19\t\n",
      "1748 \t1.47025e-04\t3.20781e-19\t\n",
      "1749 \t1.47025e-04\t3.25422e-19\t\n",
      "1750 \t1.47025e-04\t3.27351e-19\t\n",
      "1751 \t1.47025e-04\t3.25168e-19\t\n",
      "1752 \t1.47025e-04\t3.24892e-19\t\n",
      "1753 \t1.47025e-04\t3.32690e-19\t\n",
      "1754 \t1.47025e-04\t3.32690e-19\t\n",
      "1755 \t1.47025e-04\t3.30065e-19\t\n",
      "1756 \t1.47025e-04\t3.32442e-19\t\n",
      "1757 \t1.47025e-04\t3.23504e-19\t\n",
      "1758 \t1.47025e-04\t2.89429e-19\t\n",
      "1759 \t1.47025e-04\t2.89144e-19\t\n",
      "1760 \t1.47025e-04\t2.85701e-19\t\n",
      "1761 \t1.47025e-04\t2.80964e-19\t\n",
      "1762 \t1.47025e-04\t2.74131e-19\t\n",
      "1763 \t1.47025e-04\t2.68298e-19\t\n",
      "1764 \t1.47025e-04\t2.68857e-19\t\n",
      "1765 \t1.47025e-04\t2.62193e-19\t\n",
      "1766 \t1.47025e-04\t2.45782e-19\t\n",
      "1767 \t1.47025e-04\t2.24585e-19\t\n",
      "1768 \t1.47025e-04\t2.26049e-19\t\n",
      "1769 \t1.47025e-04\t2.25118e-19\t\n",
      "1770 \t1.47025e-04\t2.25816e-19\t\n",
      "1771 \t1.47025e-04\t2.18699e-19\t\n",
      "1772 \t1.47025e-04\t2.19042e-19\t\n",
      "1773 \t1.47025e-04\t5.55758e-20\t\n",
      "1774 \t1.47025e-04\t1.68783e-20\t\n",
      "1775 \t1.47025e-04\t1.64281e-20\t\n",
      "1776 \t1.47025e-04\t1.54886e-20\t\n",
      "1777 \t1.47025e-04\t1.54886e-20\t\n",
      "1778 \t1.47025e-04\t1.59653e-20\t\n",
      "1779 \t1.47025e-04\t1.54886e-20\t\n",
      "1780 \t1.47025e-04\t1.39612e-20\t\n",
      "1781 \t1.47025e-04\t1.34135e-20\t\n",
      "1782 \t1.47025e-04\t1.39612e-20\t\n",
      "1783 \t1.47025e-04\t1.34135e-20\t\n",
      "1784 \t1.47025e-04\t1.34135e-20\t\n",
      "1785 \t1.47025e-04\t1.34135e-20\t\n",
      "1786 \t1.47025e-04\t1.28425e-20\t\n",
      "1787 \t1.47025e-04\t1.39612e-20\t\n",
      "1788 \t1.47025e-04\t1.39612e-20\t\n",
      "1789 \t1.47025e-04\t1.44883e-20\t\n",
      "1790 \t1.47025e-04\t1.39612e-20\t\n",
      "1791 \t1.47025e-04\t1.39612e-20\t\n",
      "1792 \t1.47025e-04\t1.44883e-20\t\n",
      "1793 \t1.47025e-04\t1.49968e-20\t\n",
      "1794 \t1.47025e-04\t1.49968e-20\t\n",
      "1795 \t1.47025e-04\t1.59653e-20\t\n",
      "1796 \t1.47025e-04\t1.77444e-20\t\n",
      "1797 \t1.47025e-04\t1.81620e-20\t\n",
      "1798 \t1.47025e-04\t1.81620e-20\t\n",
      "1799 \t1.47025e-04\t1.81620e-20\t\n",
      "1800 \t1.47025e-04\t1.81620e-20\t\n",
      "1801 \t1.47025e-04\t1.81620e-20\t\n",
      "1802 \t1.47025e-04\t1.77444e-20\t\n",
      "1803 \t1.47025e-04\t1.77444e-20\t\n",
      "1804 \t1.47025e-04\t1.77444e-20\t\n",
      "1805 \t1.47025e-04\t1.77444e-20\t\n",
      "1806 \t1.47025e-04\t1.77444e-20\t\n",
      "1807 \t1.47025e-04\t1.77444e-20\t\n",
      "1808 \t1.47025e-04\t1.77444e-20\t\n",
      "1809 \t1.47025e-04\t1.77444e-20\t\n",
      "1810 \t1.47025e-04\t1.77444e-20\t\n",
      "1811 \t1.47025e-04\t1.77444e-20\t\n",
      "1812 \t1.47025e-04\t1.77444e-20\t\n",
      "1813 \t1.47025e-04\t1.77444e-20\t\n",
      "1814 \t1.47025e-04\t2.15592e-20\t\n",
      "1815 \t1.47025e-04\t2.15592e-20\t\n",
      "1816 \t1.47025e-04\t2.15592e-20\t\n",
      "1817 \t1.47025e-04\t2.15592e-20\t\n",
