差分进化算法-python实现

DEIndividual.py

 import numpy as np
 import ObjFunction

 class DEIndividual:

     '''
     individual of differential evolution 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 differential evolution 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)

DE.py

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

 class DifferentialEvolutionAlgorithm:

     '''
     The class for differential evolution 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 CR, scaling factor F]
         '''
         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 = DEIndividual(self.vardim, self.bound)
             ind.generate()
             self.population.append(ind)

     def evaluate(self, x):
         '''
         evaluation of the population fitnesses
         '''
         x.calculateFitness()

     def solve(self):
         '''
         evolution process of differential evolution algorithm
         '''
         self.t = 0
         self.initialize()
         for i in xrange(0, self.sizepop):
             self.evaluate(self.population[i])
             self.fitness[i] = self.population[i].fitness
         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
             for i in xrange(0, self.sizepop):
                 vi = self.mutationOperation(i)
                 ui = self.crossoverOperation(i, vi)
                 xi_next = self.selectionOperation(i, ui)
                 self.population[i] = xi_next
             for i in xrange(0, self.sizepop):
                 self.evaluate(self.population[i])
                 self.fitness[i] = self.population[i].fitness
             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, i, ui):
         '''
         selection operation for differential evolution algorithm
         '''
         xi_next = copy.deepcopy(self.population[i])
         xi_next.chrom = ui
         self.evaluate(xi_next)
         if xi_next.fitness > self.population[i].fitness:
             return xi_next
         else:
             return self.population[i]

     def crossoverOperation(self, i, vi):
         '''
         crossover operation for differential evolution algorithm
         '''
         k = np.random.random_integers(0, self.vardim - 1)
         ui = np.zeros(self.vardim)
         for j in xrange(0, self.vardim):
             pick = random.random()
             if pick < self.params[0] or j == k:
                 ui[j] = vi[j]
             else:
                 ui[j] = self.population[i].chrom[j]
         return ui

     def mutationOperation(self, i):
         '''
         mutation operation for differential evolution algorithm
         '''
         a = np.random.random_integers(0, self.sizepop - 1)
         while a == i:
             a = np.random.random_integers(0, self.sizepop - 1)
         b = np.random.random_integers(0, self.sizepop - 1)
         while b == i or b == a:
             b = np.random.random_integers(0, self.sizepop - 1)
         c = np.random.random_integers(0, self.sizepop - 1)
         while c == i or c == b or c == a:
             c = np.random.random_integers(0, self.sizepop - 1)
         vi = self.population[c].chrom + self.params[1] * \
             (self.population[a].chrom - self.population[b].chrom)
         for j in xrange(0, self.vardim):
             if vi[j] < self.bound[0, j]:
                 vi[j] = self.bound[0, j]
             if vi[j] > self.bound[1, j]:
                 vi[j] = self.bound[1, j]
         return vi

     def printResult(self):
         '''
         plot the result of the differential evolution 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("Differential Evolution Algorithm for function optimization")
         plt.legend()
         plt.show()

运行程序：

 if __name__ == "__main__":

     bound = np.tile([[-600], [600]], 25)
     dea = DEA(60, 25, bound, 1000, [0.8,  0.6])
     dea.solve()

ObjFunction见简单遗传算法-python实现。