遺傳算法屬于一種優化算法。

如果你有一個待優化函數，可以考慮次算法。假設你有一個變量x，通過某個函數可以求出對應的y，那么你通過預設的x可求出y_pred，y_pred差距與你需要的y當然越接近越好，這就需要引入適應度（fitness）的概念。假設

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

設計該算法的思路如下：

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

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

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

（3）交叉后變異函數編寫都很簡單，random一個point，指定兩個x在point位置進行切片交換即是交叉。變異也是random一個point，讓其值0變為1,1變為0。

（4）得到交叉變異后的個體，需要計算fitness進行種群淘汰，保留fitness最高的一部分種群。

（5）將最優的個體繼續上面的操作，直到你定義的iteration結束為止。

不說了，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 # 求染色體長度def getEncodeLength(decisionvariables, delta): # 將每個變量的編碼長度放入數組 lengths = [] for decisionvar in decisionvariables: uper = decisionvar[1] low = decisionvar[0] # res()返回一個數組 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('染色體長度:', lengths) return lengths # 隨機生成初始化種群def getinitialPopulation(length, populationSize): chromsomes = np.zeros((populationSize, length), dtype=np.int) for popusize in range(populationSize): # np.random.randit()產生[0,2)之間的隨機整數，第三個參數表示隨機數的數量 chromsomes[popusize, :] = np.random.randint(0, 2, length) return chromsomes # 染色體解碼得到表現形的解def getDecode(population, encodelength, decisionvariables, delta): # 得到population中有幾個元素 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組decodeVariables中 for i, populationchild in enumerate(population): # 設置起始點 start = 0 for j, lengthchild in enumerate(encodelength): power = lengthchild - 1 decimal = 0 start_end = start + lengthchild for k in range(start, start_end): # 二進制轉為十進制 decimal += populationchild[k] * (2 ** power) power = power - 1 # 從下一個染色體開始 start = start_end lower = decisionvariables[j][0] uper = decisionvariables[j][1] # 轉換為表現形 decodevalue = lower + decimal * (uper - lower) / (2 ** lengthchild - 1) # 將解添加到數組中 decodeVariables[i][j] = decodevalue return decodeVariables # 選擇新的種群def selectNewPopulation(decodepopu, cum_probability): # 獲取種群的規模和 m, n = decodepopu.shape # 初始化新種群 newPopulation = np.zeros((m, n)) for i in range(m): # 產生一個0到1之間的隨機數 randomnum = np.random.random() # 輪盤賭選擇 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將數值轉換為無符號整型 numbers = np.uint8(m * prob) # 如果選擇的交叉數量為奇數，則數量加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) # 隨機生成需要交叉的染色體的索引號 index = random.sample(range(m), numbers) # 不需要交叉的染色體直接復制到新的種群中 for i in range(m): if not index.__contains__(i): updatepopulation[i] = newpopu[i] # 交叉操作 j = 0 while j < numbers: # 隨機生成一個交叉點，np.random.randint()返回的是一個列表 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 # 計算需要變異的基因數量 mutationnums = np.uint8(m * n * mutaprob) # 隨機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度值最大的染色體生成新種群def findMaxPopulation(population, maxevaluation, maxSize): #將數組轉換為列表 #maxevalue = maxevaluation.flatten() maxevaluelist = maxevaluation # 找到前100個適應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 # 得到每個個體的適應度值及累計概率def getFitnessValue(decode,x_train,y_train): # 得到種群的規模和決策變量的個數 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))) # 得到每個個體被選擇的概率 probability = fitnessValue / np.sum(fitnessValue) # 得到每個染色體被選中的累積概率，用于輪盤賭算子使用 cum_probability = np.cumsum(probability) return fitnessValue, cum_probability def getFitnessValue_accuracy(decode,x_train,y_train): # 得到種群的規模和決策變量的個數 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)) # 得到每個個體被選擇的概率 probability = fitnessValue / np.sum(fitnessValue) # 得到每個染色體被選中的累積概率，用于輪盤賭算子使用 cum_probability = np.cumsum(probability) return fitnessValue, cum_probability def getXY(): # 要打開的文件名 data_set = pd.read_csv(’all-bp.csv’, header=None) # 取出“特征”和“標簽”，并做了轉置，將列轉置為行 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列是標簽 # 分訓練和測試集 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))

上面的計算適應度函數需要自己更具實際情況調整。

optimalvalue = []optimalvariables = [] # 兩個決策變量的上下界，多維數組之間必須加逗號decisionVariables = [[-100,100]]*49# 精度delta = 0.001# 獲取染色體長度EncodeLength = getEncodeLength(decisionVariables, delta)# 種群數量initialPopuSize = 100# 初始生成100個種群,20,5,20,4分別對用W1，V1，W2，V2population = getinitialPopulation(sum(EncodeLength), initialPopuSize)print('polpupation.shape:',population.shape)# 最大進化代數maxgeneration = 4000# 交叉概率prob = 0.8# 變異概率mutationprob = 0.5# 新生成的種群數量maxPopuSize = 30x_train, x_test, y_train, y_test = getXY() for generation in range(maxgeneration): # 對種群解碼得到表現形 print(generation) decode = getDecode(population, EncodeLength, decisionVariables, delta) #print(’the shape of decode:’,decode.shape # 得到適應度值和累計概率值 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) # 適應度評估 final_evaluation, final_cumprob = getFitnessValue_accuracy(final_decode,x_train,y_train) #選出適應度最大的100個重新生成種群 population = findMaxPopulation(totalpopulation, final_evaluation, maxPopuSize) # 找到本輪中適應度最大的值 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)# 圖例設置plt.xlabel(’Iteration’)plt.ylabel(’Accuracy’)plt.show()

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