      "1818 \t1.47025e-04\t2.15592e-20\t\n",
      "1819 \t1.47025e-04\t2.15592e-20\t\n",
      "1820 \t1.47025e-04\t2.15592e-20\t\n",
      "1821 \t1.47025e-04\t2.15592e-20\t\n",
      "1822 \t1.47025e-04\t2.15592e-20\t\n",
      "1823 \t1.47025e-04\t2.15592e-20\t\n",
      "1824 \t1.47025e-04\t2.15592e-20\t\n",
      "1825 \t1.47025e-04\t2.15592e-20\t\n",
      "1826 \t1.47025e-04\t2.08522e-20\t\n",
      "1827 \t1.47025e-04\t2.08522e-20\t\n",
      "1828 \t1.47025e-04\t2.08522e-20\t\n",
      "1829 \t1.47025e-04\t2.04895e-20\t\n",
      "1830 \t1.47025e-04\t2.04895e-20\t\n",
      "1831 \t1.47025e-04\t2.04895e-20\t\n",
      "1832 \t1.47025e-04\t2.01203e-20\t\n",
      "1833 \t1.47025e-04\t2.01203e-20\t\n",
      "1834 \t1.47025e-04\t2.01203e-20\t\n",
      "1835 \t1.47025e-04\t1.97442e-20\t\n",
      "1836 \t1.47025e-04\t1.97442e-20\t\n",
      "1837 \t1.47025e-04\t1.97442e-20\t\n",
      "1838 \t1.47025e-04\t1.97442e-20\t\n",
      "1839 \t1.47025e-04\t1.93608e-20\t\n",
      "1840 \t1.47025e-04\t1.93608e-20\t\n",
      "1841 \t1.47025e-04\t1.93608e-20\t\n",
      "1842 \t1.47025e-04\t1.93608e-20\t\n",
      "1843 \t1.47025e-04\t1.93608e-20\t\n",
      "1844 \t1.47025e-04\t1.93608e-20\t\n",
      "1845 \t1.47025e-04\t1.93608e-20\t\n",
      "1846 \t1.47025e-04\t1.93608e-20\t\n",
      "1847 \t1.47025e-04\t1.93608e-20\t\n",
      "1848 \t1.47025e-04\t1.89696e-20\t\n",
      "1849 \t1.47025e-04\t1.89696e-20\t\n",
      "1850 \t1.47025e-04\t1.85702e-20\t\n",
      "1851 \t1.47025e-04\t1.85702e-20\t\n",
      "1852 \t1.47025e-04\t1.85702e-20\t\n",
      "1853 \t1.47025e-04\t1.81620e-20\t\n",
      "1854 \t1.47025e-04\t1.81620e-20\t\n",
      "1855 \t1.47025e-04\t1.81620e-20\t\n",
      "1856 \t1.47025e-04\t1.81620e-20\t\n",
      "1857 \t1.47025e-04\t1.77444e-20\t\n",
      "1858 \t1.47025e-04\t1.77444e-20\t\n",
      "1859 \t1.47025e-04\t1.77444e-20\t\n",
      "1860 \t1.47025e-04\t1.77444e-20\t\n",
      "1861 \t1.47025e-04\t1.77444e-20\t\n",
      "1862 \t1.47025e-04\t1.73168e-20\t\n",
      "1863 \t1.47025e-04\t1.73168e-20\t\n",
      "1864 \t1.47025e-04\t1.73168e-20\t\n",
      "1865 \t1.47025e-04\t1.73168e-20\t\n",
      "1866 \t1.47025e-04\t1.73168e-20\t\n",
      "1867 \t1.47025e-04\t1.73168e-20\t\n",
      "1868 \t1.47025e-04\t1.77444e-20\t\n",
      "1869 \t1.47025e-04\t1.77444e-20\t\n",
      "1870 \t1.47025e-04\t1.77444e-20\t\n",
      "1871 \t1.47025e-04\t1.77444e-20\t\n",
      "1872 \t1.47025e-04\t1.77444e-20\t\n",
      "1873 \t1.47025e-04\t1.77444e-20\t\n",
      "1874 \t1.47025e-04\t1.77444e-20\t\n",
      "1875 \t1.47025e-04\t1.77444e-20\t\n",
      "1876 \t1.47025e-04\t1.77444e-20\t\n",
      "1877 \t1.47025e-04\t1.77444e-20\t\n",
      "1878 \t1.47025e-04\t1.77444e-20\t\n",
      "1879 \t1.47025e-04\t1.77444e-20\t\n",
      "1880 \t1.47025e-04\t1.77444e-20\t\n",
      "1881 \t1.47025e-04\t1.77444e-20\t\n",
      "1882 \t1.47025e-04\t1.77444e-20\t\n",
      "1883 \t1.47025e-04\t1.73168e-20\t\n",
      "1884 \t1.47025e-04\t1.73168e-20\t\n",
      "1885 \t1.47025e-04\t1.73168e-20\t\n",
      "1886 \t1.47025e-04\t1.73168e-20\t\n",
      "1887 \t1.47025e-04\t1.73168e-20\t\n",
      "1888 \t1.47025e-04\t1.73168e-20\t\n",
