用代码实现粒子群优化算法（PSO）求解车辆路径问题（VRP）。

这里给出一个简单的Python实现粒子群优化算法（PSO）求解车辆路径问题（VRP）的代码示例。假设我们有一些客户需求点和一个仓库，需要用多辆车辆依次访问这些点并回到仓库，最小化总行驶距离。

import random
import math

# 客户需求点和仓库的坐标
locations = [(4, 4), (2, 0), (6, 0), (0, 6), (8, 6), (0, 0), (8, 0), (8, 8)]

# 计算两个点之间的距离
def distance(p1, p2):
    return math.sqrt((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2)

# 计算车辆路径的总距离
def total_distance(vehicles):
    result = 0
    for v in vehicles:
        for i in range(len(v) - 1):
            result += distance(locations[v[i]], locations[v[i+1]])
    return result

# 粒子群优化算法
def pso_vrp(num_vehicles, max_iter):
    # 初始化粒子群
    num_particles = 20
    particles = []
    for i in range(num_particles):
        vehicles = [[] for _ in range(num_vehicles)]
        for j in range(len(locations) - 1):
            vehicles[random.randint(0, num_vehicles-1)].append(j+1)
        particles.append(vehicles)

    # 记录全局最优解
    global_best = None
    global_best_fitness = float('inf')

    # 迭代搜索
    for iter in range(max_iter):
        for p in particles:
            # 计算适应度函数（即车辆路径总距离）
            fitness = total_distance(p)
            # 更新全局最优解
            if fitness < global_best_fitness:
                global_best = p
                global_best_fitness = fitness

        # 更新每个粒子的速度和位置
        for p in particles:
            for i in range(num_vehicles):
                # 计算车辆路径的当前距离
                current_distance = total_distance(p)
                # 生成随机解
                random_solution = [[] for _ in range(num_vehicles)]
                for j in range(len(locations) - 1):
                    random_solution[random.randint(0, num_vehicles-1)].append(j+1)
                # 计算随机解的距离
                random_distance = total_distance(random_solution)
                # 更新速度和位置
                for j in range(len(p[i])):
                    if random.uniform(0, 1) < 0.5:
                        p[i][j] = global_best[i][j]
                    else:
                        p[i][j] = random_solution[i][j]
                # 如果新位置更优，则接受新位置
                if total_distance(p) < current_distance:
                    current_distance = total_distance(p)

    # 返回全局最优解
    return global_best

在这个示例中，我们使用了一个简单的随机解来更新粒子的位置和速度。实际上，还可以使用更复杂的启发式规则，以期更快地找到最优解。