python实现简单遗传算法

ObjFunction.py

import math


def GrieFunc(vardim, x, bound):
 """
 Griewangk function
 """
 s1 = 0.
 s2 = 1.
 for i in range(1, vardim + 1):
  s1 = s1 + x[i - 1] ** 2
  s2 = s2 * math.cos(x[i - 1] / math.sqrt(i))
 y = (1. / 4000.) * s1 - s2 + 1
 y = 1. / (1. + y)
 return y


def RastFunc(vardim, x, bound):
 """
 Rastrigin function
 """
 s = 10 * 25
 for i in range(1, vardim + 1):
  s = s + x[i - 1] ** 2 - 10 * math.cos(2 * math.pi * x[i - 1])
 return s

GAIndividual.py

import numpy as np
import ObjFunction


class GAIndividual:

 '''
 individual of genetic algorithm
 '''

 def __init__(self, vardim, bound):
  '''
  vardim: dimension of variables
  bound: boundaries of variables
  '''
  self.vardim = vardim
  self.bound = bound
  self.fitness = 0.

 def generate(self):
  '''
  generate a random chromsome for genetic algorithm
  '''
  len = self.vardim
  rnd = np.random.random(size=len)
  self.chrom = np.zeros(len)
  for i in xrange(0, len):
   self.chrom[i] = self.bound[0, i] + \
    (self.bound[1, i] - self.bound[0, i]) * rnd[i]

 def calculateFitness(self):
  '''
  calculate the fitness of the chromsome
  '''
  self.fitness = ObjFunction.GrieFunc(
   self.vardim, self.chrom, self.bound)

GeneticAlgorithm.py

import numpy as np
from GAIndividual import GAIndividual
import random
import copy
import matplotlib.pyplot as plt


class GeneticAlgorithm:

 '''
 The class for genetic algorithm
 '''

 def __init__(self, sizepop, vardim, bound, MAXGEN, params):
  '''
  sizepop: population sizepop
  vardim: dimension of variables
  bound: boundaries of variables
  MAXGEN: termination condition
  param: algorithm required parameters, it is a list which is consisting of crossover rate, mutation rate, alpha
  '''
  self.sizepop = sizepop
  self.MAXGEN = MAXGEN
  self.vardim = vardim
  self.bound = bound
  self.population = []
  self.fitness = np.zeros((self.sizepop, 1))
  self.trace = np.zeros((self.MAXGEN, 2))
  self.params = params

 def initialize(self):
  '''
  initialize the population
  '''
  for i in xrange(0, self.sizepop):
   ind = GAIndividual(self.vardim, self.bound)
   ind.generate()
   self.population.append(ind)

 def evaluate(self):
  '''
  evaluation of the population fitnesses
  '''
  for i in xrange(0, self.sizepop):
   self.population[i].calculateFitness()
   self.fitness[i] = self.population[i].fitness

 def solve(self):
  '''
  evolution process of genetic algorithm
  '''
  self.t = 0
  self.initialize()
  self.evaluate()
  best = np.max(self.fitness)
  bestIndex = np.argmax(self.fitness)
  self.best = copy.deepcopy(self.population[bestIndex])
  self.avefitness = np.mean(self.fitness)
  self.trace[self.t, 0] = (1 - self.best.fitness) / self.best.fitness
  self.trace[self.t, 1] = (1 - self.avefitness) / self.avefitness
  print("Generation %d: optimal function value is: %f; average function value is %f" % (
   self.t, self.trace[self.t, 0], self.trace[self.t, 1]))
  while (self.t < self.MAXGEN - 1):
   self.t += 1
   self.selectionOperation()
   self.crossoverOperation()
   self.mutationOperation()
   self.evaluate()
   best = np.max(self.fitness)
   bestIndex = np.argmax(self.fitness)
   if best > self.best.fitness:
    self.best = copy.deepcopy(self.population[bestIndex])
   self.avefitness = np.mean(self.fitness)
   self.trace[self.t, 0] = (1 - self.best.fitness) / self.best.fitness
   self.trace[self.t, 1] = (1 - self.avefitness) / self.avefitness
   print("Generation %d: optimal function value is: %f; average function value is %f" % (
    self.t, self.trace[self.t, 0], self.trace[self.t, 1]))

