NSGA2 算法解决车辆路径问题 (VRP) | Python 代码示例和帕累托前沿可视化

使用 NSGA2 算法解决车辆路径问题 (VRP) - Python 代码示例

本示例展示如何使用 NSGA2 算法解决一个典型的车辆路径问题 (VRP)，并可视化帕累托前沿和车辆配送路径。

问题描述:

• 随机生成一个仓库和一百个客户坐标，横纵坐标在 0 到 50 范围内。* 每个客户有随机需求量 (2-10 之间)。* 车辆容量约束为 100。* 车辆行驶速度为 40。* 每个客户有随机的预期配送到达时间 (0 到 8 之间)。* 目标函数有两个： * 成本最小化 (包括车辆固定成本和路径行驶成本)。 * 客户满意度最大化 (与预期到达时间和实际到达时间的差值相关)。

**代码:**pythonimport randomimport numpy as npimport matplotlib.pyplot as pltfrom platypus import NSGAII, Problem, Real, Integer, Subset, nondominatedfrom scipy.spatial import distance

class VRP(Problem): def init(self, n_customers): # 定义决策变量 super().init(n_customers+1, 2, 2) self.types[:] = [Real(0, 50) for i in range(n_customers)] + [Subset(range(n_customers), 1)] self.constraints[:] = '<=0'

    # 定义客户需求        self.demand = [random.randint(2, 10) for i in range(n_customers)]

    # 定义车辆容量        self.capacity = 100

    # 定义车辆行驶速度和固定成本        self.speed = 40        self.fixed_cost = 500

    # 定义预期配送到达时间        self.expected_time = [random.uniform(0, 8) for i in range(n_customers)]

def evaluate(self, solution):        # 计算路径距离和时间        routes = self.get_routes(solution.variables)        distances = [self.get_distance(route) for route in routes]        times = [self.get_time(route) for route in routes]

    # 计算成本        cost = sum([self.fixed_cost + distance * 0.05 for distance in distances])

    # 计算客户满意度        satisfaction = sum([(self.expected_time[i] - times[solution.variables[-1][i]]) * (0.8 if self.expected_time[i] - times[solution.variables[-1][i]] > 0 else 1.3) for i in range(len(self.expected_time))])

    # 设置目标函数        solution.objectives[:] = [cost, -satisfaction]

def get_distance(self, route):        distance = 0        for i in range(len(route)-1):            distance += distance.euclidean(route[i], route[i+1])        return distance

def get_time(self, route):        time = 0        demand = 0        for i in range(len(route)-1):            time += distance.euclidean(route[i], route[i+1]) / self.speed            demand += self.demand[i]            if demand > self.capacity:                time += 2 * (demand - self.capacity) / self.capacity                demand = 0        time += distance.euclidean(route[-1], [0, 0]) / self.speed        return time

def get_routes(self, variables):        routes = []        for subset in variables[-1]:            route = [variables[i] for i in subset]            route = sorted(route, key=lambda x: distance.euclidean(x, [0, 0]))            route = [[0, 0]] + route + [[0, 0]]            routes.append(route)        return routes

n_customers = 100problem = VRP(n_customers)

algorithm = NSGAII(problem)algorithm.run(1000)

front = nondominated(algorithm.result)

plt.figure(figsize=(8, 8))for solution in front: routes = problem.get_routes(solution.variables) for route in routes: x = [point[0] for point in route] y = [point[1] for point in route] plt.plot(x, y, '-o')plt.xlabel('x')plt.ylabel('y')plt.title('Vehicle Routing Problem')plt.show