给我一个多目标优化的代码

以下是一个多目标优化的代码示例，使用遗传算法进行优化：

import random

# 定义目标函数
def objective_function(x):
    # 目标函数有两个目标：最小化 x 的平方和和最小化 x 的绝对值和
    return sum([xi**2 for xi in x]), sum([abs(xi) for xi in x])

# 定义遗传算法参数
population_size = 50
num_generations = 100
mutation_rate = 0.1
crossover_rate = 0.9

# 定义变量范围
variable_range = (-10, 10)
num_variables = 5

# 初始化种群
def init_population():
    population = []
    for i in range(population_size):
        individual = [random.uniform(variable_range[0], variable_range[1]) for j in range(num_variables)]
        population.append(individual)
    return population

# 计算适应度
def calculate_fitness(population):
    fitness_scores = []
    for individual in population:
        obj1, obj2 = objective_function(individual)
        fitness_scores.append((obj1, obj2))
    return fitness_scores

# 选择
def selection(population, fitness_scores):
    population_size = len(population)
    new_population = []
    total_fitness = sum([sum(score) for score in fitness_scores])
    for i in range(population_size):
        selected_individual = None
        while selected_individual is None:
            random_number = random.uniform(0, total_fitness)
            cumulative_fitness = 0
            for j in range(population_size):
                cumulative_fitness += sum(fitness_scores[j])
                if cumulative_fitness > random_number:
                    selected_individual = population[j]
                    break
        new_population.append(selected_individual)
    return new_population

# 交叉
def crossover(population):
    new_population = []
    for i in range(population_size):
        parent1 = population[random.randint(0, population_size-1)]
        parent2 = population[random.randint(0, population_size-1)]
        if random.random() < crossover_rate:
            crossover_point = random.randint(1, num_variables-1)
            child1 = parent1[:crossover_point] + parent2[crossover_point:]
            child2 = parent2[:crossover_point] + parent1[crossover_point:]
            new_population.append(child1)
            new_population.append(child2)
        else:
            new_population.append(parent1)
            new_population.append(parent2)
    return new_population

# 变异
def mutation(population):
    new_population = []
    for individual in population:
        if random.random() < mutation_rate:
            mutation_point = random.randint(0, num_variables-1)
            individual[mutation_point] += random.uniform(-0.5, 0.5)
        new_population.append(individual)
    return new_population

# 进化
def evolve(population):
    fitness_scores = calculate_fitness(population)
    new_population = selection(population, fitness_scores)
    new_population = crossover(new_population)
    new_population = mutation(new_population)
    return new_population

# 运行遗传算法
population = init_population()
for i in range(num_generations):
    population = evolve(population)
    best_individual = min(population, key=lambda x: sum(objective_function(x)))
    print(f"Generation {i}: Objective 1 = {objective_function(best_individual)[0]}, Objective 2 = {objective_function(best_individual)[1]}")

这个代码使用遗传算法优化一个具有两个目标的函数，分别是最小化变量的平方和和最小化变量的绝对值和。代码中的变量范围为 (-10, 10)，共有 5 个变量，种群大小为 50，进化代数为 100，变异率为 0.1，交叉率为 0.9。在每一代中，都会输出当前最优个体的两个目标函数值。