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lucasmpavelski/trabalho_rnas_1.ipynb

Created October 18, 2017 11:35
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Testes RNAs para o flowshop - Parte I
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trabalho_rnas_1.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Testes RNAs para o flowshop - Parte I"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Os primeiros testes para resolução do problema flowshop com redes neurais artificiais (RNAs) utilizou-se se uma implementação simples, sem uso de bibliotecas especializadas. O objetivo foi entender o funcionamento das RNAs e seu algoritmo de treinamento, bem como exercitar os conceitos vistos em aula.\n",
"\n",
"Foram utilizadas a linguagem Python e a biblioteca de álgebra linear numpy. Esta implementação tomou como base o código disponível em [ML-Exercise4](https://github.com/jdwittenauer/ipython-notebooks/blob/master/notebooks/ml/ML-Exercise4.ipynb) de Wittenauer (2017)."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Pré-processamento dos dados\n",
"\n",
"Cada linha do arquivo `N_M_makespan.csv` possui uma instância do problema flowshop com N tarefas e M máquinas, juntamente com a sequência ótima e o makespan correspondente (não utilizado). Para cada linha, são geradas N exemplos de treinamento (um para cada saída da rede). Finalmente, as entradas e saídas são normalizadas para valores entre 0 e 1."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"((70000, 30), (70000, 1))"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"no_jobs = 7\n",
"no_mach = 10\n",
"dt = pd.read_csv('data/%d_%d_makespan.csv' % (no_jobs, no_mach))\n",
"no_data = dt.shape[0]\n",
"no_samples = no_data * no_jobs\n",
"input_dim = no_mach * 3\n",
"output_dim = 1\n",
"\n",
"proc_times = np.reshape(dt.values[:,0:no_jobs*no_mach] / 100, (no_data, no_jobs, no_mach))\n",
"means = np.repeat(proc_times.mean(axis=1), no_jobs, axis=0)\n",
"stds = np.repeat(proc_times.std(axis=1), no_jobs, axis=0)\n",
"\n",
"input_data = np.empty((no_samples, input_dim))\n",
"input_data[:,0:no_mach] = proc_times.reshape((no_samples, no_mach))\n",
"input_data[:,no_mach:2*no_mach] = means\n",
"input_data[:,2*no_mach:3*no_mach] = stds\n",
"\n",
"output_data = dt.values[:,no_jobs*no_mach:(no_jobs*no_mach+no_jobs)].reshape((no_data * no_jobs, output_dim))\n",
"output_data = 0.1 + (0.8 / (no_jobs - 1)) * output_data\n",
"\n",
"X = input_data\n",
"y = output_data\n",
"\n",
"X.shape, y.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Definição do modelo\n",
"\n",
"A função sigmoid foi utilizada como ativação da camada oculta:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# função sigmoid e sua derivada\n",
"def sigmoid(z):\n",
" return 1 / (1 + np.exp(-z))\n",
"\n",
"def sigmoid_gradient(z):\n",
" return np.multiply(sigmoid(z), (1 - sigmoid(z)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A rede é constituída por três camadas: entrada, intermediária e saída. A função que realiza a passagem dos valores para frente é:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def forward_propagate(X, w1, w2):\n",
" m = X.shape[0]\n",
" a1 = np.insert(X, 0, values=np.ones(m), axis=1)\n",
" z2 = a1 * w1.T\n",
" a2 = np.insert(sigmoid(z2), 0, values=np.ones(m), axis=1)\n",
" z3 = a2 * w2.T\n",
