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   源码介绍

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遗传算法

import numpy as np  
from scipy.optimize import fsolve, basinhopping  
import random  
import timeit  
  
  
# 根据解的精度确定染色体(chromosome)的长度  
# 需要根据决策变量的上下边界来确定  
def getEncodedLength(delta=0.0001, boundarylist=[]):  
    # 每个变量的编码长度  
    lengths = []  
    for i in boundarylist:  
        lower = i[0]  
        upper = i[1]  
        # lamnda 代表匿名函数f(x)=0,50代表搜索的初始解  
        res = fsolve(lambda x: ((upper - lower) * 1 / delta) - 2 ** x - 1, 50)  
        length = int(np.floor(res[0]))  
        lengths.append(length)  
    return lengths  
    pass  
  
  
# 随机生成初始编码种群  
def getIntialPopulation(encodelength, populationSize):  
    # 随机化初始种群为0  
    chromosomes = np.zeros((populationSize, sum(encodelength)), dtype=np.uint8)  
    for i in range(populationSize):  
        chromosomes[i, :] = np.random.randint(0, 2, sum(encodelength))  
    # print('chromosomes shape:', chromosomes.shape)  
    return chromosomes  
  
  
# 染色体解码得到表现型的解  
def decodedChromosome(encodelength, chromosomes, boundarylist, delta=0.0001):  
    populations = chromosomes.shape[0]  
    variables = len(encodelength)  
    decodedvalues = np.zeros((populations, variables))  
    for k, chromosome in enumerate(chromosomes):  
        chromosome = chromosome.tolist()  
        start = 0  
        for index, length in enumerate(encodelength):  
            # 将一个染色体进行拆分，得到染色体片段  
            power = length - 1  
            # 解码得到的10进制数字  
            demical = 0  
            for i in range(start, length   start):  
                demical  = chromosome[i] * (2 ** power)  
                power -= 1  
            lower = boundarylist[index][0]  
            upper = boundarylist[index][1]  
            decodedvalue = lower   demical * (upper - lower) / (2 ** length - 1)  
            decodedvalues[k, index] = decodedvalue  
            # 开始去下一段染色体的编码  
            start = length  
    return decodedvalues  
  
  
# 得到个体的适应度值及每个个体被选择的累积概率  
def getFitnessValue(func, chromosomesdecoded):  
    # 得到种群规模和决策变量的个数  
    population, nums = chromosomesdecoded.shape  
    # 初始化种群的适应度值为0  
    fitnessvalues = np.zeros((population, 1))  
    # 计算适应度值  
    for i in range(population):  
        fitnessvalues[i, 0] = func(chromosomesdecoded[i, :])  
    # 计算每个染色体被选择的概率  
    probability = fitnessvalues / np.sum(fitnessvalues)  
    # 得到每个染色体被选中的累积概率  
    cum_probability = np.cumsum(probability)  
    return fitnessvalues, cum_probability  
  
  
# 新种群选择  
def selectNewPopulation(chromosomes, cum_probability):  
    m, n = chromosomes.shape  
    newpopulation = np.zeros((m, n), dtype=np.uint8)  
    # 随机产生M个概率值  
    randoms = np.random.rand(m)  
    for i, randoma in enumerate(randoms):  
        logical = cum_probability >= randoma  
        index = np.where(logical == 1)  
        # index是tuple,tuple中元素是ndarray  
        newpopulation[i, :] = chromosomes[index[0][0], :]  
    return newpopulation  
    pass  
  
  
# 新种群交叉  
def crossover(population, Pc=0.8):  
    """ 
    :param population: 新种群 
    :param Pc: 交叉概率默认是0.8 
    :return: 交叉后得到的新种群 
    """  
    # 根据交叉概率计算需要进行交叉的个体个数  
    m, n = population.shape  
    numbers = np.uint8(m * Pc)  
    # 确保进行交叉的染色体个数是偶数个  
    if numbers % 2 != 0:  
        numbers  = 1  
    # 交叉后得到的新种群  
    updatepopulation = np.zeros((m, n), dtype=np.uint8)  
    # 产生随机索引  
    index = random.sample(range(m), numbers)  
    # 不进行交叉的染色体进行复制  
    for i in range(m):  
        if not index.__contains__(i):  
            updatepopulation[i, :] = population[i, :]  
    # crossover  
    while len(index) > 0:  
        a = index.pop()  
        b = index.pop()  
        # 随机产生一个交叉点  
        crossoverPoint = random.sample(range(1, n), 1)  
        crossoverPoint = crossoverPoint[0]  
        # one-single-point crossover  
        updatepopulation[a, 0:crossoverPoint] = population[a, 0:crossoverPoint]  
        updatepopulation[a, crossoverPoint:] = population[b, crossoverPoint:]  
        updatepopulation[b, 0:crossoverPoint] = population[b, 0:crossoverPoint]  
        updatepopulation[b, crossoverPoint:] = population[a, crossoverPoint:]  
    return updatepopulation  
    pass  
  
