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 np
import pandas as pd
import random
from scipy.optimize import fsolve
import matplotlib.pyplot as plt
import heapq
from sklearn.model_selection import train_test_split
from tkinter import _flatten
from sklearn.utils import shuffle
from sklearn import preprocessing
from sklearn.decomposition import PCA
from 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，V2
population = 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 = 30
x_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()