" h = sigmoid(z3)\n",
" # retorna a saida de cada camada\n",
" return a1, z2, a2, z3, h"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A função custo abaixo realiza uma propagação e calcula o erro da rede com o MSE:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def cost(params, input_size, hidden_size, num_labels, X, y, learning_rate):\n",
" m = X.shape[0]\n",
" X = np.matrix(X)\n",
" y = np.matrix(y)\n",
" \n",
" theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))\n",
" theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))\n",
" \n",
" a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)\n",
" \n",
" J = 0\n",
" for i in range(m):\n",
" J += np.sum((h[i,:] - y[i,:]) ** 2)\n",
" J = J / m\n",
" \n",
" return J"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inicialização da rede e parâmetros\n",
"\n",
"Os valores de pesos são inicializados entre -0.25 e 0.25, a taxa de aprendizado é 1 e o número de neurônos ocultos é 25:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"((25, 31), (1, 26))"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"input_size = X.shape[1]\n",
"hidden_size = 25\n",
"num_labels = y.shape[1]\n",
"learning_rate = 1\n",
"\n",
"params = (np.random.random(size=hidden_size * (input_size + 1) + num_labels * (hidden_size + 1)) - 0.5) * 0.25\n",
"\n",
"m = X.shape[0]\n",
"X = np.matrix(X)\n",
"y = np.matrix(y)\n",
"\n",
"theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))\n",
"theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))\n",
"\n",
"theta1.shape, theta2.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Treinamento\n",
"\n",
"O algoritmo de retropropagação é implementado para calcular o gradiente de cada camada e retorná-los como um único vetor, juntamente com o erro de treinamento atual:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def backprop(params, input_size, hidden_size, num_labels, X, y, learning_rate):\n",
" m = X.shape[0]\n",
" X = np.matrix(X)\n",
" y = np.matrix(y)\n",
" # divide os parâmetros de cada camada (duas matrizes com os termos de bias)\n",
" theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))\n",
" theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))\n",
" # propaga os valores de entrada\n",
" a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)\n",
" # zera os valores dos gradientes\n",
" delta1 = np.zeros(theta1.shape) # (25, 401)\n",
" delta2 = np.zeros(theta2.shape) # (10, 26)\n",
" # calcula o erro atual\n",
" J = 0\n",
" for i in range(m):\n",
" J += np.sum((h[i,:] - y[i,:]) ** 2)\n",
" J = J / m\n",
" # retropropagação\n",
" for t in range(m):\n",
" a1t = a1[t,:]\n",
" z2t = z2[t,:]\n",
" a2t = a2[t,:]\n",
" ht = h[t,:]\n",
" yt = y[t,:]\n",
" d3t = ht - yt\n",
" z2t = np.insert(z2t, 0, values=np.ones(1))\n",
" d2t = np.multiply((theta2.T * d3t.T).T, sigmoid_gradient(z2t))\n",
" delta1 = delta1 + (d2t[:,1:]).T * a1t\n",
" delta2 = delta2 + d3t.T * a2t\n",
" delta1 = delta1 / m\n",
" delta2 = delta2 / m\n",
" # concatena os gradientes em um único vetor\n",
" grad = np.concatenate((np.ravel(delta1), np.ravel(delta2)))\n",
" return J, grad"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Em seguida otimiza os pesos iterativamente utilizando o algoritmo de Newton truncado, similar ao gradiente descenente, pois não usa os valores da Hessiana, apenas atualiza os parâmetros com base na derivada."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
