python实现高效的遗传算法

遗传算法属于一种优化算法。

如果你有一个待优化函数，可以考虑次算法。假设你有一个变量x，通过某个函数可以求出对应的y，那么你通过预设的x可求出y_pred，y_pred差距与你需要的y当然越接近越好，这就需要引入适应度（fitness）的概念。假设

fitness = 1/(1+ads(y_pred - y)),那么误差越小，适应度越大，即该个体越易于存活。

设计该算法的思路如下：

（1）初始化种群，即在我需要的区间如[-100,100]内random一堆初始个体[x1,x2,x3...],这些个体是10进制形式的，为了后面的交叉与变异我们不妨将其转化为二进制形式。那么现在的问题是二进制取多少位合适呢？即编码（code）的长度是多少呢？

这就涉及一些信号方面的知识，比如两位的二进制表示的最大值是3（11），可以将区间化为4分，那么每一份区间range长度range/4，我们只需要让range/n小于我们定义的精度即可。n是二进制需要表示的最大，可以反解出二进制位数 。

（2）我们需要编写编码与解码函数。即code：将x1，x2...化为二进制，decode：在交叉变异后重新得到十进制数，用于计算fitness。

（3）交叉后变异函数编写都很简单，random一个point，指定两个x在point位置进行切片交换即是交叉。变异也是random一个point，让其值0变为1,1变为0。

（4）得到交叉变异后的个体，需要计算fitness进行种群淘汰，保留fitness最高的一部分种群。

（5）将最优的个体继续上面的操作，直到你定义的iteration结束为止。

不说了，上代码：

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 # 求染色体长度def getEncodeLength(decisionvariables, delta): # 将每个变量的编码长度放入数组 lengths = [] for decisionvar in decisionvariables: uper = decisionvar[1] low = decisionvar[0] # res()返回一个数组 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('染色体长度:', lengths) return lengths # 随机生成初始化种群def getinitialPopulation(length, populationSize): chromsomes = np.zeros((populationSize, length), dtype=np.int) for popusize in range(populationSize): # np.random.randit()产生[0,2)之间的随机整数，第三个参数表示随机数的数量 chromsomes[popusize, :] = np.random.randint(0, 2, length) return chromsomes # 染色体解码得到表现形的解def getDecode(population, encodelength, decisionvariables, delta): # 得到population中有几个元素 populationsize = population.shape[0] length = len(encodelength) decodeVariables = np.zeros((populationsize, length), dtype=np.float) # 将染色体拆分添加到解码数组decodeVariables中 for i, populationchild in enumerate(population): # 设置起始点 start = 0 for j, lengthchild in enumerate(encodelength): power = lengthchild - 1 decimal = 0 start_end = start + lengthchild for k in range(start, start_end): # 二进制转为十进制 decimal += populationchild[k] * (2 ** power) power = power - 1 # 从下一个染色体开始 start = start_end lower = decisionvariables[j][0] uper = decisionvariables[j][1] # 转换为表现形 decodevalue = lower + decimal * (uper - lower) / (2 ** lengthchild - 1) # 将解添加到数组中 decodeVariables[i][j] = decodevalue return decodeVariables # 选择新的种群def selectNewPopulation(decodepopu, cum_probability): # 获取种群的规模和 m, n = decodepopu.shape # 初始化新种群 newPopulation = np.zeros((m, n)) for i in range(m): # 产生一个0到1之间的随机数 randomnum = np.random.random() # 轮盘赌选择 for j in range(m): if (randomnum < cum_probability[j]): newPopulation[i] = decodepopu[j] break return newPopulation # 新种群交叉def crossNewPopulation(newpopu, prob): m, n = newpopu.shape # uint8将数值转换为无符号整型 numbers = np.uint8(m * prob) # 如果选择的交叉数量为奇数，则数量加1 if numbers % 2 != 0: numbers = numbers + 1 # 初始化新的交叉种群 updatepopulation = np.zeros((m, n), dtype=np.uint8) # 随机生成需要交叉的染色体的索引号 index = random.sample(range(m), numbers) # 不需要交叉的染色体直接复制到新的种群中 for i in range(m): if not index.__contains__(i): updatepopulation[i] = newpopu[i] # 交叉操作 j = 0 while j < numbers: # 随机生成一个交叉点，np.random.randint()返回的是一个列表 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 # 变异操作def mutation(crosspopulation, mutaprob): # 初始化变异种群 mutationpopu = np.copy(crosspopulation) m, n = crosspopulation.shape # 计算需要变异的基因数量 mutationnums = np.uint8(m * n * mutaprob) # 随机生成变异基因的位置 mutationindex = random.sample(range(m * n), mutationnums) # 变异操作 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 # 找到重新生成的种群中适应度值最大的染色体生成新种群def findMaxPopulation(population, maxevaluation, maxSize): #将数组转换为列表 #maxevalue = maxevaluation.flatten() maxevaluelist = maxevaluation # 找到前100个适应度最大的染色体的索引 maxIndex = map(maxevaluelist.index, heapq.nlargest(maxSize, maxevaluelist)) index = list(maxIndex) colume = population.shape[1] # 根据索引生成新的种群 maxPopulation = np.zeros((maxSize, colume)) i = 0 for ind in index: maxPopulation[i] = population[ind] i = i + 1 return maxPopulation # 得到每个个体的适应度值及累计概率def getFitnessValue(decode,x_train,y_train): # 得到种群的规模和决策变量的个数 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))) # 得到每个个体被选择的概率 probability = fitnessValue / np.sum(fitnessValue) # 得到每个染色体被选中的累积概率，用于轮盘赌算子使用 cum_probability = np.cumsum(probability) return fitnessValue, cum_probability def getFitnessValue_accuracy(decode,x_train,y_train): # 得到种群的规模和决策变量的个数 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)) # 得到每个个体被选择的概率 probability = fitnessValue / np.sum(fitnessValue) # 得到每个染色体被选中的累积概率，用于轮盘赌算子使用 cum_probability = np.cumsum(probability) return fitnessValue, cum_probability def getXY(): # 要打开的文件名 data_set = pd.read_csv(’all-bp.csv’, header=None) # 取出“特征”和“标签”，并做了转置，将列转置为行 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列是标签 # 分训练和测试集 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))

