redes_neurais.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](img/ifsclogo.jpg)\n",
    "<h2><center> Instituto Federal de Educação, Ciência e Tecnologia de Santa Catarina</center></h2>\n",
    "<h3><center>Título: Algoritmo Evolucionário Multi-Objetivo aplicado ao Problema de Despacho de Sistemas Elétricos</center></h3>\n",
    "<h3><center>Professor: Dr. Eng. Sergio Luciano Avila</center></h3>\n",
    "<h4><center>Acadêmicos: Fábio Matheus Mantelli e Douglas Pereira Dias</center><h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "### Justificativa do trabalho:\n",
    "Usinas termelétricas são os empreendimentos que mais poluem a atmosfera por meio da emissão de óxidos de enxofre (SOx) e óxidos de nitrogênio (NOx). Atualmente, o problema de minimização de poluição tem ganhado grande destaque e requer medidas para manter o ar das grandes cidades mais limpo. Além disso, o aumento da conscientização pública sobre a proteção ambiental e a aprovação de leis força as concessionárias a modificar os seus projetos e as estratégias operacionais com o objetivo de reduzir a poluição e as emissões de gases à atmosfera.\n",
    "\n",
    "#### Algumas estratégias foram propostas na literatura, tais como:\n",
    "#### - Instalação de equipamentos (precipatadores eletrostáticos);\n",
    "#### - Mudança para combustíveis de baixa emissão;\n",
    "#### - Substituição de unidades geradoras antigas e ineficientes;\n",
    "#### - Despacho de emissão.\n",
    "\n",
    "As três primeiras alternativas requerem a instalação de novos equipamentos ou modificação dos existentes. Porém, há um grande gasto de capital a ser investido para a substituição, portanto, podem apenas ser consideradas a longo prazo. Por outro lado, a opção de despacho de emissões é uma alternativa de curto prazo, na qual a emissão, além do custo do combustível, podem ser minimizados.\n",
    "\n",
    "Com uma nova função objetivo (reduzir a emissão de gases poluentes), o problema de despacho econômico pode ser tratado como um problema de otimização multi-objetivo com objetivos contraditórios, uma vez que a solução ótima do problema de despacho econômico não é a melhor solução ambiental. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sistema IEEE 30 barras e 6 geradores termelétricos\n",
    "\n",
    "No presente estudo, o problema de EED (Despacho Econômico/Ambiental, em tradução livre) é formulado como um problema de otimização multi-objetivo com restrição não-linear, onde o custo do combustível e o impacto ambientel são tratados como objetivos conflitantes. O algoritmo NSGA (Non-dominated Sorte Genetic Algorithm) é aplicado a um sistema teste IEEE 30 barras e com 6 geradores termelétricos. Na Figura abaixo é possível visualizar o sistema IEEE 30 barras.\n",
    "\n",
    "![title](img/ieee30.jpg)\n",
    "<h5><center>Figura 1 - Sistema teste IEEE 30 barras com 6 geradores</center></h5>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dados dos Geradores\n",
    "\n",
    "Sistema IEEE com 30 barras e 6 geradores parâmetros: https://rwl.github.io/PYPOWER/api/pypower.case30-pysrc.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PYPOWER Version 5.1.4, 27-June-2018 -- AC Power Flow (Newton)\n",
      "\n",
      "\n",
      "Newton's method power flow converged in 3 iterations.\n",
      "\n",
      "Converged in 0.03 seconds\n",
      "================================================================================\n",
      "|     System Summary                                                           |\n",
