遺傳算法屬于一種優(yōu)化算法。

如果你有一個(gè)待優(yōu)化函數(shù)，可以考慮次算法。假設(shè)你有一個(gè)變量x，通過(guò)某個(gè)函數(shù)可以求出對(duì)應(yīng)的y，那么你通過(guò)預(yù)設(shè)的x可求出y_pred，y_pred差距與你需要的y當(dāng)然越接近越好，這就需要引入適應(yīng)度（fitness）的概念。假設(shè)

fitness = 1/(1+ads(y_pred - y)),那么誤差越小，適應(yīng)度越大，即該個(gè)體越易于存活。

設(shè)計(jì)該算法的思路如下：

（1）初始化種群，即在我需要的區(qū)間如[-100,100]內(nèi)random一堆初始個(gè)體[x1,x2,x3...],這些個(gè)體是10進(jìn)制形式的，為了后面的交叉與變異我們不妨將其轉(zhuǎn)化為二進(jìn)制形式。那么現(xiàn)在的問(wèn)題是二進(jìn)制取多少位合適呢？即編碼（code）的長(zhǎng)度是多少呢？

這就涉及一些信號(hào)方面的知識(shí)，比如兩位的二進(jìn)制表示的最大值是3（11），可以將區(qū)間化為4分，那么每一份區(qū)間range長(zhǎng)度range/4，我們只需要讓range/n小于我們定義的精度即可。n是二進(jìn)制需要表示的最大，可以反解出二進(jìn)制位數(shù) 。

（2）我們需要編寫(xiě)編碼與解碼函數(shù)。即code：將x1，x2...化為二進(jìn)制，decode：在交叉變異后重新得到十進(jìn)制數(shù)，用于計(jì)算fitness。

（3）交叉后變異函數(shù)編寫(xiě)都很簡(jiǎn)單，random一個(gè)point，指定兩個(gè)x在point位置進(jìn)行切片交換即是交叉。變異也是random一個(gè)point，讓其值0變?yōu)?,1變?yōu)?。