      "1889 \t1.47025e-04\t1.73168e-20\t\n",
      "1890 \t1.47025e-04\t1.73168e-20\t\n",
      "1891 \t1.47025e-04\t1.73168e-20\t\n",
      "1892 \t1.47025e-04\t1.68783e-20\t\n",
      "1893 \t1.47025e-04\t1.68783e-20\t\n",
      "1894 \t1.47025e-04\t1.68783e-20\t\n",
      "1895 \t1.47025e-04\t1.64281e-20\t\n",
      "1896 \t1.47025e-04\t1.64281e-20\t\n",
      "1897 \t1.47025e-04\t1.64281e-20\t\n",
      "1898 \t1.47025e-04\t1.64281e-20\t\n",
      "1899 \t1.47025e-04\t1.64281e-20\t\n",
      "1900 \t1.47025e-04\t1.64281e-20\t\n",
      "1901 \t1.47025e-04\t1.59653e-20\t\n",
      "1902 \t1.47025e-04\t1.59653e-20\t\n",
      "1903 \t1.47025e-04\t1.59653e-20\t\n",
      "1904 \t1.47025e-04\t1.59653e-20\t\n",
      "1905 \t1.47025e-04\t1.59653e-20\t\n",
      "1906 \t1.47025e-04\t1.59653e-20\t\n",
      "1907 \t1.47025e-04\t1.54886e-20\t\n",
      "1908 \t1.47025e-04\t1.54886e-20\t\n",
      "1909 \t1.47025e-04\t1.54886e-20\t\n",
      "1910 \t1.47025e-04\t1.54886e-20\t\n",
      "1911 \t1.47025e-04\t1.54886e-20\t\n",
      "1912 \t1.47025e-04\t1.54886e-20\t\n",
      "1913 \t1.47025e-04\t1.54886e-20\t\n",
      "1914 \t1.47025e-04\t1.54886e-20\t\n",
      "1915 \t1.47025e-04\t1.54886e-20\t\n",
      "1916 \t1.47025e-04\t1.54886e-20\t\n",
      "1917 \t1.47025e-04\t1.49968e-20\t\n",
      "1918 \t1.47025e-04\t1.49968e-20\t\n",
      "1919 \t1.47025e-04\t1.49968e-20\t\n",
      "1920 \t1.47025e-04\t1.44883e-20\t\n",
      "1921 \t1.47025e-04\t1.44883e-20\t\n",
      "1922 \t1.47025e-04\t1.44883e-20\t\n",
      "1923 \t1.47025e-04\t1.44883e-20\t\n",
      "1924 \t1.47025e-04\t1.44883e-20\t\n",
      "1925 \t1.47025e-04\t1.44883e-20\t\n",
      "1926 \t1.47025e-04\t1.44883e-20\t\n",
      "1927 \t1.47025e-04\t1.44883e-20\t\n",
      "1928 \t1.47025e-04\t1.44883e-20\t\n",
      "1929 \t1.47025e-04\t1.44883e-20\t\n",
      "1930 \t1.47025e-04\t1.44883e-20\t\n",
      "1931 \t1.47025e-04\t1.44883e-20\t\n",
      "1932 \t1.47025e-04\t1.44883e-20\t\n",
      "1933 \t1.47025e-04\t1.44883e-20\t\n",
      "1934 \t1.47025e-04\t1.44883e-20\t\n",
      "1935 \t1.47025e-04\t1.44883e-20\t\n",
      "1936 \t1.47025e-04\t1.44883e-20\t\n",
      "1937 \t1.47025e-04\t1.44883e-20\t\n",
      "1938 \t1.47025e-04\t1.44883e-20\t\n",
      "1939 \t1.47025e-04\t1.44883e-20\t\n",
      "1940 \t1.47025e-04\t1.44883e-20\t\n",
      "1941 \t1.47025e-04\t1.44883e-20\t\n",
      "1942 \t1.47025e-04\t1.44883e-20\t\n",
      "1943 \t1.47025e-04\t1.44883e-20\t\n",
      "1944 \t1.47025e-04\t1.44883e-20\t\n",
      "1945 \t1.47025e-04\t1.44883e-20\t\n",
      "1946 \t1.47025e-04\t1.44883e-20\t\n",
      "1947 \t1.47025e-04\t1.39612e-20\t\n",
      "1948 \t1.47025e-04\t1.34135e-20\t\n",
      "1949 \t1.47025e-04\t1.34135e-20\t\n",
      "1950 \t1.47025e-04\t1.34135e-20\t\n",
      "1951 \t1.47025e-04\t1.34135e-20\t\n",
      "1952 \t1.47025e-04\t1.34135e-20\t\n",
      "1953 \t1.47025e-04\t1.34135e-20\t\n",
      "1954 \t1.47025e-04\t1.34135e-20\t\n",
      "1955 \t1.47025e-04\t1.34135e-20\t\n",
      "1956 \t1.47025e-04\t1.34135e-20\t\n",
      "1957 \t1.47025e-04\t1.28425e-20\t\n",
      "1958 \t1.47025e-04\t1.28425e-20\t\n",
      "1959 \t1.47025e-04\t1.28425e-20\t\n",