      "================================================================================\n",
      "\n",
      "How many?                How much?              P (MW)            Q (MVAr)\n",
      "---------------------    -------------------  -------------  -----------------\n",
      "Buses             30     Total Gen Capacity     335.0         -95.0 to 405.9\n",
      "Generators         6     On-line Capacity       335.0         -95.0 to 405.9\n",
      "Committed Gens     6     Generation (actual)    191.6             100.4\n",
      "Loads             20     Load                   189.2             107.2\n",
      "  Fixed           20       Fixed                189.2             107.2\n",
      "  Dispatchable     0       Dispatchable           0.0 of 0.0        0.0\n",
      "Shunts             2     Shunt (inj)             -0.0               0.2\n",
      "Branches          41     Losses (I^2 * Z)         2.44              8.99\n",
      "Transformers       0     Branch Charging (inj)     -               15.6\n",
      "Inter-ties         7     Total Inter-tie Flow    33.2              27.1\n",
      "Areas              3\n",
      "\n",
      "                          Minimum                      Maximum\n",
      "                 -------------------------  --------------------------------\n",
      "Voltage Magnitude   0.961 p.u. @ bus 8          1.000 p.u. @ bus 1   \n",
      "Voltage Angle      -3.96 deg   @ bus 19         1.48 deg   @ bus 13  \n",
      "P Losses (I^2*R)             -                  0.29 MW    @ line 2-6\n",
      "Q Losses (I^2*X)             -                  2.10 MVAr  @ line 12-13\n",
      "\n",
      "================================================================================\n",
      "|     Bus Data                                                                 |\n",
      "================================================================================\n",
      " Bus      Voltage          Generation             Load        \n",
      "  #   Mag(pu) Ang(deg)   P (MW)   Q (MVAr)   P (MW)   Q (MVAr)\n",
      "----- ------- --------  --------  --------  --------  --------\n",
      "    1  1.000    0.000*    25.97     -1.00       -         -   \n",
      "    2  1.000   -0.415     60.97     32.00     21.70     12.70 \n",
      "    3  0.983   -1.522       -         -        2.40      1.20 \n",
      "    4  0.980   -1.795       -         -        7.60      1.60 \n",
      "    5  0.982   -1.864       -         -         -         -   \n",
      "    6  0.973   -2.267       -         -         -         -   \n",
      "    7  0.967   -2.652       -         -       22.80     10.90 \n",
      "    8  0.961   -2.726       -         -       30.00     30.00 \n",
      "    9  0.981   -2.997       -         -         -         -   \n",
      "   10  0.984   -3.375       -         -        5.80      2.00 \n",
      "   11  0.981   -2.997       -         -         -         -   \n",
      "   12  0.985   -1.537       -         -       11.20      7.50 \n",
      "   13  1.000    1.476     37.00     11.35       -         -   \n",
      "   14  0.977   -2.308       -         -        6.20      1.60 \n",
      "   15  0.980   -2.312       -         -        8.20      2.50 \n",
      "   16  0.977   -2.644       -         -        3.50      1.80 \n",
      "   17  0.977   -3.392       -         -        9.00      5.80 \n",
      "   18  0.968   -3.478       -         -        3.20      0.90 \n",
      "   19  0.965   -3.958       -         -        9.50      3.40 \n",
