多目标遗传算法code

多目标遗传算法（Multi-Objective Genetic Algorithm，MOGA）是一种用于解决多目标优化问题的进化算法。它基于遗传算法的思想，通过模拟自然界的进化过程，逐步搜索最优解的近似集合。

下面是一个简单的多目标遗传算法的代码示例：

import random

# 定义目标函数
def objective_function(x):
    return [x[0]**2, (x[0]-2)**2]

# 初始化种群
def initialize_population(population_size, num_variables):
    population = []
    for _ in range(population_size):
        individual = [random.uniform(-5, 5) for _ in range(num_variables)]
        population.append(individual)
    return population

# 计算个体的适应度值
def calculate_fitness(individual):
    return objective_function(individual)

# 选择操作
def selection(population, num_parents):
    parents = []
    for _ in range(num_parents):
        parent = random.choice(population)
        parents.append(parent)
    return parents

# 交叉操作
def crossover(parents, offspring_size):
    offspring = []
    for _ in range(offspring_size):
        parent1, parent2 = random.sample(parents, 2)
        child = [parent1[i] if random.random() < 0.5 else parent2[i] for i in range(len(parent1))]
        offspring.append(child)
    return offspring

# 变异操作
def mutation(offspring):
    mutated_offspring = []
    for child in offspring:
        mutated_child = [gene + random.uniform(-0.5, 0.5) for gene in child]
        mutated_offspring.append(mutated_child)
    return mutated_offspring

# 多目标遗传算法主函数
def multi_objective_genetic_algorithm(population_size, num_variables, num_generations):
    population = initialize_population(population_size, num_variables)
    for _ in range(num_generations):
        parents = selection(population, population_size // 2)
        offspring = crossover(parents, population_size - len(parents))
        offspring = mutation(offspring)
        population = parents + offspring
    return population

# 测试
population_size = 100
num_variables = 1
num_generations = 50
result = multi_objective_genetic_algorithm(population_size, num_variables, num_generations)
print(result)

这段代码实现了一个简单的多目标遗传算法，其中定义了目标函数、初始化种群、计算适应度值、选择操作、交叉操作和变异操作等基本步骤。通过调用`multi_objective_genetic_algorithm`函数，可以得到最终的近似最优解集合。