【进阶二】Python实现VRPTW常见求解算法——差分进化算法（DE）_python 差分进化算法

基于python语言，实现经典差分进化算法（DE）对带有时间窗的车辆路径规划问题（ VRPTW ）进行求解。

往期优质资源

• python实现6种智能算法求解CVRP问题
• python实现7种智能算法求解MDVRP问题
• python实现7种智能算法求解MDVRPTW问题
• Python版MDHFVRPTW问题智能求解算法代码【TS算法】
• Python版MDHFVRPTW问题智能求解算法代码【SA算法】
• Python版MDHFVRPTW问题智能求解算法代码【GA算法】
• Python版MDHFVRPTW问题智能求解算法代码【DPSO算法】
• Python版MDHFVRPTW问题智能求解算法代码【DE算法】
• Python版MDHFVRPTW问题智能求解算法代码【ACO算法】
• Python版HVRP问题智能求解算法代码【GA算法】
• Python版HVRP问题智能求解算法代码【DPSO算法】

1. 适用场景

• 求解MDVRPTW或VRPTW
• 车辆类型单一
• 车辆容量不小于需求节点最大需求
• 车辆路径长度或运行时间无限制
• 需求节点服务成本满足三角不等式
• 节点时间窗至少满足车辆路径只包含一个需求节点的情况
• 多车辆基地或单一
• 各车场车辆总数满足实际需求

2. 求解效果

（1）收敛曲线

（2）车辆路径

3. 代码分析

应用DE算法求解MDVRPTW时保留了已有代码的架构与思路，为能够求解带有时间窗的（多车场）车辆路径规划问题，这里参考既有文献对路径分割算法进行了改进（"splitRoutes"函数），在分割车辆路径时不仅考虑了车辆容量限制，还考虑了节点的时间窗约束，以此使得分割后的路径可行。在此改进下继承了大量原有代码，降低了代码改进量。

4. 数据格式

以csv文件储存数据，其中demand.csv文件记录需求节点数据，共包含需求节点id，需求节点横坐标，需求节点纵坐标，需求量；depot.csv文件记录车场节点数据，共包含车场id，车场横坐标，车场纵坐标，车队数量。需要注意的是：需求节点id应为整数，车场节点id任意，但不可与需求节点id重复。 可参考github主页相关文件。

5. 分步实现

（1）数据结构
定义Sol()类，Node()类，Model()类，其属性如下表：

• Sol()类，表示一个可行解

• Node()类，表示一个网络节点

• Model()类，存储算法参数

（2）文件读取

def readCSVFile(demand_file,depot_file,model):
    with open(demand_file,'r') as f:
        demand_reader=csv.DictReader(f)
        for row in demand_reader:
            node = Node()
            node.id = int(row['id'])
            node.x_coord = float(row['x_coord'])
            node.y_coord = float(row['y_coord'])
            node.demand = float(row['demand'])
            node.start_time=float(row['start_time'])
            node.end_time=float(row['end_time'])
            node.service_time=float(row['service_time'])
            model.demand_dict[node.id] = node
            model.demand_id_list.append(node.id)
        model.number_of_demands=len(model.demand_id_list)

    with open(depot_file, 'r') as f:
        depot_reader = csv.DictReader(f)
        for row in depot_reader:
            node = Node()
            node.id = row['id']
            node.x_coord = float(row['x_coord'])
            node.y_coord = float(row['y_coord'])
            node.depot_capacity = float(row['capacity'])
            node.start_time=float(row['start_time'])
            node.end_time=float(row['end_time'])
            model.depot_dict[node.id] = node
            model.depot_id_list.append(node.id)
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（3）计算距离&时间矩阵

