写一段代码用粒子群优化求解VRPPD问题

VRPPD（Vehicle Routing Problem with Pickup and Delivery）问题是一类经典的物流配送问题，它的目标是在满足所有需求的前提下，最小化配送车辆的数量和总行驶距离。下面是使用粒子群优化算法求解VRPPD问题的示例代码：

import numpy as np

# VRPPD问题的目标函数
def objective_function(x, c, q, d):
    """
    x: [n, m] 二维矩阵，表示每个客户分配的车辆编号
    c: [m, n, n] 三维矩阵，表示每辆车的路径距离
    q: [n] 一维矩阵，表示每个客户的需求量
    d: [n, 2] 二维矩阵，表示每个客户的坐标位置
    """
    n, m = x.shape
    f = 0
    for i in range(m):
        # 计算每辆车的路径距离
        route_distance = 0
        for j in range(n):
            if x[j, i] == 1:
                for k in range(n):
                    if x[k, i] == 1:
                        route_distance += c[i, j, k]
        f += route_distance
    # 计算每个客户的惩罚项
    for j in range(n):
        demand = q[j]
        for i in range(m):
            if x[j, i] == 1:
                capacity = np.sum(q * x[:, i])
                if demand > capacity:  # 客户需求不能满足
                    dist_to_depot = np.linalg.norm(d[j, :] - d[0, :])
                    f += 10000 * (demand - capacity) * dist_to_depot
    return f

# 粒子群优化算法
def PSO(n_particles, n_dim, max_iter, c1, c2, w, bounds, c, q, d):
    """
    n_particles: 粒子数
    n_dim: 粒子维度
    max_iter: 迭代次数
    c1, c2, w: PSO算法参数
    bounds: 取值范围
    c, q, d: VRPPD问题参数
    """
    # 初始化粒子位置和速度
    x = np.random.uniform(bounds[:, 0], bounds[:, 1], size=(n_particles, n_dim))
    v = np.zeros((n_particles, n_dim))
    # 初始化全局最优解和个体最优解
    pbest = x.copy()
    gbest = pbest[np.argmin([objective_function(xi, c, q, d) for xi in pbest]), :]
    # 开始迭代
    for i in range(max_iter):
        # 更新粒子速度和位置
        v = w * v + c1 * np.random.rand() * (pbest - x) + c2 * np.random.rand() * (gbest - x)
        x = np.clip(x + v, bounds[:, 0], bounds[:, 1])
        # 更新个体最优解和全局最优解
        for j in range(n_particles):
            if objective_function(x[j, :], c, q, d) < objective_function(pbest[j, :], c, q, d):
                pbest[j, :] = x[j, :]
            if objective_function(pbest[j, :], c, q, d) < objective_function(gbest, c, q, d):
                gbest = pbest[j, :]
    return gbest

# 测试代码
if __name__ == '__main__':
    # VRPPD问题参数
    n = 10  # 客户数量
    m = 3  # 车辆数量
    q = np.random.randint(1, 5, size=n)  # 客户需求
    d = np.random.rand(n, 2) * 100  # 客户位置
    c = np.zeros((m, n, n))  # 路径距离
    for i in range(m):
        for j in range(n):
            for k in range(n):
                if j != k:
                    c[i, j, k] = np.linalg.norm(d[j, :] - d[k, :])
    # PSO算法参数和取值范围
    n_particles = 20
    n_dim = n
    max_iter = 100
    c1 = 1.5
    c2 = 1.5
    w = 0.8
    bounds = np.tile(np.array([[0, 1]]), (n_dim, 1))
    # 求解VRPPD问题
    x = np.zeros((n, m))
    for i in range(n):
        x[i, i % m] = 1  # 将客户均匀分配到各个车辆
    result = PSO(n_particles, n_dim, max_iter, c1, c2, w, bounds, c, q, d)
    for i in range(n):
        x[i, int(result[i])] = 1  # 根据PSO算法的结果，重新分配客户到各个车辆
    print(x)
    print(objective_function(x, c, q, d))