Python使用遗传算法求解Ackley函数的最小值源代码

import math import random import numpy as np import matplotlib.pyplot as plot ''' Parameters. ''' individuals_count = 30 childs_count = 200 ackley_n = 30 ackley_x_min = -40 ackley_x_max = 40 gaussian_deviation_min = 0.0001 gaussian_deviation_max = 12 learning_rate = 1/math.sqrt(2*math.sqrt(individuals_count)) learning_rate_l = 1/math.sqrt(2*individuals_count) max_iteration_count = 500 ''' Metrics. ''' solution = [] sample_rate = 10 sampled_axis = [] sampled_bests = [] sampled_averages = [] sampled_deviations = [] ''' Ackley function implementation. ''' def ackley(v): const_n = len(v) const_c1 = 20.0 const_c2 = 0.2 const_c3 = 2*math.pi a = sum([math.pow(x, 2) for x in v]) b = (1/const_n)*a c = (-const_c2)*math.sqrt(b) d = (-const_c1)*math.exp(c) e = sum([math.cos(const_c3*x) for x in v]) f = (1/const_n)*e g = math.exp(f) h = d - g + const_c1 + math.exp(1) return h ''' Assumes the fitness is equal to the ackley function evaluation. ''' def fitness(individual): return ackley(individual[:ackley_n]) ''' Generates a random individual. The individuals are represented as lists of floats, composed by: the first "ackley_n" numbers are the solution vector, the following "ackley_n" values are the mutation step size in each direction and then a single number representing the individual fitness. ''' def generateIndividual(): min = gaussian_deviation_min max = gaussian_deviation_max x_vals = [random.uniform(ackley_x_min, ackley_x_max) for _ in range(ackley_n)] sigma_vals = [random.uniform(min, max) for _ in range(ackley_n)] individual = x_vals + sigma_vals + [0] individual[-1] = fitness(individual) return individual ''' Generate the initial population. ''' population = [] for i in range(individuals_count): population.append(generateIndividual()) ''' Include the initial population in the metrics calculation. ''' solution = population[0] fitnesses = [p[-1] for p in population] best = population[0][-1] mean = np.mean(fitnesses) std_deviation = np.std(fitnesses) sampled_axis.append(0) sampled_bests.append(best) sampled_averages.append(mean) sampled_deviations.append(std_deviation) ''' Main algorithm loop. ''' for iteration in range(max_iteration_count): ''' Print the current iteration and the best fitness found. ''' print("{:7.0f}".format(iteration+1) + " " + str(solution[-1])) ''' Parents selection & Recombination. We adopt a global recombination strategy along with a discrete recombination for the object part and an intermediate recombination for the strategy parameters. So, basically, each family can have multiple parents generating a child whose alleles [x1...xi] are selected randomically from their parents and the strategy parameters are averaged. ''' childs = [] for i in range(childs_count): count = random.randint(2, (individuals_count/2)) family = [random.choice(population) for _ in range(count)] x_vals = [random.choice(family)[k] for k in range(ackley_n)] sigma_vals = [(sum(a[k+ackley_n] for a in family)/count) for k in range(ackley_n)] child = x_vals + sigma_vals + [0] child[-1] = fitness(child) childs.append(child) ''' Mutate childs (Uncorrelated Mutation With N Step Sizes, Eiben Pag. 60). ''' for child in childs: const_g = random.gauss(0, 1) for i in range(ackley_n): g = random.gauss(0, 1) a = learning_rate_l*const_g b = learning_rate*g sigma = child[i+ackley_n] sigma_l = sigma*math.exp(a+b) if sigma_l < gaussian_deviation_min: sigma_l = gaussian_deviation_min child[i+ackley_n] = sigma_l for i in range(ackley_n): g = random.gauss(0, 1) x = child[i]+(child[i+ackley_n]*g) if ackley_x_min <= x and x <= ackley_x_max: child[i] = x child[-1] = fitness(child) ''' Survivor selection. ''' childs.sort(key=lambda x: x[-1], reverse=False) population = childs[:individuals_count] ''' Update metrics (retain best solution found). ''' if solution[-1] > population[0][-1]: solution = population[0] ''' Sampling, populate data sources to generate graphs later. ''' if (iteration % sample_rate == 0): fitnesses = [p[-1] for p in population] best = population[0][-1] mean = np.mean(fitnesses) std_deviation = np.std(fitnesses) sampled_axis.append(iteration+1) sampled_bests.append(best) sampled_averages.append(mean) sampled_deviations.append(std_deviation) ''' Present results. ''' print("") print("Best solution (" + str(solution[-1]) + "):") print("") ''' Generate graphs for the best individual, fitnesses mean and fitnesses standard deviation over the iterations. ''' plot.figure() plot.plot(sampled_axis, sampled_bests) plot.xlabel("Iter") plot.ylabel("Best Value") plot.savefig("results/algorithm2-best.png", bbox_inches="tight") plot.figure() plot.plot(sampled_axis, sampled_averages) plot.xlabel("Iteration") plot.ylabel("Fitness Averages") plot.savefig("results/algorithm2-averages.png", bbox_inches="tight") plot.figure() plot.plot(sampled_axis, sampled_deviations) plot.xlabel("Iteration") plot.ylabel("Fitness Standard Deviations") plot.savefig("results/algorithm2-deviations.png", bbox_inches="tight")