      "   20  0.969   -3.871       -         -        2.20      0.70 \n",
      "   21  0.993   -3.488       -         -       17.50     11.20 \n",
      "   22  1.000   -3.393     21.59     39.57       -         -   \n",
      "   23  1.000   -1.589     19.20      7.95      3.20      1.60 \n",
      "   24  0.989   -2.631       -         -        8.70      6.70 \n",
      "   25  0.990   -1.690       -         -         -         -   \n",
      "   26  0.972   -2.139       -         -        3.50      2.30 \n",
      "   27  1.000   -0.828     26.91     10.54       -         -   \n",
      "   28  0.975   -2.266       -         -         -         -   \n",
      "   29  0.980   -2.128       -         -        2.40      0.90 \n",
      "   30  0.968   -3.042       -         -       10.60      1.90 \n",
      "                        --------  --------  --------  --------\n",
      "               Total:    191.64    100.41    189.20    107.20\n",
      "\n",
      "================================================================================\n",
      "|     Branch Data                                                              |\n",
      "================================================================================\n",
      "Brnch   From   To    From Bus Injection   To Bus Injection     Loss (I^2 * Z)  \n",
      "  #     Bus    Bus    P (MW)   Q (MVAr)   P (MW)   Q (MVAr)   P (MW)   Q (MVAr)\n",
      "-----  -----  -----  --------  --------  --------  --------  --------  --------\n",
      "   0      1      2     10.89     -5.09    -10.86      2.17     0.026      0.08\n",
      "   1      1      3     15.08      4.09    -14.96     -5.57     0.127      0.48\n",
      "   2      2      4     16.07      5.21    -15.89     -6.66     0.178      0.50\n",
      "   3      3      4     12.56      4.37    -12.54     -4.30     0.018      0.07\n",
      "   4      2      5     13.79      4.51    -13.68     -6.03     0.110      0.44\n",
      "   5      2      6     20.28      7.42    -19.99     -8.50     0.289      0.87\n",
      "   6      4      6     22.50     11.38    -22.43    -11.12     0.066      0.26\n",
      "   7      5      7     13.68      6.21    -13.56     -6.88     0.120      0.29\n",
      "   8      6      7      9.27      3.17     -9.24     -4.02     0.031      0.08\n",
      "   9      6      8     24.82     24.43    -24.69    -23.92     0.128      0.51\n",
      "  10      6      9      5.79     -3.36     -5.79      3.46    -0.000      0.10\n",
      "  11      6     10      3.31     -1.92     -3.31      2.00    -0.000      0.09\n",
      "  12      9     11      0.00      0.00      0.00      0.00    -0.000      0.00\n",
      "  13      9     10      5.79     -3.46     -5.79      3.51    -0.000      0.05\n",
      "  14      4     12     -1.67     -2.02      1.67      2.04    -0.000      0.02\n",
      "  15     12     13    -37.00     -9.26     37.00     11.35    -0.000      2.10\n",
      "  16     12     14      5.39      0.88     -5.35     -0.80     0.037      0.08\n",
      "  17     12     15      9.48     -1.06     -9.41      1.19     0.066      0.12\n",
      "  18     12     16      9.26     -0.10     -9.18      0.28     0.080      0.18\n",
      "  19     14     15     -0.85     -0.80      0.85      0.80     0.003      0.00\n",
      "  20     16     17      5.68     -2.08     -5.65      2.15     0.031      0.07\n",
      "  21     15     18      9.16      0.76     -9.07     -0.57     0.097      0.19\n",
      "  22     18     19      5.87     -0.33     -5.85      0.38     0.022      0.05\n",