      "1960 \t1.47025e-04\t1.28425e-20\t\n",
      "1961 \t1.47025e-04\t1.28425e-20\t\n",
      "1962 \t1.47025e-04\t1.28425e-20\t\n",
      "1963 \t1.47025e-04\t1.28425e-20\t\n",
      "1964 \t1.47025e-04\t1.28425e-20\t\n",
      "1965 \t1.47025e-04\t1.28425e-20\t\n",
      "1966 \t1.47025e-04\t1.28425e-20\t\n",
      "1967 \t1.47025e-04\t1.28425e-20\t\n",
      "1968 \t1.47025e-04\t1.28425e-20\t\n",
      "1969 \t1.47025e-04\t1.28425e-20\t\n",
      "1970 \t1.47025e-04\t1.28425e-20\t\n",
      "1971 \t1.47025e-04\t1.28425e-20\t\n",
      "1972 \t1.47025e-04\t1.28425e-20\t\n",
      "1973 \t1.47025e-04\t1.28425e-20\t\n",
      "1974 \t1.47025e-04\t1.28425e-20\t\n",
      "1975 \t1.47025e-04\t1.28425e-20\t\n",
      "1976 \t1.47025e-04\t1.28425e-20\t\n",
      "1977 \t1.47025e-04\t1.28425e-20\t\n",
      "1978 \t1.47025e-04\t1.28425e-20\t\n",
      "1979 \t1.47025e-04\t1.28425e-20\t\n",
      "1980 \t1.47025e-04\t1.28425e-20\t\n",
      "1981 \t1.47025e-04\t1.28425e-20\t\n",
      "1982 \t1.47025e-04\t1.28425e-20\t\n",
      "1983 \t1.47025e-04\t1.28425e-20\t\n",
      "1984 \t1.47025e-04\t1.28425e-20\t\n",
      "1985 \t1.47025e-04\t1.28425e-20\t\n",
      "1986 \t1.47025e-04\t1.28425e-20\t\n",
      "1987 \t1.47025e-04\t1.28425e-20\t\n",
      "1988 \t1.47025e-04\t1.28425e-20\t\n",
      "1989 \t1.47025e-04\t1.28425e-20\t\n",
      "1990 \t1.47025e-04\t1.22448e-20\t\n",
      "1991 \t1.47025e-04\t1.22448e-20\t\n",
      "1992 \t1.47025e-04\t1.22448e-20\t\n",
      "1993 \t1.47025e-04\t1.22448e-20\t\n",
      "1994 \t1.47025e-04\t1.22448e-20\t\n",
      "1995 \t1.47025e-04\t1.22448e-20\t\n",
      "1996 \t1.47025e-04\t1.22448e-20\t\n",
      "1997 \t1.47025e-04\t1.22448e-20\t\n",
      "1998 \t1.47025e-04\t1.22448e-20\t\n",
      "1999 \t1.47025e-04\t1.22448e-20\t\n",
      "2000 \t1.47025e-04\t1.22448e-20\t\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0×0 Matrix{Float64}"
      ]
     },
     "metadata": {},
     "execution_count": 39
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "source": [
    "# note that the fitness refers to the SSE\r\n",
    "best_sse = best_fitness(de)\r\n",
    "@printf(\"sse = %e\\n\", best_sse)\r\n",
    "best_rmse = sqrt(best_sse / size(data_PW, 1))\r\n",
    "@printf(\"Min RMSE (DDM + Photowatt-PWP201) = %.5e\", best_rmse)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "sse = 1.470247e-04\n",
      "Min RMSE (DDM + Photowatt-PWP201) = 2.42507e-03"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "source": [
    "println(\"Best parameter values (DDM + Photowatt-PWP201):\")\r\n",
    "best = best_individual(de)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Best parameter values (DDM + Photowatt-PWP201):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "7-element Vector{Float64}:\n",
       "   1.0305142983163214\n",
       "   0.009811361202764433\n",
       "   3.4724518695030833\n",
       "  48.64281805992416\n",
       "  48.64283525732562\n",
       "   1.2012710019514121\n",
       " 981.9823987416182"
      ]
     },
     "metadata": {},
     "execution_count": 41
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Visualization"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "source": [
