遗传算法求(6.452*(x+0.125*y)*(cos(x)-cos(2*y))**2)/(0.8+(x-4.2)**2+2*(y-7)**2)+3.226*y最大值与最小值的代码

遗传算法是一种基于生物进化理论的优化算法，其目的是通过模拟自然选择和遗传机制，不断地进化出更优秀的解。在求解(6.452*(x+0.125*y)*(cos(x)-cos(2*y))**2)/(0.8+(x-4.2)**2+2*(y-7)**2)+3.226*y的最大值和最小值时，我们可以使用遗传算法。

下面是使用Python实现该问题的遗传算法代码：

import random

# 目标函数
def target_function(x, y):
    return (6.452*(x+0.125*y)*(cos(x)-cos(2*y))**2)/(0.8+(x-4.2)**2+2*(y-7)**2)+3.226*y

# 生成初始种群
def generate_population(size):
    population = []
    for i in range(size):
        x = random.uniform(-10, 10)
        y = random.uniform(-10, 10)
        population.append((x, y))
    return population

# 计算适应度
def calculate_fitness(population):
    fitness = []
    for individual in population:
        x, y = individual
        fitness.append(target_function(x, y))
    return fitness

# 选择
def selection(population, fitness):
    new_population = []
    total_fitness = sum(fitness)
    for i in range(len(population)):
        probability = fitness[i] / total_fitness
        if random.random() < probability:
            new_population.append(population[i])
    return new_population

# 交叉
def crossover(population):
    new_population = []
    for i in range(len(population)):
        parent1 = random.choice(population)
        parent2 = random.choice(population)
        child = (parent1, parent2)
        new_population.append(child)
    return new_population

# 变异
def mutation(population, probability):
    new_population = []
    for individual in population:
        x, y = individual
        if random.random() < probability:
            x += random.uniform(-1, 1)
            y += random.uniform(-1, 1)
        new_population.append((x, y))
    return new_population

# 遗传算法主函数
def genetic_algorithm(size, generations, mutation_probability):
    population = generate_population(size)
    for i in range(generations):
        fitness = calculate_fitness(population)
        population = selection(population, fitness)
        population = crossover(population)
        population = mutation(population, mutation_probability)
    best_individual = max(population, key=lambda x: target_function(x, x))
    worst_individual = min(population, key=lambda x: target_function(x, x))
    return best_individual, worst_individual

# 示例运行
best_individual, worst_individual = genetic_algorithm(size=100, generations=100, mutation_probability=0.1)
print("最大值：", target_function(*best_individual))
print("最小值：", target_function(*worst_individual))