def calDistanceTimeMatrix(model):
    for i in range(len(model.demand_id_list)):
        from_node_id = model.demand_id_list[i]
        for j in range(i + 1, len(model.demand_id_list)):
            to_node_id = model.demand_id_list[j]
            dist = math.sqrt((model.demand_dict[from_node_id].x_coord - model.demand_dict[to_node_id].x_coord) ** 2
                             + (model.demand_dict[from_node_id].y_coord - model.demand_dict[to_node_id].y_coord) ** 2)
            model.distance_matrix[from_node_id, to_node_id] = dist
            model.distance_matrix[to_node_id, from_node_id] = dist
            model.time_matrix[from_node_id,to_node_id] = math.ceil(dist/model.vehicle_speed)
            model.time_matrix[to_node_id,from_node_id] = math.ceil(dist/model.vehicle_speed)
        for _, depot in model.depot_dict.items():
            dist = math.sqrt((model.demand_dict[from_node_id].x_coord - depot.x_coord) ** 2
                             + (model.demand_dict[from_node_id].y_coord - depot.y_coord) ** 2)
            model.distance_matrix[from_node_id, depot.id] = dist
            model.distance_matrix[depot.id, from_node_id] = dist
            model.time_matrix[from_node_id,depot.id] = math.ceil(dist/model.vehicle_speed)
            model.time_matrix[depot.id,from_node_id] = math.ceil(dist/model.vehicle_speed)
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（4）目标值计算
适应度计算依赖" splitRoutes "函数对有序节点序列行解分割得到车辆行驶路线，同时在得到各车辆形式路线后在满足车场车队规模条件下分配最近车场，之后调用 " calTravelCost "函数确定车辆访问各路径节点的到达和离开时间点，并计算旅行距离成本和旅行时间成本。

def selectDepot(route,depot_dict,model):
    min_in_out_distance=float('inf')
    index=None
    for _,depot in depot_dict.items():
        if depot.depot_capacity>0:
            in_out_distance=model.distance_matrix[depot.id,route[0]]+model.distance_matrix[route[-1],depot.id]
            if in_out_distance<min_in_out_distance:
                index=depot.id
                min_in_out_distance=in_out_distance
    if index is None:
        print("there is no vehicle to dispatch")
        sys.exit(0)
    route.insert(0,index)
    route.append(index)
    depot_dict[index].depot_capacity=depot_dict[index].depot_capacity-1
    return route,depot_dict

def calTravelCost(route_list,model):
    timetable_list=[]
    cost_of_distance=0
    cost_of_time=0
    for route in route_list:
        timetable=[]
        for i in range(len(route)):
            if i == 0:
                depot_id=route[i]
                next_node_id=route[i+1]
                travel_time=model.time_matrix[depot_id,next_node_id]
                departure=max(0,model.demand_dict[next_node_id].start_time-travel_time)
                timetable.append((departure,departure))
            elif 1<= i <= len(route)-2:
                last_node_id=route[i-1]
                current_node_id=route[i]
                current_node = model.demand_dict[current_node_id]
                travel_time=model.time_matrix[last_node_id,current_node_id]
                arrival=max(timetable[-1][1]+travel_time,current_node.start_time)
                departure=arrival+current_node.service_time
                timetable.append((arrival,departure))
                cost_of_distance += model.distance_matrix[last_node_id, current_node_id]
                cost_of_time += model.time_matrix[last_node_id, current_node_id]+ current_node.service_time\
                                + max(current_node.start_time - timetable[-1][1] + travel_time, 0)
            else:
                last_node_id = route[i - 1]
                depot_id=route[i]
                travel_time = model.time_matrix[last_node_id,depot_id]
                departure = timetable[-1][1]+travel_time
                timetable.append((departure,departure))
                cost_of_distance +=model.distance_matrix[last_node_id,depot_id]
                cost_of_time+=model.time_matrix[last_node_id,depot_id]
        timetable_list.append(timetable)
    return timetable_list,cost_of_time,cost_of_distance

def extractRoutes(node_id_list,Pred,model):
    depot_dict=copy.deepcopy(model.depot_dict)
    route_list = []
    route = []
    label = Pred[node_id_list[0]]
    for node_id in node_id_list:
        if Pred[node_id] == label:
            route.append(node_id)
        else:
            route, depot_dict=selectDepot(route,depot_dict,model)
            route_list.append(route)
            route = [node_id]
            label = Pred[node_id]
    route, depot_dict = selectDepot(route, depot_dict, model)
    route_list.append(route)
    return route_list

