Python实现简单遗传算法(SGA)

# !/usr/bin/env python # -*- coding:utf-8 -*- # Author: wsw # 简单实现SGA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 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)