      "  23     19     20     -3.65     -3.78      3.66      3.80     0.009      0.02\n",
      "  24     10     20      5.92      4.62     -5.86     -4.50     0.052      0.12\n",
      "  25     10     17      3.37      8.01     -3.35     -7.95     0.023      0.06\n",
      "  26     10     21     -2.23    -11.67      2.28     11.77     0.044      0.10\n",
      "  27     10     22     -3.75     -8.48      3.82      8.62     0.062      0.13\n",
      "  28     21     22    -19.78    -22.97     19.87     23.16     0.093      0.19\n",
      "  29     15     23     -8.81     -5.25      8.91      5.47     0.109      0.22\n",
      "  30     22     24     -2.10      7.80      2.18     -7.68     0.078      0.12\n",
      "  31     23     24      7.09      0.88     -7.02     -0.75     0.066      0.14\n",
      "  32     24     25     -3.86      1.77      3.89     -1.71     0.035      0.06\n",
      "  33     25     26      3.55      2.37     -3.50     -2.30     0.046      0.07\n",
      "  34     25     27     -7.44     -0.66      7.50      0.78     0.063      0.12\n",
      "  35     28     27     -6.11     -6.08      6.11      6.40    -0.000      0.31\n",
      "  36     27     29      6.17      1.68     -6.08     -1.51     0.090      0.17\n",
      "  37     27     30      7.12      1.67     -6.95     -1.35     0.171      0.32\n",
      "  38     29     30      3.68      0.61     -3.65     -0.55     0.035      0.07\n",
      "  39      8     28     -5.31     -6.08      5.34      4.33     0.036      0.12\n",
      "  40      6     28     -0.77     -2.70      0.77      1.75     0.001      0.00\n",
      "                                                             --------  --------\n",
      "                                                    Total:     2.444      8.99\n"
     ]
    }
   ],
   "source": [
    "from pypower.api import case30, ppoption, runpf, printpf\n",
    "import numpy as np\n",
    "\n",
    "# utiliza o sistema IEEE de 30 barras e 6 geradores\n",
    "ppc = case30()\n",
    "ppopt = ppoption(PF_ALG=1)\n",
    "r = runpf(ppc, ppopt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calcula o somatório de potência dos geradores\n",
    "potencia = 0\n",
    "for i in range(0, len(r[0]['gen'][:])):\n",
    "    potencia += r[0]['gen'][i][1]\n",
    "\n",
    "# calcula o somatório da demanda das cargas\n",
    "demanda = 0\n",
    "for i in range(0, len(r[0]['bus'])):\n",
    "    demanda += r[0]['bus'][i][2]\n",
    "\n",
    "# calcula a potência que sai da barra e que entra na barra i\n",
    "pot_from_bus = 0\n",
    "pot_to_bus = 0\n",
    "for i in r[0]['branch'][:]:\n",
    "    pot_from_bus += i[13]\n",
    "    pot_to_bus += i[15]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Coeficientes de Emissão de COx e de Custos dos Geradores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "from mpmath import mp\n",
    "mp.dps = 300\n",
    "\n",
    "# parâmetros do gerador\n",
    "gerador = [\n",
    "    {\n",
    "        \"Cost\": [10, 200, 100],\n",
    "        \"Emission\": [4.091, -5.554, 6.490, 20E-4, 2.857]\n",
    "    },\n",
    "    {\n",
    "        \"Cost\": [10, 150, 120],\n",
    "        \"Emission\": [2.543, -6.047, 5.638, 5.0E-4, 3.333]\n",
    "    },\n",
    "    {\n",
    "        \"Cost\": [20, 180, 40],\n",
    "        \"Emission\": [4.258, -5.094, 4.586, 1.0E-6, 8.000]\n",
    "    },\n",
    "    {\n",
    "        \"Cost\": [10, 100, 60],\n",
    "        \"Emission\": [5.326, -3.550, 3.380, 2.0E-3, 1.0E-6, 1.0E-5]\n",