（4）得到交叉變異后的個(gè)體，需要計(jì)算fitness進(jìn)行種群淘汰，保留fitness最高的一部分種群。

（5）將最優(yōu)的個(gè)體繼續(xù)上面的操作，直到你定義的iteration結(jié)束為止。

不說(shuō)了，上代碼：

import numpy as npimport pandas as pdimport randomfrom scipy.optimize import fsolveimport matplotlib.pyplot as pltimport heapqfrom sklearn.model_selection import train_test_splitfrom tkinter import _flattenfrom sklearn.utils import shufflefrom sklearn import preprocessingfrom sklearn.decomposition import PCAfrom matplotlib import rcParams # 求染色體長(zhǎng)度def getEncodeLength(decisionvariables, delta): # 將每個(gè)變量的編碼長(zhǎng)度放入數(shù)組 lengths = [] for decisionvar in decisionvariables: uper = decisionvar[1] low = decisionvar[0] # res()返回一個(gè)數(shù)組 res = fsolve(lambda x: ((uper - low) / delta - 2 ** x + 1), 30) # ceil()向上取整 length = int(np.ceil(res[0])) lengths.append(length) # print('染色體長(zhǎng)度:', lengths) return lengths # 隨機(jī)生成初始化種群def getinitialPopulation(length, populationSize): chromsomes = np.zeros((populationSize, length), dtype=np.int) for popusize in range(populationSize): # np.random.randit()產(chǎn)生[0,2)之間的隨機(jī)整數(shù)，第三個(gè)參數(shù)表示隨機(jī)數(shù)的數(shù)量 chromsomes[popusize, :] = np.random.randint(0, 2, length) return chromsomes # 染色體解碼得到表現(xiàn)形的解def getDecode(population, encodelength, decisionvariables, delta): # 得到population中有幾個(gè)元素 populationsize = population.shape[0] length = len(encodelength) decodeVariables = np.zeros((populationsize, length), dtype=np.float) # 將染色體拆分添加到解碼數(shù)組decodeVariables中 for i, populationchild in enumerate(population): # 設(shè)置起始點(diǎn) start = 0 for j, lengthchild in enumerate(encodelength): power = lengthchild - 1 decimal = 0 start_end = start + lengthchild for k in range(start, start_end): # 二進(jìn)制轉(zhuǎn)為十進(jìn)制 decimal += populationchild[k] * (2 ** power) power = power - 1 # 從下一個(gè)染色體開(kāi)始 start = start_end lower = decisionvariables[j][0] uper = decisionvariables[j][1] # 轉(zhuǎn)換為表現(xiàn)形 decodevalue = lower + decimal * (uper - lower) / (2 ** lengthchild - 1) # 將解添加到數(shù)組中 decodeVariables[i][j] = decodevalue return decodeVariables # 選擇新的種群def selectNewPopulation(decodepopu, cum_probability): # 獲取種群的規(guī)模和 m, n = decodepopu.shape # 初始化新種群 newPopulation = np.zeros((m, n)) for i in range(m): # 產(chǎn)生一個(gè)0到1之間的隨機(jī)數(shù) randomnum = np.random.random() # 輪盤(pán)賭選擇 for j in range(m): if (randomnum < cum_probability[j]): newPopulation[i] = decodepopu[j] break return newPopulation # 新種群交叉def crossNewPopulation(newpopu, prob): m, n = newpopu.shape # uint8將數(shù)值轉(zhuǎn)換為無(wú)符號(hào)整型 numbers = np.uint8(m * prob) # 如果選擇的交叉數(shù)量為奇數(shù)，則數(shù)量加1 if numbers % 2 != 0: numbers = numbers + 1 # 初始化新的交叉種群 updatepopulation = np.zeros((m, n), dtype=np.uint8) # 隨機(jī)生成需要交叉的染色體的索引號(hào) index = random.sample(range(m), numbers) # 不需要交叉的染色體直接復(fù)制到新的種群中 for i in range(m): if not index.__contains__(i): updatepopulation[i] = newpopu[i] # 交叉操作 j = 0 while j < numbers: # 隨機(jī)生成一個(gè)交叉點(diǎn)，np.random.randint()返回的是一個(gè)列表 crosspoint = np.random.randint(0, n, 1) crossPoint = crosspoint[0] # a = index[j] # b = index[j+1] updatepopulation[index[j]][0:crossPoint] = newpopu[index[j]][0:crossPoint] updatepopulation[index[j]][crossPoint:] = newpopu[index[j + 1]][crossPoint:] updatepopulation[index[j + 1]][0:crossPoint] = newpopu[j + 1][0:crossPoint] updatepopulation[index[j + 1]][crossPoint:] = newpopu[index[j]][crossPoint:] j = j + 2 return updatepopulation # 變異操作def mutation(crosspopulation, mutaprob): # 初始化變異種群 mutationpopu = np.copy(crosspopulation) m, n = crosspopulation.shape # 計(jì)算需要變異的基因數(shù)量 mutationnums = np.uint8(m * n * mutaprob) # 隨機(jī)生成變異基因的位置 mutationindex = random.sample(range(m * n), mutationnums) # 變異操作 for geneindex in mutationindex: # np.floor()向下取整返回的是float型 row = np.uint8(np.floor(geneindex / n)) colume = geneindex % n if mutationpopu[row][colume] == 0: mutationpopu[row][colume] = 1 else: mutationpopu[row][colume] = 0 return mutationpopu # 找到重新生成的種群中適應(yīng)度值最大的染色體生成新種群def findMaxPopulation(population, maxevaluation, maxSize): #將數(shù)組轉(zhuǎn)換為列表 #maxevalue = maxevaluation.flatten() maxevaluelist = maxevaluation # 找到前100個(gè)適應(yīng)度最大的染色體的索引 maxIndex = map(maxevaluelist.index, heapq.nlargest(maxSize, maxevaluelist)) index = list(maxIndex) colume = population.shape[1] # 根據(jù)索引生成新的種群 maxPopulation = np.zeros((maxSize, colume)) i = 0 for ind in index: maxPopulation[i] = population[ind] i = i + 1 return maxPopulation # 得到每個(gè)個(gè)體的適應(yīng)度值及累計(jì)概率def getFitnessValue(decode,x_train,y_train): # 得到種群的規(guī)模和決策變量的個(gè)數(shù) popusize, decisionvar = decode.shape fitnessValue = [] for j in range(len(decode)): W1 = decode[j][0:20].reshape(4,5) V1 = decode[j][20:25].T W2 = decode[j][25:45].reshape(5,4) V2 = decode[j][45:].T error_all = [] for i in range(len(x_train)): #get values of hidde layer X2 = sigmoid(x_train[i].T.dot(W1)+V1) #get values of prediction y Y_hat = sigmoid(X2.T.dot(W2)+V2) #get error when input dimension is i error = sum(abs(Y_hat - y_train[i])) error_all.append(error) #get fitness when W and V is j fitnessValue.append(1/(1+sum(error_all))) # 得到每個(gè)個(gè)體被選擇的概率 probability = fitnessValue / np.sum(fitnessValue) # 得到每個(gè)染色體被選中的累積概率，用于輪盤(pán)賭算子使用 cum_probability = np.cumsum(probability) return fitnessValue, cum_probability def getFitnessValue_accuracy(decode,x_train,y_train): # 得到種群的規(guī)模和決策變量的個(gè)數(shù) popusize, decisionvar = decode.shape fitnessValue = [] for j in range(len(decode)): W1 = decode[j][0:20].reshape(4,5) V1 = decode[j][20:25].T W2 = decode[j][25:45].reshape(5,4) V2 = decode[j][45:].T accuracy = [] for i in range(len(x_train)): #get values of hidde layer X2 = sigmoid(x_train[i].T.dot(W1)+V1) #get values of prediction y Y_hat = sigmoid(X2.T.dot(W2)+V2) #get error when input dimension is i accuracy.append(sum(abs(np.round(Y_hat) - y_train[i]))) fitnessValue.append(sum([m == 0 for m in accuracy])/len(accuracy)) # 得到每個(gè)個(gè)體被選擇的概率 probability = fitnessValue / np.sum(fitnessValue) # 得到每個(gè)染色體被選中的累積概率，用于輪盤(pán)賭算子使用 cum_probability = np.cumsum(probability) return fitnessValue, cum_probability def getXY(): # 要打開(kāi)的文件名 data_set = pd.read_csv(’all-bp.csv’, header=None) # 取出“特征”和“標(biāo)簽”，并做了轉(zhuǎn)置，將列轉(zhuǎn)置為行 X_minMax1 = data_set.iloc[:, 0:12].values # 前12列是特征 min_max_scaler = preprocessing.MinMaxScaler() X_minMax = min_max_scaler.fit_transform(X_minMax1) # 0-1 range transfer = PCA(n_components=0.9) data1 = transfer.fit_transform(X_minMax) #print(’PCA processed shape:’,data1.shape) X = data1 Y = data_set.iloc[ : , 12:16].values # 后3列是標(biāo)簽 # 分訓(xùn)練和測(cè)試集 x_train, x_test, y_train, y_test = train_test_split(X, Y, test_size=0.3) return x_train, x_test, y_train, y_test def sigmoid(z): return 1 / (1 + np.exp(-z))

