遗传算法求函数最大值代码

以下是一个使用遗传算法求解函数最大值的示例代码（使用Python语言）：

import random

# 定义目标函数
def f(x):
    return x**2

# 遗传算法参数设置
POPULATION_SIZE = 100  # 种群大小
CHROMOSOME_LENGTH = 8  # 染色体长度（二进制编码）
CROSSOVER_RATE = 0.8  # 交叉概率
MUTATION_RATE = 0.01  # 变异概率
GENERATIONS = 50  # 迭代次数

# 初始化种群
def create_population():
    population = []
    for _ in range(POPULATION_SIZE):
        chromosome = ''.join(random.choices(['0', '1'], k=CHROMOSOME_LENGTH))
        population.append(chromosome)
    return population

# 计算染色体对应的函数值
def calculate_fitness(chromosome):
    x = int(chromosome, 2)
    return f(x)

# 选择操作（轮盘赌选择）
def selection(population):
    fitness_values = [calculate_fitness(chromosome) for chromosome in population]
    total_fitness = sum(fitness_values)
    probabilities = [fitness / total_fitness for fitness in fitness_values]
    selected_indices = random.choices(range(POPULATION_SIZE), probabilities, k=POPULATION_SIZE)
    selected_population = [population[i] for i in selected_indices]
    return selected_population

# 交叉操作（单点交叉）
def crossover(parent1, parent2):
    if random.random() < CROSSOVER_RATE:
        crossover_point = random.randint(1, CHROMOSOME_LENGTH - 1)
        child1 = parent1[:crossover_point] + parent2[crossover_point:]
        child2 = parent2[:crossover_point] + parent1[crossover_point:]
        return child1, child2
    else:
        return parent1, parent2

# 变异操作（单点变异）
def mutation(chromosome):
    mutated_chromosome = list(chromosome)
    for i in range(CHROMOSOME_LENGTH):
        if random.random() < MUTATION_RATE:
            mutated_chromosome[i] = '0' if chromosome[i] == '1' else '1'
    return ''.join(mutated_chromosome)

# 遗传算法主过程
def genetic_algorithm():
    population = create_population()

    for _ in range(GENERATIONS):
        new_population = []

        # 选择
        selected_population = selection(population)

        # 交叉和变异
        for i in range(0, POPULATION_SIZE, 2):
            parent1 = selected_population[i]
            parent2 = selected_population[i + 1]

            child1, child2 = crossover(parent1, parent2)

            child1 = mutation(child1)
            child2 = mutation(child2)

            new_population.extend([child1, child2])

        population = new_population

    # 寻找最优解
    best_chromosome = max(population, key=lambda chromosome: calculate_fitness(chromosome))
    best_x = int(best_chromosome, 2)
    best_fitness = f(best_x)

    return best_x, best_fitness

# 运行遗传算法
best_x, best_fitness = genetic_algorithm()
print("最优解 x =", best_x)
print("最大值 f(x) =", best_fitness)

上述代码中使用了简单的二进制编码表示染色体，轮盘赌选择、单点交叉和单点变异作为遗传算法的基本操作。通过迭代多次，最终找到函数的最大值。你可以根据自己的需求进行参数调整和算法改进。