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()