用Python写一段遗传算法

好的，下面是一个简单的遗传算法的Python代码示例：

import random

# 遗传算法的参数设置
POPULATION_SIZE = 10  # 种群数量
CROSSOVER_PROBABILITY = 0.8  # 交叉概率
MUTATION_PROBABILITY = 0.2  # 变异概率
GENERATIONS = 10  # 迭代次数

# 假设我们要优化的函数为 f(x) = x^2
def objective_function(x):
    return x**2

# 初始化种群，每个个体随机生成一个 x 值
def initialize_population():
    population = []
    for i in range(POPULATION_SIZE):
        x = random.uniform(-10, 10)
        population.append({'x': x, 'fitness': None})
    return population

# 计算个体的适应度
def calculate_fitness(individual):
    x = individual['x']
    fitness = objective_function(x)
    individual['fitness'] = fitness
    return fitness

# 选择操作，使用轮盘赌选择算法
def selection(population):
    total_fitness = sum([individual['fitness'] for individual in population])
    selected_individuals = []
    for i in range(POPULATION_SIZE):
        pick = random.uniform(0, total_fitness)
        current = 0
        for individual in population:
            current += individual['fitness']
            if current > pick:
                selected_individuals.append(individual)
                break
    return selected_individuals

# 交叉操作，使用单点交叉算法
def crossover(parent1, parent2):
    if random.random() < CROSSOVER_PROBABILITY:
        crossover_point = random.randint(0, 1)
        child1 = {'x': None, 'fitness': None}
        child2 = {'x': None, 'fitness': None}
        child1['x'] = parent1['x'][0:crossover_point] + parent2['x'][crossover_point:]
        child2['x'] = parent2['x'][0:crossover_point] + parent1['x'][crossover_point:]
        return child1, child2
    else:
        return parent1, parent2

# 变异操作，使用随机变异算法
def mutation(child):
    if random.random() < MUTATION_PROBABILITY:
        mutation_point = random.randint(0, len(child['x'])-1)
        child['x'][mutation_point] = random.uniform(-10, 10)
    return child

# 遗传算法主程序
def genetic_algorithm():
    # 初始化种群
    population = initialize_population()
    
    # 迭代
    for i in range(GENERATIONS):
        # 计算个体适应度
        for individual in population:
            calculate_fitness(individual)
        
        # 选择
        selected_individuals = selection(population)
        
        # 交叉
        children = []
        for i in range(0, POPULATION_SIZE, 2):
            child1, child2 = crossover(selected_individuals[i], selected_individuals[i+1])
            children.append(mutation(child1))
            children.append(mutation(child2))
        
        # 替换原始种群
        population = children
    
    # 返回最优解
    best_individual = max(population, key=lambda x: x['fitness'])
    return best_individual['x']

上述代码实现了一个简单的遗传算法，用于求解 $f(x)=x^2$ 函数在 $[-10, 10]$ 区间内的最大值。在遗传算法的迭代过程中，每个个体表示为一个字典，包含一个 x 值和一个适应度值。在初始化种群时，随机生成每个个体的 x 值；在计算适应度时，根据目标函数计算个体的适应度；在选择操作中，使用轮盘赌选择算法选择个体；在交叉操作中，使用单点交叉算法对个体进行交叉；在变异操作中，使用随机变异算法对个体进行变异。最终返回种群中适应度最高的个体的 x 值作为最优解。