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" 6.81624151e-04, 6.80469711e-04, 6.79031542e-04,\n",
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" 3.52139996e-04, 3.52359740e-04, 3.52449342e-04,\n",
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" -2.63605627e-02, -2.63631251e-02, -2.72048205e-02])\n",
" message: 'Max. number of function evaluations reached'\n",
" nfev: 2\n",
" nit: 0\n",
" status: 3\n",
" success: False\n",
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" -8.95753525e-02, 1.44886981e-02, 2.52888348e-02,\n",
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" 3.21184473e-02, 7.18275766e-02, -4.90966497e-02,\n",
" 1.12374830e-01, -7.70413966e-02, -1.18050061e-01,\n",
" 9.25673025e-02, -5.63656077e-02, 3.58796865e-02,\n",
" 6.30322736e-02, -1.12092039e-01, -9.09552896e-02,\n",
" -2.00078157e-02, -1.91220344e-02, -1.34185096e-02,\n",
" -1.70743244e-02, -1.04779989e-01, -6.58404925e-02,\n",
" 4.06562223e-02, -2.57796897e-02, -4.80793966e-02,\n",
" -5.82135366e-02, 1.17761843e-01, 5.97710202e-02,\n",
" 3.56875364e-03, 1.13943342e-01, -1.13211144e-01,\n",
" 1.21689186e-01, 1.07201040e-01, 4.05497634e-02,\n",
" 2.22329774e-02, 5.89476127e-03, -1.08163694e-01,\n",
" 8.33948914e-02, 3.33529172e-02, -1.15250333e-01,\n",
" 8.67043677e-02, -4.67282411e-02, 1.07859040e-01,\n",
" 5.51873641e-02, -1.47855956e-02, 2.80795830e-02,\n",
" 3.49517619e-02, 5.85206844e-02, -4.52447042e-02,\n",
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" -8.91706670e-02, 3.55074771e-02, 5.59928887e-02,\n",
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" -7.15199341e-02, -4.73612148e-02, 1.08580770e-01,\n",
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" -7.54875666e-02, -1.36464596e-02, -7.71573480e-02,\n",
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" -3.81380127e-02, -5.05663866e-02, -8.24695715e-02,\n",
" -1.13404344e-01, 5.15800625e-02, -3.66510057e-03,\n",
" 7.28371262e-02, -9.21072276e-02, 1.42359266e-02,\n",
" -1.01002721e-02, -1.03648470e-01, -5.34525459e-03,\n",
" -8.25366426e-02, -9.67566272e-02, -1.64295830e-02,\n",
" -9.41195064e-02, 2.65334885e-02, -5.19784262e-02,\n",
" -4.54976814e-02, 5.67521335e-03, 4.43265268e-02,\n",
" -7.62736510e-02, -5.93229831e-02, -1.23981227e-01,\n",
" 7.31516644e-02, -5.95764649e-02, -1.18860096e-01,\n",
" -1.07534123e-01, 1.11174421e-01, 3.70504970e-02,\n",
" -1.16826433e-01, 9.91950541e-02, -2.46058583e-03,\n",
" 1.17291188e-01, 8.89449030e-02, 6.87024196e-02,\n",
" 7.03853365e-02, 9.01544287e-02, 8.00773174e-02,\n",
" -6.04898167e-02, -1.18795521e-01, 7.18502636e-02,\n",
" 5.69794249e-02, 7.96901024e-02, -4.81569808e-02,\n",
" -3.73464691e-02, 1.01958881e-02, -2.74985893e-02,\n",
" 1.00229813e-01, -9.69046979e-02, -5.52187747e-02,\n",
" 8.18466663e-02, 6.26641441e-02, 2.06996989e-02,\n",
" -7.29335012e-02, -8.19657086e-02, -8.16010265e-02,\n",
" 4.72417590e-02, 8.53051327e-02, 1.57985738e-03,\n",
" -9.80869743e-02, -5.97252516e-02, -4.05151788e-02,\n",
" -1.08644971e-02, -8.34748282e-02, -8.47595910e-02,\n",
" 5.40605655e-02, 3.75889472e-02, -1.08633863e-01,\n",
" -2.44132006e-02, -5.57597804e-02, -9.85676116e-02,\n",
" -7.01857986e-02, 1.07918721e-03, -9.46009194e-02,\n",