    "    },\n",
    "    {\n",
    "        \"Cost\": [20, 180, 40],\n",
    "        \"Emission\": [4.258, -5.094, 4.586, 1.0E-6, 8.000]\n",
    "    },\n",
    "    {\n",
    "        \"Cost\": [10, 150, 100],\n",
    "        \"Emission\": [6.131, -5.555, 5.151, 1.0E-5, 6.667]\n",
    "    }\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### IEEE 30-bus\n",
    "#### Demanda de potência ativa e reativa pelas cargas\n",
    "| PD (MW) | QD (MVAr) |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "bus_data = [\n",
    "     [0.00, 0.00],\n",
    "     [21.70, 12.70],\n",
    "     [2.40, 120],\n",
    "     [7.60, 1.60],\n",
    "     [94.20, 19.00],\n",
    "     [0.00, 0.00],\n",
    "     [22.80, 10.90],\n",
    "     [30.00, 30.00],\n",
    "     [0.00, 0.00],\n",
    "     [5.80, 2.00],\n",
    "     [0.00, 0.00],\n",
    "     [11.20, 7.50],\n",
    "     [0.00, 0.00],\n",
    "     [6.20, 1.60],\n",
    "     [8.20, 2.50],\n",
    "     [3.50, 1.80],\n",
    "     [9.00, 5.80],\n",
    "     [3.20, 0.90],\n",
    "     [9.50, 3.40],\n",
    "     [2.20, 0.70],\n",
    "     [17.50, 11.20],\n",
    "     [0.00, 0.00],\n",
    "     [3.20, 1.60],\n",
    "     [8.70, 6.70],\n",
    "     [0.00, 0.00],\n",
    "     [3.50, 2.30],\n",
    "     [0.00, 0.00],\n",
    "     [0.00, 0.00],\n",
    "     [2.40, 0.90],\n",
    "     [10.60, 1.90]\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### IEEE 30-bus \n",
    "#### Dados das barras e linhas\n",
    "| Line | From Bus | To Bus | Resistance | Reactance | Susceptance | Rating (MVA) |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "line_data = [\n",
    "     [ 1,  2, 0.0192, 0.0575, 0.0264, 130],\n",
    "     [ 1,  3, 0.0452, 0.1852, 0.0204, 130],\n",
    "     [ 2,  4, 0.0570, 0.1737, 0.0184,  65],\n",
    "     [ 3,  4, 0.0132, 0.0379, 0.0042, 130],\n",
    "     [ 2,  5, 0.0472, 0.1983, 0.0209, 130],\n",
    "     [ 2,  6, 0.0581, 0.1763, 0.0187,  65],\n",
    "     [ 4,  6, 0.0119, 0.0414, 0.0045,  90],\n",
    "     [ 5,  7, 0.0460, 0.1160, 0.0102,  70],\n",
    "     [ 6,  7, 0.0267, 0.0820, 0.0085, 130],\n",
    "     [ 6,  8, 0.0120, 0.0420, 0.0045,  32],\n",
    "     [ 6,  9, 0.0000, 0.2080, 0.0000,  65],\n",
    "     [ 6, 10, 0.0000, 0.5560, 0.0000,  32],\n",
    "     [ 9, 11, 0.0000, 0.2080, 0.0000,  65],\n",
    "     [ 9, 10, 0.0000, 0.1100, 0.0000,  65],\n",
    "     [ 4, 12, 0.0000, 0.2560, 0.0000,  65],\n",
    "     [12, 13, 0.0000, 0.1400, 0.0000,  65],\n",
    "     [12, 14, 0.1231, 0.2559, 0.0000,  32],\n",
    "     [12, 15, 0.0662, 0.1304, 0.0000,  32],\n",
    "     [12, 16, 0.0945, 0.1987, 0.0000,  32],\n",
    "     [14, 15, 0.2210, 0.1997, 0.0000,  16],\n",
    "     [16, 17, 0.0824, 0.1923, 0.0000,  16],\n",
    "     [15, 18, 0.1070, 0.2185, 0.0000,  16],\n",
    "     [18, 19, 0.0639, 0.1292, 0.0000,  16],\n",
    "     [19, 20, 0.0340, 0.0680, 0.0000,  32],\n",
    "     [10, 20, 0.0936, 0.2090, 0.0000,  32],\n",
    "     [10, 17, 0.0324, 0.0845, 0.0000,  32],\n",
    "     [10, 21, 0.0348, 0.0749, 0.0000,  32],\n",
    "     [10, 22, 0.0727, 0.1499, 0.0000,  32],\n",
    "     [21, 22, 0.0116, 0.0236, 0.0000,  32],\n",
    "     [15, 23, 0.1000, 0.2020, 0.0000,  16],\n",
    "     [22, 24, 0.1150, 0.1790, 0.0000,  16],\n",
    "     [23, 24, 0.1320, 0.2700, 0.0000,  16],\n",
    "     [24, 25, 0.1885, 0.3292, 0.0000,  16],\n",
    "     [25, 26, 0.2544, 0.3800, 0.0000,  16],\n",
    "     [25, 27, 0.1093, 0.2087, 0.0000,  16],\n",