    "I_PW_DDM = [model_ddm(V, I, best..., T_PW) for (V, I) in eachrow(data_PW)];\r\n",
    "plot!(p_PW, data_PW[:, 1], I_PW_DDM; label=\"DDM\", linestyle=:dash, linecolor=:green)\r\n",
    "plot!(p_PW; legend=:bottomleft, xlabel=\"Voltage(V)\", ylabel=\"Current(A)\", framestyle=:box, labelfontsize=10)\r\n",
    "lens!(p_PW, [10, 13.3], [0.8, 1.05], inset=(1, bbox(0.15, 0.23, 0.5, 0.4)), framestyle=:box)\r\n",
    "savefig(p_PW, joinpath(img_dir, \"DE_PW.pdf\"))\r\n",
    "p_PW # also display here"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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     },
     "metadata": {},
     "execution_count": 42
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- RMSE statistics"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "source": [
    "println(\"RMSE statistics in $ntrials runs (DDM + Photowatt-PWP201):\")\r\n",
    "measure_rmse_stats(model_ddm, data_PW, T_PW, bounds_PW_ddm, np, F, Cr, G_ddm)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "RMSE statistics in 30 runs (DDM + Photowatt-PWP201):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Dict{Symbol, Float64} with 4 entries:\n",
       "  :max  => 0.00242507\n",
       "  :std  => 2.73556e-17\n",
       "  :mean => 0.00242507\n",
       "  :min  => 0.00242507"
      ]
     },
     "metadata": {},
     "execution_count": 43
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "- Measure average runtime"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "source": [
    "println(\"Measure the running time (DDM + Photowatt-PWP201):\")\r\n",
    "@benchmark begin\r\n",
    "    de = StdDE(np, bounds_PW_ddm, StdOptions(F, Cr); senses=-1)\r\n",
    "    evolve!(de, evaluator, G_ddm; stats=[])\r\n",
    "end evals=1 samples=ntrials seconds=1000"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Measure the running time (DDM + Photowatt-PWP201):\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 30 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m785.853 ms\u001b[22m\u001b[39m … \u001b[35m   1.195 s\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m5.58% … 7.75%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m902.010 ms               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m5.56%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m938.699 ms\u001b[22m\u001b[39m ± \u001b[32m115.394 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m5.86% ± 0.90%\n",
       "\n",
       "  \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m▁\u001b[32m \u001b[39m\u001b[39m▁\u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m \n",
       "  \u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[32m▁\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[39m \u001b[39m▁\n",
       "  786 ms\u001b[90m           Histogram: frequency by time\u001b[39m           1.2 s \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m499.89 MiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m30138815\u001b[39m."
      ]
     },
     "metadata": {},
     "execution_count": 44
    }
   ],
   "metadata": {}
  }
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