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" -8.96843460e-02, -7.44907054e-02, -7.37676377e-02,\n",
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" 7.64446470e-02, 8.55285574e-03, -4.71039007e-02,\n",
" -9.07868449e-02, 5.88761053e-02, 1.42775654e-02,\n",
" -4.48080372e-02, -9.66816643e-02, 1.15159944e-01,\n",
" -1.01961203e-01, 3.46479379e-02, -1.05328608e-01,\n",
" -3.52798131e-05, 4.91123771e-02, -1.24593827e-02,\n",
" 1.09669421e-01, 1.19981532e-01, 3.31333715e-02,\n",
" -8.91624082e-02, -8.39736724e-02, -9.94654804e-02,\n",
" -1.10629315e-01, -4.27813984e-02, 2.73388502e-03,\n",
" -1.57413494e-02, -1.21876513e-01, 8.96638520e-02,\n",
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" 9.21133037e-02, 9.71186494e-02, -8.12240310e-02,\n",
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" -1.22626607e-01, 1.02768154e-01, 5.89245680e-03,\n",
" 5.98690529e-02, 1.03655961e-01, -1.23348847e-01,\n",
" 9.74269851e-02, 4.58720201e-02, 1.28668591e-02,\n",
" -1.17337654e-01, -3.22647475e-02, -1.16642387e-02,\n",
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" -7.24899059e-02, -8.77139472e-02, 5.29197867e-03,\n",
" 4.04586368e-02, -2.47712196e-02, 1.07108267e-01,\n",
" 1.32330162e-02, 6.10819164e-02, 1.68997096e-02,\n",
" 2.24005158e-02, -1.16974941e-02, -1.11778952e-02,\n",
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" -5.29157400e-02, -1.12003399e-01, -8.95586718e-02,\n",
" 6.84295341e-03, 4.58174350e-02, 7.72624607e-02,\n",
" 1.03048706e-01, -5.27648087e-02, -2.70823565e-02,\n",
" -5.72125305e-02, -4.29143672e-02, -7.49979218e-02,\n",
" -3.66755631e-02, -1.85301112e-02, 6.15696021e-02,\n",
" -1.12007006e-01, 5.79944410e-02, 6.59277695e-02,\n",
" -1.00806096e-01, -1.02739253e-01, 3.83940687e-02,\n",
" -8.96987221e-02, -6.99505749e-02, 1.08068756e-01,\n",
" 4.23218390e-02, 4.60837060e-03, 1.06295758e-01,\n",
" -1.11758149e-01, 3.76292812e-02, 6.30945765e-02,\n",
" -1.20905514e-01, 6.56509655e-02, -9.26557924e-02,\n",
" -7.84248040e-02, -1.06195526e-01, -5.83900725e-02,\n",
" -1.09854219e-01, -1.04942777e-01, 1.19193557e-01,\n",
" -9.69883858e-02, -1.23364181e-02, 8.59977542e-02,\n",
" 1.22783047e-01, 1.85859255e-02, -1.01694149e-01,\n",
" 7.45597138e-02, 1.08103416e-01, -7.13870256e-02,\n",
" 1.10763573e-01, -9.78190593e-02, 1.21717088e-01,\n",
" 2.17584811e-02, -4.20167615e-02, -2.23513985e-02,\n",
" 6.87849143e-02, 1.01027185e-01, 9.71781261e-02,\n",
" -4.55811565e-02, -9.41280740e-02, 4.25590912e-03,\n",
" 9.36397260e-02, 1.12313080e-01, 4.43989602e-02,\n",
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" 1.12660642e-01, 1.16185156e-01, 4.03551379e-02,\n",
" -2.37625318e-02, -4.30299556e-02, 6.14176061e-02,\n",
" -1.28718470e-02, -3.63712667e-02, -4.27056290e-02,\n",
" -7.90924010e-02, -8.72041987e-02, 1.16898735e-01,\n",
" -4.32005729e-02, -6.87679342e-03, -4.72371068e-02,\n",
" -1.21289484e-01, -6.67406661e-02, 6.47198713e-02,\n",
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" -1.17450985e-01, -5.19511442e-02, 9.13224733e-02,\n",
" 8.74282908e-02, 9.44942019e-02, 2.13691747e-02,\n",
" -7.34423224e-02, 1.18736616e-01, -2.91985312e-02,\n",
" 8.64289281e-02, -1.13842522e-01, -6.12030623e-02,\n",
" 8.89420331e-02, 3.62042881e-02, 4.91349050e-02,\n",
" 1.20398563e-01, 5.79289354e-03, 7.90363626e-02,\n",
