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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