遗传算法python实例

遗传算法是一种优化算法，用于解决复杂问题，其原理基于进化论中的自然选择和遗传机制。下面是一个简单的遗传算法 Python 实例，用于求解函数 f(x)=x^2 在 [-10,10] 区间内的最大值：

import random

# 定义适应度函数
def fitness(x):
    return x**2

# 初始化种群
def init_population(pop_size, chromo_size):
    population = []
    for i in range(pop_size):
        chromosome = [random.randint(0, 1) for j in range(chromo_size)]
        population.append(chromosome)
    return population

# 选择操作
def selection(population):
    fitness_values = [fitness(chromosome) for chromosome in population]
    total_fitness = sum(fitness_values)
    probabilities = [fitness_value / total_fitness for fitness_value in fitness_values]
    cum_probabilities = [sum(probabilities[:i+1]) for i in range(len(probabilities))]
    selected_population = []
    for i in range(len(population)):
        r = random.random()
        for j in range(len(cum_probabilities)):
            if r <= cum_probabilities[j]:
                selected_population.append(population[j])
                break
    return selected_population

# 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 mutation(chromosome, mutation_rate):
    for i in range(len(chromosome)):
        if random.random() < mutation_rate:
            chromosome[i] = 1 - chromosome[i]
    return chromosome

# 遗传算法主程序
def genetic_algorithm(pop_size, chromo_size, max_generation, mutation_rate):
    population = init_population(pop_size, chromo_size)
    for generation in range(max_generation):
        selected_population = selection(population)
        new_population = []
        for i in range(pop_size//2):
            parent1, parent2 = selected_population[2*i], selected_population[2*i+1]
            child1, child2 = crossover(parent1, parent2)
            child1 = mutation(child1, mutation_rate)
            child2 = mutation(child2, mutation_rate)
            new_population.append(child1)
            new_population.append(child2)
        population = new_population
    fitness_values = [fitness(chromosome) for chromosome in population]
    max_fitness_index = fitness_values.index(max(fitness_values))
    return population[max_fitness_index]

# 设置参数并运行遗传算法
pop_size = 100
chromo_size = 10
max_generation = 100
mutation_rate = 0.01
result = genetic_algorithm(pop_size, chromo_size, max_generation, mutation_rate)
print('x:', int(''.join(map(str, result)), 2))
print('f(x):', fitness(result))

此代码中实现了遗传算法的主要步骤：初始化种群、选择、交叉和变异。其中，适应度函数 fitness(x) 中计算了 x^2 的值，init_population() 中初始化了二进制编码的染色体，selection() 中使用了轮盘赌算法进行选择，crossover() 中采用了单点交叉，mutation() 中采用了随机单点变异。最后，genetic_algorithm() 函数将上述操作组合在一起，并返回最优解。在此例中，最优解为函数 f(x)=x^2 在 [-10,10] 区间内的最大值，即 x=0。