ObjFunction.py
1 import math 2 3 4 def GrieFunc(vardim, x, bound): 5 """ 6 Griewangk function 7 """ 8 s1 = 0. 9 s2 = 1. 10 for i in range(1, vardim + 1): 11 s1 = s1 + x[i - 1] ** 2 12 s2 = s2 * math.cos(x[i - 1] / math.sqrt(i)) 13 y = (1. / 4000.) * s1 - s2 + 1 14 y = 1. / (1. + y) 15 return y 16 17 18 def RastFunc(vardim, x, bound): 19 """ 20 Rastrigin function 21 """ 22 s = 10 * 25 23 for i in range(1, vardim + 1): 24 s = s + x[i - 1] ** 2 - 10 * math.cos(2 * math.pi * x[i - 1]) 25 return s
GAIndividual.py
1 import numpy as np 2 import ObjFunction 3 4 5 class GAIndividual: 6 7 ''' 8 individual of genetic algorithm 9 ''' 10 11 def __init__(self, vardim, bound): 12 ''' 13 vardim: dimension of variables 14 bound: boundaries of variables 15 ''' 16 self.vardim = vardim 17 self.bound = bound 18 self.fitness = 0. 19 20 def generate(self): 21 ''' 22 generate a random chromsome for genetic algorithm 23 ''' 24 len = self.vardim 25 rnd = np.random.random(size=len) 26 self.chrom = np.zeros(len) 27 for i in xrange(0, len): 28 self.chrom[i] = self.bound[0, i] + 29 (self.bound[1, i] - self.bound[0, i]) * rnd[i] 30 31 def calculateFitness(self): 32 ''' 33 calculate the fitness of the chromsome 34 ''' 35 self.fitness = ObjFunction.GrieFunc( 36 self.vardim, self.chrom, self.bound)
GeneticAlgorithm.py
1 import numpy as np 2 from GAIndividual import GAIndividual 3 import random 4 import copy 5 import matplotlib.pyplot as plt 6 7 8 class GeneticAlgorithm: 9 10 ''' 11 The class for genetic algorithm 12 ''' 13 14 def __init__(self, sizepop, vardim, bound, MAXGEN, params): 15 ''' 16 sizepop: population sizepop 17 vardim: dimension of variables 18 bound: boundaries of variables 19 MAXGEN: termination condition 20 param: algorithm required parameters, it is a list which is consisting of crossover rate, mutation rate, alpha 21 ''' 22 self.sizepop = sizepop 23 self.MAXGEN = MAXGEN 24 self.vardim = vardim 25 self.bound = bound 26 self.population = [] 27 self.fitness = np.zeros((self.sizepop, 1)) 28 self.trace = np.zeros((self.MAXGEN, 2)) 29 self.params = params 30 31 def initialize(self): 32 ''' 33 initialize the population 34 ''' 35 for i in xrange(0, self.sizepop): 36 ind = GAIndividual(self.vardim, self.bound) 37 ind.generate() 38 self.population.append(ind) 39 40 def evaluate(self): 41 ''' 42 evaluation of the population fitnesses 43 ''' 44 for i in xrange(0, self.sizepop): 45 self.population[i].calculateFitness() 46 self.fitness[i] = self.population[i].fitness 47 48 def solve(self): 49 ''' 50 evolution process of genetic algorithm 51 ''' 52 self.t = 0 53 self.initialize() 54 self.evaluate() 55 best = np.max(self.fitness) 56 bestIndex = np.argmax(self.fitness) 57 self.best = copy.deepcopy(self.population[bestIndex]) 58 self.avefitness = np.mean(self.fitness) 59 self.trace[self.t, 0] = (1 - self.best.fitness) / self.best.fitness 60 self.trace[self.t, 1] = (1 - self.avefitness) / self.avefitness 61 print("Generation %d: optimal function value is: %f; average function value is %f" % ( 62 self.t, self.trace[self.t, 0], self.trace[self.t, 1])) 63 while (self.t < self.MAXGEN - 1): 64 self.t += 1 65 self.selectionOperation() 66 self.crossoverOperation() 67 self.mutationOperation() 68 self.evaluate() 69 best = np.max(self.fitness) 70 bestIndex = np.argmax(self.fitness) 71 if best > self.best.fitness: 72 self.best = copy.deepcopy(self.population[bestIndex]) 73 self.avefitness = np.mean(self.fitness) 74 self.trace[self.t, 0] = (1 - self.best.fitness) / self.best.fitness 75 self.trace[self.t, 1] = (1 - self.avefitness) / self.avefitness 76 print("Generation %d: optimal function value is: %f; average function value is %f" % ( 77 self.t, self.trace[self.t, 0], self.trace[self.t, 1])) 78 79 print("Optimal function value is: %f; " % 80 self.trace[self.t, 0]) 81 print "Optimal solution is:" 82 print self.best.chrom 83 self.printResult() 84 85 def selectionOperation(self): 86 ''' 87 selection operation for Genetic Algorithm 88 ''' 89 newpop = [] 90 totalFitness = np.sum(self.fitness) 91 accuFitness = np.zeros((self.sizepop, 1)) 92 93 sum1 = 0. 94 for i in xrange(0, self.sizepop): 95 accuFitness[i] = sum1 + self.fitness[i] / totalFitness 96 sum1 = accuFitness[i] 97 98 for i in xrange(0, self.sizepop): 99 r = random.random() 100 idx = 0 101 for j in xrange(0, self.sizepop - 1): 102 if j == 0 and r < accuFitness[j]: 103 idx = 0 104 break 105 elif r >= accuFitness[j] and r < accuFitness[j + 1]: 106 idx = j + 1 107 break 108 newpop.append(self.population[idx]) 109 self.population = newpop 110 111 def crossoverOperation(self): 112 ''' 113 crossover operation for genetic algorithm 114 ''' 115 newpop = [] 116 for i in xrange(0, self.sizepop, 2): 117 idx1 = random.randint(0, self.sizepop - 1) 118 idx2 = random.randint(0, self.sizepop - 1) 119 while idx2 == idx1: 120 idx2 = random.randint(0, self.sizepop - 1) 121 newpop.append(copy.deepcopy(self.population[idx1])) 122 newpop.append(copy.deepcopy(self.population[idx2])) 123 r = random.random() 124 if r < self.params[0]: 125 crossPos = random.randint(1, self.vardim - 1) 126 for j in xrange(crossPos, self.vardim): 127 newpop[i].chrom[j] = newpop[i].chrom[ 128 j] * self.params[2] + (1 - self.params[2]) * newpop[i + 1].chrom[j] 129 newpop[i + 1].chrom[j] = newpop[i + 1].chrom[j] * self.params[2] + 130 (1 - self.params[2]) * newpop[i].chrom[j] 131 self.population = newpop 132 133 def mutationOperation(self): 134 ''' 135 mutation operation for genetic algorithm 136 ''' 137 newpop = [] 138 for i in xrange(0, self.sizepop): 139 newpop.append(copy.deepcopy(self.population[i])) 140 r = random.random() 141 if r < self.params[1]: 142 mutatePos = random.randint(0, self.vardim - 1) 143 theta = random.random() 144 if theta > 0.5: 145 newpop[i].chrom[mutatePos] = newpop[i].chrom[ 146 mutatePos] - (newpop[i].chrom[mutatePos] - self.bound[0, mutatePos]) * (1 - random.random() ** (1 - self.t / self.MAXGEN)) 147 else: 148 newpop[i].chrom[mutatePos] = newpop[i].chrom[ 149 mutatePos] + (self.bound[1, mutatePos] - newpop[i].chrom[mutatePos]) * (1 - random.random() ** (1 - self.t / self.MAXGEN)) 150 self.population = newpop 151 152 def printResult(self): 153 ''' 154 plot the result of the genetic algorithm 155 ''' 156 x = np.arange(0, self.MAXGEN) 157 y1 = self.trace[:, 0] 158 y2 = self.trace[:, 1] 159 plt.plot(x, y1, 'r', label='optimal value') 160 plt.plot(x, y2, 'g', label='average value') 161 plt.xlabel("Iteration") 162 plt.ylabel("function value") 163 plt.title("Genetic algorithm for function optimization") 164 plt.legend() 165 plt.show()
运行程序：
1 if __name__ == "__main__": 2 3 bound = np.tile([[-600], [600]], 25) 4 ga = GA(60, 25, bound, 1000, [0.9, 0.1, 0.5]) 5 ga.solve()