简单遗传算法-python实现

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()