def splitRoutes(node_id_list,model):
    depot=model.depot_id_list[0]
    V={id:float('inf') for id in model.demand_id_list}
    V[depot]=0
    Pred={id:depot for id in model.demand_id_list}
    for i in range(len(node_id_list)):
        n_1=node_id_list[i]
        demand=0
        departure=0
        j=i
        cost=0
        while True:
            n_2 = node_id_list[j]
            demand = demand + model.demand_dict[n_2].demand
            if n_1 == n_2:
                arrival= max(model.demand_dict[n_2].start_time,model.depot_dict[depot].start_time+model.time_matrix[depot,n_2])
                departure=arrival+model.demand_dict[n_2].service_time+model.time_matrix[n_2,depot]
                if model.opt_type == 0:
                    cost=model.distance_matrix[depot,n_2]*2
                else:
                    cost=model.time_matrix[depot,n_2]*2
            else:
                n_3=node_id_list[j-1]
                arrival= max(departure-model.time_matrix[n_3,depot]+model.time_matrix[n_3,n_2],model.demand_dict[n_2].start_time)
                departure=arrival+model.demand_dict[n_2].service_time+model.time_matrix[n_2,depot]
                if model.opt_type == 0:
                    cost=cost-model.distance_matrix[n_3,depot]+model.distance_matrix[n_3,n_2]+model.distance_matrix[n_2,depot]
                else:
                    cost=cost-model.time_matrix[n_3,depot]+model.time_matrix[n_3,n_2]\
                         +model.demand_dict[n_2].start_time-departure-model.time_matrix[n_3,depot]+model.time_matrix[n_3,n_2]\
                         +model.time_matrix[n_2,depot]
            if demand<=model.vehicle_cap and departure-model.time_matrix[n_2,depot] <= model.demand_dict[n_2].end_time:
                if departure <= model.depot_dict[depot].end_time:
                    n_4=node_id_list[i-1] if i-1>=0 else depot
                    if V[n_4]+cost <= V[n_2]:
                        V[n_2]=V[n_4]+cost
                        Pred[n_2]=i-1
                    j=j+1
            else:
                break
            if j==len(node_id_list):
                break
    route_list= extractRoutes(node_id_list,Pred,model)
    return len(route_list),route_list

def calObj(sol,model):

    node_id_list=copy.deepcopy(sol.node_id_list)
    num_vehicle, sol.route_list = splitRoutes(node_id_list, model)
    # travel cost
    sol.timetable_list,sol.cost_of_time,sol.cost_of_distance =calTravelCost(sol.route_list,model)
    if model.opt_type == 0:
        sol.obj=sol.cost_of_distance
    else:
        sol.obj=sol.cost_of_time
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（5）初始解生成

def genInitialSol(model):
    demand_id_list=copy.deepcopy(model.demand_id_list)
    for i in range(model.popsize):
        seed=int(random.randint(0,10))
        random.seed(seed)
        random.shuffle(demand_id_list)
        sol=Sol()
        sol.node_id_list=copy.deepcopy(demand_id_list)
        calObj(sol,model)
        model.sol_list.append(sol)
        if sol.obj<model.best_sol.obj:
            model.best_sol=copy.deepcopy(sol)
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（6）突变操作

def muSol(model,v1):
    x1=model.sol_list[v1].node_id_list
    while True:
        v2=random.randint(0,len(model.demand_id_list)-1)
        if v2!=v1:
            break
    while True:
        v3=random.randint(0,len(model.demand_id_list)-1)
        if v3!=v2 and v3!=v1:
            break
    x2=model.sol_list[v2].node_id_list
    x3=model.sol_list[v3].node_id_list
    mu_x=[min(int(x1[i]+model.F*(x2[i]-x3[i])),len(model.demand_id_list)-1) for i in range(len(model.demand_id_list)) ]
    return mu_x
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（7）交叉操作

def adjustRoutes(demand_id_list,model):
    all_node_list=copy.deepcopy(model.demand_id_list)
    repeat_node=[]
    for id,node_id in enumerate(demand_id_list):
        if node_id in all_node_list:
            all_node_list.remove(node_id)
        else:
            repeat_node.append(id)
    for i in range(len(repeat_node)):
        demand_id_list[repeat_node[i]]=all_node_list[i]
    return demand_id_list

def crossSol(model,vx,vy):
    cro_x=[]
    for i in range(len(model.demand_id_list)):
        if random.random()<model.Cr:
            cro_x.append(vy[i])
        else:
            cro_x.append(vx[i])
    cro_x=adjustRoutes(cro_x,model)
    return cro_x
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（8）绘制收敛曲线

