使用python用遗传算法编程实现Ackley函数优化问题

好的，下面是使用Python实现Ackley函数优化问题的遗传算法的步骤：

1.导入必要的库

import numpy as np
import matplotlib.pyplot as plt

2.定义Ackley函数

def ackley(x):
    n = len(x)
    sum1 = sum([x[i] ** 2 for i in range(n)])
    sum2 = sum([np.cos(2 * np.pi * x[i]) for i in range(n)])
    return -20 * np.exp(-0.2 * np.sqrt(sum1 / n)) - np.exp(sum2 / n) + 20 + np.exp(1)

3.初始化种群

def init_population(pop_size, chromosome_length):
    population = np.random.uniform(-32.768, 32.768, size=(pop_size, chromosome_length))
    return population

4.计算适应度函数

def cal_fitness(population):
    fitness = np.zeros(population.shape[0])
    for i in range(population.shape[0]):
        fitness[i] = ackley(population[i])
    return fitness

5.选择操作

def selection(population, fitness):
    idx = np.random.choice(np.arange(population.shape[0]), size=2, replace=False, p=fitness / np.sum(fitness))
    return population[idx]

6.交叉操作

def crossover(parents, pc):
    if np.random.rand() < pc:
        child1 = np.zeros(parents[0].shape)
        child2 = np.zeros(parents[1].shape)
        pos = np.random.randint(1, parents[0].shape[0] - 1)
        child1[:pos] = parents[0][:pos]
        child1[pos:] = parents[1][pos:]
        child2[:pos] = parents[1][:pos]
        child2[pos:] = parents[0][pos:]
        return child1, child2
    else:
        return parents[0], parents[1]

7.变异操作

def mutation(child, pm):
    if np.random.rand() < pm:
        pos = np.random.randint(child.shape[0])
        child[pos] = np.random.uniform(-32.768, 32.768)
    return child

8.遗传算法主函数

def genetic_algorithm(pop_size, chromosome_length, pc, pm, max_iter):
    population = init_population(pop_size, chromosome_length)
    fitness = cal_fitness(population)
    best_idx = np.argmin(fitness)
    best_individual = population[best_idx]
    best_fitness = fitness[best_idx]

    for i in range(max_iter):
        new_population = np.zeros(population.shape)
        for j in range(int(pop_size / 2)):
            parents = selection(population, fitness)
            child1, child2 = crossover(parents, pc)
            child1 = mutation(child1, pm)
            child2 = mutation(child2, pm)
            new_population[j * 2] = child1
            new_population[j * 2 + 1] = child2

        population = new_population
        fitness = cal_fitness(population)
        best_idx = np.argmin(fitness)
        if fitness[best_idx] < best_fitness:
            best_individual = population[best_idx]
            best_fitness = fitness[best_idx]

    return best_individual, best_fitness

9.测试代码

best_individual, best_fitness = genetic_algorithm(pop_size=100, chromosome_length=2, pc=0.8, pm=0.1, max_iter=100)
print("最优解：", best_individual)
print("最优解的适应度：", best_fitness)

运行以上代码即可得到Ackley函数的最优解和最优解的适应度。

希望我的回答对你有所帮助！