    "     [28, 27, 0.0000, 0.3960, 0.0000,  65],\n",
    "     [27, 29, 0.2198, 0.4153, 0.0000,  16],\n",
    "     [27, 30, 0.3202, 0.6027, 0.0000,  16],\n",
    "     [29, 30, 0.2399, 0.4533, 0.0000,  16],\n",
    "     [ 8, 28, 0.0636, 0.2000, 0.0214,  32],\n",
    "     [ 6, 28, 0.0169, 0.0599, 0.0065,  32]\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problema de Despacho Econômico/Ambiental\n",
    "\n",
    "### ------------------------------------------------------------------------------------\n",
    "## Problema proposto no livro \"Intelligent Systems\"\n",
    "##### Autores: Christine L. Mumford e Lakhmi C. Jain\n",
    "### ------------------------------------------------------------------------------------\n",
    "## Objetivos do Problema\n",
    "\n",
    "#### Minimizar o Custo do Combustível: $F(P_{G})=\\sum_{i=1}^{N}a_{i}+b_{i}P_{G_{i}}+c_{i}P_{G_{i}}^{2}$\n",
    "\n",
    "O vetor da energia ativa dos geradores é definida da seguinte forma: $P_{G}= \\left [ P_{G_{1}}, P_{G_{2}}, ..., P_{G_{N}}  \\right ]$\n",
    "\n",
    "#### Minimizar a Emissão de SO$_{x}$: $E(P_{G}) = \\sum_{i=1}^{N}10^{-2}\\left ( \\alpha_{i}+\\beta _{i}P_{G_{i}}+\\gamma_{i}P_{G{i}}^{2} \\right )+\\zeta_{i}e^{\\lambda_{i}P_{G_{i}}}$\n",
    "\n",
    "Onde: $\\alpha_{i}$, $\\beta_{i}$, $\\gamma_{i}$, $\\zeta_{i}$ e $\\lambda_{i}$ são coeficientes das características de emissão do gerador $i^{th}$\n",
    "\n",
    "\n",
    "## Restrições do Problema\n",
    "\n",
    "#### Restrição de Capacidade de Geração: $P_{G_{i}}^{min}\\leq P_{G_{i}}\\leq P_{G_{i}}^{max}, i=1, ..., N$\n",
    "\n",
    "#### Restrições de Balanço de Energia: $\\sum_{i=1}^{N}P_{G_{i}}-P_{D}-P_{loss}=0$\n",
    "\n",
    "#### Perdas nas LTs: $P_{loss}=\\sum_{k=1}^{NL}g_{k}\\left [ V_{i}^{2}+V_{j}^{2}-2V_{i}V_{j}cos(\\delta_{i}-\\delta{j}) \\right ]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processo finalizado.\n"
     ]
    }
   ],
   "source": [
    "# importa bibliotecas do Platypus (Framework de computação evolucionária multiobjetivo em Python)\n",
    "from platypus import NSGAII, Problem, Real\n",
    "\n",
    "# Definição da classe otimizacao\n",
    "class otimizacao(Problem):\n",
    "\n",
    "    def __init__(self):\n",
    "        \n",
    "        # init (6 variaveis, 2 objetivos, 13 restrições)\n",
    "        super(otimizacao, self).__init__(6, 2, 13)\n",
    "        \n",
    "        # definição dos limites de cada uma das variáveis (são 6 variáveis)\n",
    "        self.types[:] = [Real(0, 10000), Real(0, 10000), Real(0, 10000), Real(0, 10000), Real(0, 10000), Real(0, 10000)]\n",
    "        \n",
    "        # primeira restrição de igualdade\n",
    "        self.constraints[0:6] = \">=0\"\n",
    "        \n",
    "        # segunda, terça e quarta restrições definidas como inequações (maior ou igual a zero)\n",
    "        self.constraints[6:12] = \"<=0\"\n",
    "        \n",
    "        # demais restrições como inequações (menor ou igual a zero)\n",
    "        self.constraints[12] = \"==0\"\n",
    "        \n",
    "\n",
    "    # função para calcular o problema de otimização multiobjetivo\n",
    "    def evaluate(self, solution):\n",
    "        \n",
    "        # P[1:6] são 6 variáveis do problema\n",
    "        P = solution.variables[:]\n",
    "        \n",
    "        # calcula o somatório dos 2 objetivos do problema\n",
    "        min_custo_combustivel = 0\n",
    "        min_emissao = 0\n",
    "        for i in range(0, len(gerador)):\n",