上面的計(jì)算適應(yīng)度函數(shù)需要自己更具實(shí)際情況調(diào)整。

optimalvalue = []optimalvariables = [] # 兩個(gè)決策變量的上下界，多維數(shù)組之間必須加逗號(hào)decisionVariables = [[-100,100]]*49# 精度delta = 0.001# 獲取染色體長(zhǎng)度EncodeLength = getEncodeLength(decisionVariables, delta)# 種群數(shù)量initialPopuSize = 100# 初始生成100個(gè)種群,20,5,20,4分別對(duì)用W1，V1，W2，V2population = getinitialPopulation(sum(EncodeLength), initialPopuSize)print('polpupation.shape:',population.shape)# 最大進(jìn)化代數(shù)maxgeneration = 4000# 交叉概率prob = 0.8# 變異概率mutationprob = 0.5# 新生成的種群數(shù)量maxPopuSize = 30x_train, x_test, y_train, y_test = getXY() for generation in range(maxgeneration): # 對(duì)種群解碼得到表現(xiàn)形 print(generation) decode = getDecode(population, EncodeLength, decisionVariables, delta) #print(’the shape of decode:’,decode.shape # 得到適應(yīng)度值和累計(jì)概率值 evaluation, cum_proba = getFitnessValue_accuracy(decode,x_train,y_train) # 選擇新的種群 newpopulations = selectNewPopulation(population, cum_proba) # 新種群交叉 crossPopulations = crossNewPopulation(newpopulations, prob) # 變異操作 mutationpopulation = mutation(crossPopulations, mutationprob) # 將父母和子女合并為新的種群 totalpopulation = np.vstack((population, mutationpopulation)) # 最終解碼 final_decode = getDecode(totalpopulation, EncodeLength, decisionVariables, delta) # 適應(yīng)度評(píng)估 final_evaluation, final_cumprob = getFitnessValue_accuracy(final_decode,x_train,y_train) #選出適應(yīng)度最大的100個(gè)重新生成種群 population = findMaxPopulation(totalpopulation, final_evaluation, maxPopuSize) # 找到本輪中適應(yīng)度最大的值 optimalvalue.append(np.max(final_evaluation)) index = np.where(final_evaluation == max(final_evaluation)) optimalvariables.append(list(final_decode[index[0][0]]))

fig = plt.figure(dpi = 160,figsize=(5,4)) config = {'font.family':'serif', #serif'font.size': 10,'mathtext.fontset':’stix’,}rcParams.update(config)plt.plot(np.arange(len(optimalvalue)), optimalvalue, color='y', lw=0.8, ls=’-’, marker=’o’, ms=8)# 圖例設(shè)置plt.xlabel(’Iteration’)plt.ylabel(’Accuracy’)plt.show()

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