遗传算法求函数最小值Python

遗传算法是一种基于生物进化原理的优化算法，可以用来求解函数的最小值。下面是一个使用遗传算法求函数最小值的Python示例代码：

import random

# 定义目标函数
def fitness_func(x):
    return x ** 2

# 初始化种群
def init_population(pop_size, chromo_len):
    return [[random.randint(0, 1) for _ in range(chromo_len)] for _ in range(pop_size)]

# 计算个体适应度
def calc_fitness(population):
    return [fitness_func(int(''.join(str(gene) for gene in individual)), 2) for individual in population]

# 精英选择
def select_elite(population, fitness):
    elite_idx = fitness.index(min(fitness))
    return population[elite_idx]

# 交叉操作
def crossover(parent1, parent2):
    crossover_point = random.randint(0, len(parent1) - 1)
    child1 = parent1[:crossover_point] + parent2[crossover_point:]
    child2 = parent2[:crossover_point] + parent1[crossover_point:]
    return child1, child2

# 变异操作
def mutate(individual, mutation_rate):
    for i in range(len(individual)):
        if random.random() < mutation_rate:
            individual[i] = 1 - individual[i]  # 二进制基因取反
    return individual

# 遗传算法主函数
def genetic_algorithm(pop_size, chromo_len, max_generations, mutation_rate):
    population = init_population(pop_size, chromo_len)
    
    for _ in range(max_generations):
        fitness = calc_fitness(population)
        elite = select_elite(population, fitness)
        new_population = [elite]
        
        while len(new_population) < pop_size:
            parent1 = random.choice(population)
            parent2 = random.choice(population)
            child1, child2 = crossover(parent1, parent2)
            child1 = mutate(child1, mutation_rate)
            child2 = mutate(child2, mutation_rate)
            new_population.extend([child1, child2])
        
        population = new_population
    
    best_solution = select_elite(population, calc_fitness(population))
    
    return int(''.join(str(gene) for gene in best_solution), 2)

# 示例调用
pop_size = 100  # 种群大小
chromo_len = 10  # 染色体长度
max_generations = 50  # 最大迭代次数
mutation_rate = 0.01  # 变异率

best_solution = genetic_algorithm(pop_size, chromo_len, max_generations, mutation_rate)
print("最小值为:", best_solution)

在示例代码中，我们定义了一个简单的目标函数 `fitness_func(x)`，并使用二进制编码来表示染色体。通过选择、交叉和变异等操作，不断优化种群中的个体，最终得到一个逼近函数最小值的解。通过调整种群大小、染色体长度、迭代次数和变异率等参数，可以对算法的性能进行调优。