  print("Optimal function value is: %f; " %
    self.trace[self.t, 0])
  print "Optimal solution is:"
  print self.best.chrom
  self.printResult()

 def selectionOperation(self):
  '''
  selection operation for Genetic Algorithm
  '''
  newpop = []
  totalFitness = np.sum(self.fitness)
  accuFitness = np.zeros((self.sizepop, 1))

  sum1 = 0.
  for i in xrange(0, self.sizepop):
   accuFitness[i] = sum1 + self.fitness[i] / totalFitness
   sum1 = accuFitness[i]

  for i in xrange(0, self.sizepop):
   r = random.random()
   idx = 0
   for j in xrange(0, self.sizepop - 1):
    if j == 0 and r < accuFitness[j]:
     idx = 0
     break
    elif r >= accuFitness[j] and r < accuFitness[j + 1]:
     idx = j + 1
     break
   newpop.append(self.population[idx])
  self.population = newpop

 def crossoverOperation(self):
  '''
  crossover operation for genetic algorithm
  '''
  newpop = []
  for i in xrange(0, self.sizepop, 2):
   idx1 = random.randint(0, self.sizepop - 1)
   idx2 = random.randint(0, self.sizepop - 1)
   while idx2 == idx1:
    idx2 = random.randint(0, self.sizepop - 1)
   newpop.append(copy.deepcopy(self.population[idx1]))
   newpop.append(copy.deepcopy(self.population[idx2]))
   r = random.random()
   if r < self.params[0]:
    crossPos = random.randint(1, self.vardim - 1)
    for j in xrange(crossPos, self.vardim):
     newpop[i].chrom[j] = newpop[i].chrom[
      j] * self.params[2] + (1 - self.params[2]) * newpop[i + 1].chrom[j]
     newpop[i + 1].chrom[j] = newpop[i + 1].chrom[j] * self.params[2] + \
      (1 - self.params[2]) * newpop[i].chrom[j]
  self.population = newpop

 def mutationOperation(self):
  '''
  mutation operation for genetic algorithm
  '''
  newpop = []
  for i in xrange(0, self.sizepop):
   newpop.append(copy.deepcopy(self.population[i]))
   r = random.random()
   if r < self.params[1]:
    mutatePos = random.randint(0, self.vardim - 1)
    theta = random.random()
    if theta > 0.5:
     newpop[i].chrom[mutatePos] = newpop[i].chrom[
      mutatePos] - (newpop[i].chrom[mutatePos] - self.bound[0, mutatePos]) * (1 - random.random() ** (1 - self.t / self.MAXGEN))
    else:
     newpop[i].chrom[mutatePos] = newpop[i].chrom[
      mutatePos] + (self.bound[1, mutatePos] - newpop[i].chrom[mutatePos]) * (1 - random.random() ** (1 - self.t / self.MAXGEN))
  self.population = newpop

 def printResult(self):
  '''
  plot the result of the genetic algorithm
  '''
  x = np.arange(0, self.MAXGEN)
  y1 = self.trace[:, 0]
  y2 = self.trace[:, 1]
  plt.plot(x, y1, 'r', label='optimal value')
  plt.plot(x, y2, 'g', label='average value')
  plt.xlabel("Iteration")
  plt.ylabel("function value")
  plt.title("Genetic algorithm for function optimization")
  plt.legend()
  plt.show()

运行程序：

if __name__ == "__main__":
 
  bound = np.tile([[-600], [600]], 25)
  ga = GA(60, 25, bound, 1000, [0.9, 0.1, 0.5])
  ga.solve()

作者：Alex Yu
出处：http://www.cnblogs.com/biaoyu/

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