请写一段用于求解多目标优化问题的粒子群算法代码

下面是一个简单的用于求解多目标优化问题的粒子群算法代码：

import numpy as np

# 定义多目标适应度函数
def multi_objective_fitness(x):
    f1 = x[0]**2 + x[1]**2
    f2 = (x[0]-1)**2 + x[1]**2
    return [f1, f2]

# 定义粒子群算法函数
def multi_objective_pso(fitness_func, n_particles, n_dimensions, n_iterations):
    # 初始化粒子和速度
    particles = np.random.rand(n_particles, n_dimensions)
    velocities = np.zeros((n_particles, n_dimensions))
    
    # 初始化最优解和全局最优解
    p_best = particles.copy()
    g_best = particles[0].copy()
    
    # 初始化最优解的适应度值和全局最优解的适应度值
    p_best_fitness = np.zeros(n_particles)
    g_best_fitness = np.zeros(n_dimensions)
    
    # 初始化粒子的适应度值
    fitness = np.zeros(n_particles)
    
    # 开始迭代
    for i in range(n_iterations):
        for j in range(n_particles):
            # 更新速度
            r1 = np.random.rand(n_dimensions)
            r2 = np.random.rand(n_dimensions)
            velocities[j] = velocities[j] + r1 * (p_best[j] - particles[j]) + r2 * (g_best - particles[j])
            
            # 更新位置
            particles[j] = particles[j] + velocities[j]
            
            # 计算适应度值
            fitness[j] = fitness_func(particles[j])
            
            # 更新最优解和全局最优解
            if np.all(fitness[j] < p_best_fitness[j]):
                p_best[j] = particles[j].copy()
                p_best_fitness[j] = fitness[j].copy()
            
            if np.all(fitness[j] < g_best_fitness):
                g_best = particles[j].copy()
                g_best_fitness = fitness[j].copy()
                
        # 输出每轮迭代的全局最优解
        print("Iteration {}: {}, fitness = {}".format(i, g_best, g_best_fitness))
        
    return g_best, g_best_fitness

# 运行多目标粒子群算法
multi_objective_pso(multi_objective_fitness, n_particles=10, n_dimensions=2, n_iterations=50)

这段代码实现了一个简单的多目标优化问题的粒子群算法。其中，`multi_objective_fitness`函数定义了多目标适应度函数。在主函数`multi_objective_pso`中，首先进行了粒子和速度的初始化，然后在每轮迭代中更新粒子的位置和速度，并计算适应度值。同时，也更新了最优解和全局最优解。最后，输出每轮迭代的全局最优解。