  
# 染色体变异  
def mutation(population, Pm=0.01):  
    """ 
 
    :param population: 经交叉后得到的种群 
    :param Pm: 变异概率默认是0.01 
    :return: 经变异操作后的新种群 
    """  
    updatepopulation = np.copy(population)  
    m, n = population.shape  
    # 计算需要变异的基因个数  
    gene_num = np.uint8(m * n * Pm)  
    # 将所有的基因按照序号进行10进制编码，则共有m*n个基因  
    # 随机抽取gene_num个基因进行基本位变异  
    mutationGeneIndex = random.sample(range(0, m * n), gene_num)  
    # 确定每个将要变异的基因在整个染色体中的基因座(即基因的具体位置)  
    for gene in mutationGeneIndex:  
        # 确定变异基因位于第几个染色体  
        chromosomeIndex = gene // n  
        # 确定变异基因位于当前染色体的第几个基因位  
        geneIndex = gene % n  
        # mutation  
        if updatepopulation[chromosomeIndex, geneIndex] == 0:  
            updatepopulation[chromosomeIndex, geneIndex] = 1  
        else:  
            updatepopulation[chromosomeIndex, geneIndex] = 0  
    return updatepopulation  
    pass  
  
  
# 定义适应度函数    目标函数
# maxf(x1,x2) = 21.5 x1*sin(4*pi*x1) x2*sin(20*pi*x2)
#    s.t. -3.0<=x1<=12.1   4.1<=x2<=5.8
def fitnessFunction():  
    return lambda x: 21.5   x[0] * np.sin(4 * np.pi * x[0])   x[1] * np.sin(20 * np.pi * x[1])  
    pass  
  
  
def main(max_iter=500):  
    # 每次迭代得到的最优解  
    optimalSolutions = []  
    optimalValues = []  
    # 决策变量的取值范围  
    decisionVariables = [[-3.0, 12.1], [4.1, 5.8]]  
    # 得到染色体编码长度  
    lengthEncode = getEncodedLength(boundarylist=decisionVariables)  
    for iteration in range(max_iter):  
        # 得到初始种群编码  
        chromosomesEncoded = getIntialPopulation(lengthEncode, 10)  
        # 种群解码  
        decoded = decodedChromosome(lengthEncode, chromosomesEncoded, decisionVariables)  
        # 得到个体适应度值和个体的累积概率  
        evalvalues, cum_proba = getFitnessValue(fitnessFunction(), decoded)  
        # 选择新的种群  
        newpopulations = selectNewPopulation(chromosomesEncoded, cum_proba)  
        # 进行交叉操作  
        crossoverpopulation = crossover(newpopulations)  
        # mutation  
        mutationpopulation = mutation(crossoverpopulation)  
        # 将变异后的种群解码，得到每轮迭代最终的种群  
        final_decoded = decodedChromosome(lengthEncode, mutationpopulation, decisionVariables)  
        # 适应度评价  
        fitnessvalues, cum_individual_proba = getFitnessValue(fitnessFunction(), final_decoded)  
        # 搜索每次迭代的最优解，以及最优解对应的目标函数的取值  
        optimalValues.append(np.max(list(fitnessvalues)))  
        index = np.where(fitnessvalues == max(list(fitnessvalues)))  
        optimalSolutions.append(final_decoded[index[0][0], :])  
    # 搜索最优解  
    optimalValue = np.max(optimalValues)  
    optimalIndex = np.where(optimalValues == optimalValue)  
    optimalSolution = optimalSolutions[optimalIndex[0][0]]  
    return optimalSolution, optimalValue  
  
  
solution, value = main()  
print('最优解: x1, x2')  
print(solution[0], solution[1])  
print('最优目标函数值:', value)  
# 测量运行时间  
elapsedtime = timeit.timeit(stmt=main, number=1)  
print('Searching Time Elapsed:(S)', elapsedtime)