    "            min_custo_combustivel += gerador[i]['Cost'][0] + gerador[i]['Cost'][1] * P[i] + gerador[i]['Cost'][2] * P[i] ** 2\n",
    "            min_emissao += 10 ** (-2) * (gerador[i]['Emission'][0] + gerador[i]['Emission'][1] * P[i] + gerador[i]['Emission'][2] * P[i] ** 2) + gerador[i]['Emission'][3] * mp.exp(gerador[i]['Emission'][4] * P[i])\n",
    "               \n",
    "        # definição da funções multiobjetivo\n",
    "        solution.objectives[:] = [ min_custo_combustivel, min_emissao]\n",
    "  \n",
    "        # definição das restrições\n",
    "        solution.constraints[:] = [P[0], P[1], P[2], P[3], P[4], P[5], P[0] - 80, P[1] - 80, P[2] - 50, P[3] - 55, P[4] - 30, P[5] - 40, potencia - demanda - (pot_from_bus + pot_to_bus)]\n",
    "\n",
    "# utiliza o algoritmo NSGAII para otimizar o problema        \n",
    "algorithm = NSGAII(otimizacao())\n",
    "\n",
    "# otimiza o problema usando 19000 funções de avaliação\n",
    "funcoes_de_avaliacao = 19000\n",
    "algorithm.run(funcoes_de_avaliacao)\n",
    "\n",
    "# conclui o processo\n",
    "print(\"Processo finalizado.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define uma tela para imprimir os resultados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resultado da Computacao Evolucionaria Multi-Objetivo em Python\n",
      "\n",
      "\n",
      "Número de Funções de Avaliacao: 19000\n",
      "\n",
      "\n",
      "=================================================================================\n",
      "|\t\t\t\tSumario \t\t\t\t\t|\n",
      "---------------------------------------------------------------------------------\n",
      "\t Funcao Objetivo 1 \t\t\t Funcao Objetivo 2\n",
      "---------------------------------------------------------------------------------\n",
      "\t 81.3059 \t\t\t\t 0.2702\n",
      "\t 576.7554 \t\t\t\t 0.1977\n",
      "\t 174.1372 \t\t\t\t 0.2443\n",
      "\t 165.1309 \t\t\t\t 0.2470\n",
      "\t 269.8730 \t\t\t\t 0.2252\n",
      "\t 91.9916 \t\t\t\t 0.2664\n",
      "\t 96.3781 \t\t\t\t 0.2651\n",
      "\t 187.3963 \t\t\t\t 0.2413\n",
      "\t 111.8328 \t\t\t\t 0.2604\n",
      "\t 101.7808 \t\t\t\t 0.2637\n",
      "\t 427.1417 \t\t\t\t 0.2056\n",
      "\t 196.8507 \t\t\t\t 0.2400\n",
      "\t 185.1960 \t\t\t\t 0.2424\n",
      "\t 263.3341 \t\t\t\t 0.2263\n",
      "\t 528.2271 \t\t\t\t 0.1998\n",
      "\t 377.5646 \t\t\t\t 0.2103\n",
      "\t 507.7188 \t\t\t\t 0.2003\n",
      "\t 484.6895 \t\t\t\t 0.2018\n",
      "\t 215.0867 \t\t\t\t 0.2356\n",
      "\t 518.9374 \t\t\t\t 0.2001\n",
      "\t 177.7883 \t\t\t\t 0.2436\n",
      "\t 86.7414 \t\t\t\t 0.2682\n",
      "\t 259.9216 \t\t\t\t 0.2274\n",
      "\t 278.6357 \t\t\t\t 0.2238\n",
      "\t 498.8237 \t\t\t\t 0.2008\n",
      "\t 253.2987 \t\t\t\t 0.2282\n",
      "\t 554.3575 \t\t\t\t 0.1988\n",
      "\t 134.3273 \t\t\t\t 0.2542\n",
      "\t 148.5991 \t\t\t\t 0.2505\n",
      "\t 562.7561 \t\t\t\t 0.1987\n",
      "\t 490.8579 \t\t\t\t 0.2011\n",
      "\t 226.9427 \t\t\t\t 0.2329\n",
      "\t 151.7974 \t\t\t\t 0.2496\n",
      "\t 570.3643 \t\t\t\t 0.1979\n",
      "\t 122.6128 \t\t\t\t 0.2574\n",
      "\t 386.0216 \t\t\t\t 0.2096\n",
      "\t 475.9114 \t\t\t\t 0.2025\n",
      "\t 439.3620 \t\t\t\t 0.2047\n",
      "\t 333.7262 \t\t\t\t 0.2157\n",
      "\t 139.7408 \t\t\t\t 0.2529\n",
      "\t 450.1236 \t\t\t\t 0.2037\n",
      "\t 331.2656 \t\t\t\t 0.2169\n",
      "\t 415.7797 \t\t\t\t 0.2064\n",
      "\t 210.7783 \t\t\t\t 0.2364\n",
      "\t 459.8936 \t\t\t\t 0.2032\n",
      "\t 290.2103 \t\t\t\t 0.2222\n",