上面的计算适应度函数需要自己更具实际情况调整。

optimalvalue = []optimalvariables = [] # 两个决策变量的上下界，多维数组之间必须加逗号decisionVariables = [[-100,100]]*49# 精度delta = 0.001# 获取染色体长度EncodeLength = getEncodeLength(decisionVariables, delta)# 种群数量initialPopuSize = 100# 初始生成100个种群,20,5,20,4分别对用W1，V1，W2，V2population = getinitialPopulation(sum(EncodeLength), initialPopuSize)print('polpupation.shape:',population.shape)# 最大进化代数maxgeneration = 4000# 交叉概率prob = 0.8# 变异概率mutationprob = 0.5# 新生成的种群数量maxPopuSize = 30x_train, x_test, y_train, y_test = getXY() for generation in range(maxgeneration): # 对种群解码得到表现形 print(generation) decode = getDecode(population, EncodeLength, decisionVariables, delta) #print(’the shape of decode:’,decode.shape # 得到适应度值和累计概率值 evaluation, cum_proba = getFitnessValue_accuracy(decode,x_train,y_train) # 选择新的种群 newpopulations = selectNewPopulation(population, cum_proba) # 新种群交叉 crossPopulations = crossNewPopulation(newpopulations, prob) # 变异操作 mutationpopulation = mutation(crossPopulations, mutationprob) # 将父母和子女合并为新的种群 totalpopulation = np.vstack((population, mutationpopulation)) # 最终解码 final_decode = getDecode(totalpopulation, EncodeLength, decisionVariables, delta) # 适应度评估 final_evaluation, final_cumprob = getFitnessValue_accuracy(final_decode,x_train,y_train) #选出适应度最大的100个重新生成种群 population = findMaxPopulation(totalpopulation, final_evaluation, maxPopuSize) # 找到本轮中适应度最大的值 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)# 图例设置plt.xlabel(’Iteration’)plt.ylabel(’Accuracy’)plt.show()

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