遗传算法求函数最大值实验.py

这是一段使用遗传算法求解函数最大值的 Python 代码，代码中使用了 Python 标准库中的 random 模块。

import random

# 目标函数
def target_function(x):
    return x**2 - 3*x + 4

# 适应度函数
def fitness_function(x):
    return target_function(x)

# 个体编码
def encode_individual():
    return random.uniform(-10, 10)

# 初始化种群
def init_population(population_size):
    population = []
    for i in range(population_size):
        population.append(encode_individual())
    return population

# 选择操作
def selection(population):
    sorted_population = sorted(population, key=lambda x: fitness_function(x), reverse=True)
    selected_population = sorted_population[:len(population)//2]
    return selected_population

# 交叉操作
def crossover(parent1, parent2):
    child1 = (parent1 + parent2) / 2
    child2 = (parent1 - parent2) / 2
    return child1, child2

# 变异操作
def mutation(child):
    mutated_child = child + random.uniform(-0.5, 0.5)
    return mutated_child

# 遗传算法主函数
def genetic_algorithm(population_size, max_generations):
    population = init_population(population_size)
    for i in range(max_generations):
        selected_population = selection(population)
        new_population = []
        while len(new_population) < population_size:
            parent1 = random.choice(selected_population)
            parent2 = random.choice(selected_population)
            child1, child2 = crossover(parent1, parent2)
            mutated_child1 = mutation(child1)
            mutated_child2 = mutation(child2)
            new_population.append(mutated_child1)
            new_population.append(mutated_child2)
        population = new_population
    best_individual = max(population, key=lambda x: fitness_function(x))
    return best_individual

# 测试遗传算法
if __name__ == '__main__':
    best_individual = genetic_algorithm(population_size=100, max_generations=1000)
    best_fitness = fitness_function(best_individual)
    print('最优个体：', best_individual)
    print('最优适应度：', best_fitness)

在这个实验中，我们使用了简单的遗传算法来求解目标函数 $f(x) = x^2 - 3x + 4$ 的最大值。首先，我们定义了目标函数和适应度函数，其中目标函数就是要求解的函数，适应度函数就是根据目标函数计算个体适应度的函数。然后，我们定义了个体编码函数，这里采用了实数编码，即每个个体是一个实数。接着，我们初始化了种群，并定义了选择、交叉和变异等遗传算法的操作。最后，我们使用遗传算法进行求解，并输出了最优个体和最优适应度。