      "\t 360.9129 \t\t\t\t 0.2125\n",
      "\t 297.3355 \t\t\t\t 0.2208\n",
      "\t 203.1366 \t\t\t\t 0.2382\n",
      "\t 340.1118 \t\t\t\t 0.2153\n",
      "\t 131.7889 \t\t\t\t 0.2550\n",
      "\t 431.4019 \t\t\t\t 0.2050\n",
      "\t 324.7777 \t\t\t\t 0.2173\n",
      "\t 197.9699 \t\t\t\t 0.2392\n",
      "\t 538.1708 \t\t\t\t 0.1992\n",
      "\t 220.2415 \t\t\t\t 0.2343\n",
      "\t 304.4460 \t\t\t\t 0.2201\n",
      "\t 444.9992 \t\t\t\t 0.2040\n",
      "\t 352.3060 \t\t\t\t 0.2134\n",
      "\t 371.2779 \t\t\t\t 0.2111\n",
      "\t 318.7982 \t\t\t\t 0.2178\n",
      "\t 232.2860 \t\t\t\t 0.2323\n",
      "\t 104.3945 \t\t\t\t 0.2625\n",
      "\t 221.9901 \t\t\t\t 0.2339\n",
      "\t 294.2179 \t\t\t\t 0.2213\n",
      "\t 117.1688 \t\t\t\t 0.2589\n",
      "\t 370.4672 \t\t\t\t 0.2118\n",
      "\t 108.2308 \t\t\t\t 0.2615\n",
      "\t 240.2370 \t\t\t\t 0.2308\n",
      "\t 541.9822 \t\t\t\t 0.1989\n",
      "\t 249.4865 \t\t\t\t 0.2291\n",
      "\t 144.6010 \t\t\t\t 0.2518\n",
      "\t 117.0818 \t\t\t\t 0.2590\n",
      "\t 470.7907 \t\t\t\t 0.2028\n",
      "\t 85.0370 \t\t\t\t 0.2689\n",
      "\t 163.4035 \t\t\t\t 0.2475\n",
      "\t 127.0848 \t\t\t\t 0.2573\n",
      "\t 364.7937 \t\t\t\t 0.2125\n",
      "\t 157.3858 \t\t\t\t 0.2486\n",
      "\t 400.8310 \t\t\t\t 0.2078\n",
      "\t 351.5416 \t\t\t\t 0.2137\n",
      "\t 464.8664 \t\t\t\t 0.2031\n",
      "\t 245.8949 \t\t\t\t 0.2294\n",
      "\t 408.1540 \t\t\t\t 0.2071\n",
      "\t 209.3022 \t\t\t\t 0.2375\n",
      "\t 347.3890 \t\t\t\t 0.2147\n",
      "\t 82.4292 \t\t\t\t 0.2697\n",
      "\t 310.5068 \t\t\t\t 0.2193\n",
      "\t 406.4690 \t\t\t\t 0.2074\n",
      "\t 281.2230 \t\t\t\t 0.2236\n",
      "\t 414.3710 \t\t\t\t 0.2066\n",
      "\t 391.5724 \t\t\t\t 0.2093\n",
      "\t 158.8301 \t\t\t\t 0.2483\n",
      "\t 315.4258 \t\t\t\t 0.2184\n",
      "\t 346.1933 \t\t\t\t 0.2148\n",
      "\t 205.3643 \t\t\t\t 0.2375\n",
      "\t 391.8137 \t\t\t\t 0.2087\n",
      "\t 313.0680 \t\t\t\t 0.2186\n",
      "\t 128.5528 \t\t\t\t 0.2560\n",
      "\t 106.7888 \t\t\t\t 0.2620\n"
     ]
    }
   ],
   "source": [
    "print(\"Resultado da Computacao Evolucionaria Multi-Objetivo em Python\")\n",
    "print(\"\\n\")\n",
    "print(f\"Número de Funções de Avaliacao: {funcoes_de_avaliacao}\")\n",
    "print(\"\\n\")\n",
    "print(\"=================================================================================\")\n",
    "print(\"|\\t\\t\\t\\tSumario \\t\\t\\t\\t\\t|\")\n",
    "print(\"---------------------------------------------------------------------------------\")\n",
    "print(\"\\t Funcao Objetivo 1 \\t\\t\\t Funcao Objetivo 2\")\n",
    "print(\"---------------------------------------------------------------------------------\")\n",
    "\n",
    "for solution in algorithm.result:\n",
    "    # imprime o resultado da função multiobjetivo\n",
    "    print('\\t %.4f'%(solution.objectives[0]), '\\t\\t\\t\\t %.4f'%(solution.objectives[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gráfico de Pareto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the results using matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter([solution.objectives[0] for solution in algorithm.result],\n",
    "            [solution.objectives[1] for solution in algorithm.result])\n",
    "#plt.xlim([600, 640])\n",
    "#plt.ylim([0.10, 0.40])\n",
    "plt.xlabel(\"F(Pg): Custo do Combustível [$/h]\")\n",
    "plt.ylabel(\"E(Pg): Emissão de SOx [ton/h]\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}