" -6.44088622e-02, -1.21776648e-01, -5.53010221e-02,\n",
" 7.34590461e-03, -3.02188125e-02, 1.23121073e-01,\n",
" 1.16406417e-01, -1.07837902e-01, -4.52308675e-02,\n",
" -9.97823628e-02, 4.55602013e-02, 5.86677757e-02,\n",
" 7.42760516e-02, 8.13179081e-02, 3.90270523e-02,\n",
" 4.56374692e-02, -7.96851693e-02, -8.72721753e-02,\n",
" -9.08583324e-02, 7.47641968e-02, -3.62796845e-02,\n",
" -1.10344844e-01, -9.60142854e-02, -1.01990296e-01,\n",
" 6.57264011e-02, 9.91527834e-02, -9.05189201e-02,\n",
" 8.18551608e-02, -7.69993309e-02, -1.22232341e-01,\n",
" 7.53107866e-02, 1.24028006e-01, -4.83372280e-02,\n",
" 6.17277371e-03, 1.12688653e-01, -6.20577724e-02,\n",
" 7.10878695e-02, 1.17302454e-01, 8.26895738e-02,\n",
" 6.56379739e-02, -1.05810739e-01, -6.12858708e-02,\n",
" -7.39834557e-02, 3.43612707e-02, -2.48933561e-02,\n",
" -7.63903800e-02, 3.08627742e-02, -3.81650237e-02,\n",
" -1.19673306e-01, 7.55765836e-02, 6.00135109e-02,\n",
" -2.28742183e-02, 3.53630139e-02, -9.96805263e-03,\n",
" 7.72938756e-03, -4.56387250e-03, -4.06815535e-02,\n",
" 6.18533622e-03, 1.47212572e-02, -2.43875197e-02,\n",
" 4.29445402e-02, -3.89498828e-02, -9.27393374e-02,\n",
" -5.22086441e-02, -2.26082583e-02, 9.57951422e-02,\n",
" 3.46120554e-02, -6.48856334e-02, -6.86339046e-02,\n",
" -1.12279742e-01, -5.05046065e-02, -1.06031523e-01,\n",
" -1.80377475e-04, 7.42575098e-03, 1.11170495e-01,\n",
" 8.25009047e-02, 1.18011169e-01, -5.29928763e-02,\n",
" -3.97497201e-02, 3.12659657e-02, -7.41696421e-02,\n",
" 9.75903964e-02, -9.35542355e-02, 8.80079439e-02,\n",
" -5.61856757e-02, 5.80452260e-02, 3.64823265e-02,\n",
" 9.15118609e-02, -1.88254288e-02, -6.10808719e-03,\n",
" 9.70787000e-02, 4.23711302e-02, 3.50691056e-02,\n",
" 9.57819568e-04, 4.26254221e-02, -5.22254409e-02,\n",
" -1.14700020e-01, 1.13905260e-01, -1.00506543e-01,\n",
" -1.15759757e-01, 3.76759741e-02, 6.83690573e-02,\n",
" -4.46735140e-02, 7.81807221e-02, -9.74186454e-02,\n",
" -6.72239414e-02, 1.06618473e-01, -2.85624594e-02,\n",
" 6.87452107e-02, -8.51354916e-02, -8.13989640e-02,\n",
" -1.09002344e-01, -4.75812514e-03, 1.15141498e-01,\n",
" -1.20282435e-01, 1.14322483e-01, 3.13306731e-02,\n",
" -1.01172873e-01, -1.22640813e-01, -1.64143127e-02,\n",
" -1.73890092e-02, -5.09458835e-02, -1.13819184e-01])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from scipy.optimize import minimize\n",
"num_epocas = 2\n",
"fmin = minimize(fun=backprop, x0=params, args=(input_size, hidden_size, num_labels, X, y, learning_rate), \n",
" method='TNC', jac=True, options={'maxiter': num_epocas})\n",
"fmin"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"O modelo é avaliado comparando-o as saídas geradas com as sequências ótimas:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Qualidade final: 115771.701975\n"
]
}
],
"source": [
"X = np.matrix(X)\n",
"theta1 = np.matrix(np.reshape(fmin.x[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))\n",
"theta2 = np.matrix(np.reshape(fmin.x[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))\n",
"\n",
"a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)\n",
"print(\"Qualidade final: \", np.sum(np.abs(h - y) * no_jobs))"
]
}
],
"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": "3.6.2"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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