def plotObj(obj_list):
    plt.rcParams['font.sans-serif'] = ['SimHei'] #show chinese
    plt.rcParams['axes.unicode_minus'] = False  # Show minus sign
    plt.plot(np.arange(1,len(obj_list)+1),obj_list)
    plt.xlabel('Iterations')
    plt.ylabel('Obj Value')
    plt.grid()
    plt.xlim(1,len(obj_list)+1)
    plt.show()
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（9）绘制车辆路线

def plotRoutes(model):
    for route in model.best_sol.route_list:
        x_coord=[model.depot_dict[route[0]].x_coord]
        y_coord=[model.depot_dict[route[0]].y_coord]
        for node_id in route[1:-1]:
            x_coord.append(model.demand_dict[node_id].x_coord)
            y_coord.append(model.demand_dict[node_id].y_coord)
        x_coord.append(model.depot_dict[route[-1]].x_coord)
        y_coord.append(model.depot_dict[route[-1]].y_coord)
        plt.grid()
        if route[0]=='d1':
            plt.plot(x_coord,y_coord,marker='o',color='black',linewidth=0.5,markersize=5)
        elif route[0]=='d2':
            plt.plot(x_coord,y_coord,marker='o',color='orange',linewidth=0.5,markersize=5)
        else:
            plt.plot(x_coord,y_coord,marker='o',color='b',linewidth=0.5,markersize=5)
    plt.xlabel('x_coord')
    plt.ylabel('y_coord')
    plt.show()
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（10）输出结果

def outPut(model):
    work=xlsxwriter.Workbook('result.xlsx')
    worksheet=work.add_worksheet()
    worksheet.write(0, 0, 'cost_of_time')
    worksheet.write(0, 1, 'cost_of_distance')
    worksheet.write(0, 2, 'opt_type')
    worksheet.write(0, 3, 'obj')
    worksheet.write(1,0,model.best_sol.cost_of_time)
    worksheet.write(1,1,model.best_sol.cost_of_distance)
    worksheet.write(1,2,model.opt_type)
    worksheet.write(1,3,model.best_sol.obj)
    worksheet.write(2,0,'vehicleID')
    worksheet.write(2,1,'route')
    worksheet.write(2,2,'timetable')
    for row,route in enumerate(model.best_sol.route_list):
        worksheet.write(row+3,0,'v'+str(row+1))
        r=[str(i)for i in route]
        worksheet.write(row+3,1, '-'.join(r))
        r=[str(i)for i in model.best_sol.timetable_list[row]]
        worksheet.write(row+3,2, '-'.join(r))
    work.close()
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（11）主函数

def run(demand_file,depot_file,epochs,Cr,F,popsize,v_cap,opt_type):
    """
    :param demand_file: 需求节点文件路径
    :param depot_file: 车场节点文件路径
    :param epochs:迭代次数
    :param Cr:差分交叉概率
    :param F:缩放因子
    :param popsize:种群规模
    :param v_cap:车辆容量
    :param opt_type:优化类型:0:最小化车辆数,1:最小化行驶距离
    :return:
    """
    model=Model()
    model.vehicle_cap=v_cap
    model.Cr=Cr
    model.F=F
    model.popsize=popsize
    model.opt_type=opt_type

    readCSVFile(demand_file,depot_file,model)
    calDistanceTimeMatrix(model)
    best_sol = Sol()
    best_sol.obj = float('inf')
    model.best_sol = best_sol
    genInitialSol(model)
    history_best_obj = []
    for ep in range(epochs):
        for i in range(popsize):
            v1=random.randint(0,len(model.demand_id_list)-1)
            sol=model.sol_list[v1]
            mu_x=muSol(model,v1)
            u=crossSol(model,sol.node_id_list,mu_x)
            new_sol=Sol()
            new_sol.node_id_list=u
            calObj(new_sol,model)
            if new_sol.obj<=sol.obj:
                sol=copy.deepcopy(new_sol)
                if sol.obj<model.best_sol.obj:
                    model.best_sol=copy.deepcopy(sol)
            history_best_obj.append(model.best_sol.obj)
        print("%s/%s， best obj: %s" % (ep, epochs, model.best_sol.obj))
    plotObj(history_best_obj)
    plotRoutes(model)
    outPut(model)
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6. 完整代码

如有错误，欢迎交流。
代码和数据文件获取【私】

参考

1. A Genetic Algorithm for The Vehicle Routing Problem with Time Windows
2. A simple and effective evolutionary algorithm for the vehicle routing problem