【进阶一】Python实现MDCVRP常见求解算法——自适应大邻域搜索算法（ALNS）

基于python语言，实现自适应大邻域搜索算法（ALNS）对多车场车辆路径规划问题（MDCVRP）进行求解。

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1. 适用场景

• 求解MDCVRP 问题
• 车辆类型单一
• 车辆容量不小于需求节点最大需求
• 多车辆基地
• 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

车俩路径规划问题按照车场数量可分为单一车场路径规划问题和多车场路径规划问题。针对单一车场条件下仅考虑车辆容量限制的路径规划问题前边帖子中已实现ALNS算法求解，本文采用ALNS算法对多车场条件下仅考虑车辆容量限制的路径规划问题进行求解。为了保持代码的延续性以及求解思路的一致性，这里对上述ALNS算法代码进行如下主要修正实现MDCVRP问题的求解。

• Model数据结构类中采用demand_dict属性存储需求节点集合，depot_dict属性储存车场节点集合，demand_id_list属性储存需求节点id集合，distance_matrix属性储存任意节点间的欧式距离；
• Node数据结构类中去掉node_seq属性，增加depot_capacity属性记录车场的车队限制
• splitRoutes函数中分割车辆路径时分配最近车场作为其车辆提供基地（满足车场车队数量限制）

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
为便于数据处理，定义Sol()类，Node()类，Model()类，其属性如下表：

• Sol()类，表示一个可行解

属性	描述
node_id_list	需求节点id有序排列集合，对应TSP的解
obj	优化目标值
routes	车辆路径集合，对应MDCVRP的解

• Node()类，表示一个网络节点

属性	描述
id	物理节点id
x_coord	物理节点x坐标
y_coord	物理节点y坐标
demand	物理节点需求
depot_capacity	车辆基地车队规模

• Model()类，存储算法参数

属性	描述
best_sol	全局最优解，值类型为Sol()
demand_dict	需求节点集合（字典），值类型为Node()
depot_dict	车场节点集合（字典），值类型为Node()
demand_id_list	需求节点id集合
distance_matrix	节点距离矩阵
opt_type	优化目标类型，0：最小车辆数，1：最小行驶距离
vehicle_cap	车辆容量
rand_d_max	随机破坏程度上限
rand_d_min	随机破坏程度下限
worst_d_max	最坏破坏程度上限
worst_d_min	最坏破坏程度下限
regret_n	次优位置个数
r1	算子奖励1
r2	算子奖励2
r3	算子奖励3
rho	算子权重衰减系数
d_weight	破坏算子权重
d_select	破坏算子被选中次数/每轮
d_score	破坏算子被奖励得分/每轮
d_history_select	破坏算子历史共计被选中次数
d_history_score	破坏算子历史共计被奖励得分
r_weight	修复算子权重
r_select	修复算子被选中次数/每轮
r_score	修复算子被奖励得分/每轮
r_history_select	修复算子历史共计被选中次数
r_history_score	修复算子历史共计被奖励得分

（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'])
            model.demand_dict[node.id] = node
            model.demand_id_list.append(node.id)

    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'])
            model.depot_dict[node.id] = node

（3）计算距离矩阵

def calDistance(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
        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

（4）目标函数计算
适应度计算依赖" splitRoutes “函数对TSP可行解分割得到车辆行驶路线和所需车辆数，在得到各车辆行驶路线后调用” selectDepot “函数，在满足车场车队规模条件下分配最近车场，” calDistance "函数计算行驶距离。

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")
    route.insert(0,index)
    route.append(index)
    depot_dict[index].depot_capacity=depot_dict[index].depot_capacity-1
    return route,depot_dict

def splitRoutes(node_id_list,model):
    num_vehicle = 0
    vehicle_routes = []
    route = []
    remained_cap = model.vehicle_cap
    depot_dict=copy.deepcopy(model.depot_dict)
    for node_id in node_id_list:
        if remained_cap - model.demand_dict[node_id].demand >= 0:
            route.append(node_id)
            remained_cap = remained_cap - model.demand_dict[node_id].demand
        else:
            route,depot_dict=selectDepot(route,depot_dict,model)
            vehicle_routes.append(route)
            route = [node_id]
            num_vehicle = num_vehicle + 1
            remained_cap =model.vehicle_cap - model.demand_dict[node_id].demand

    route, depot_dict = selectDepot(route, depot_dict, model)
    vehicle_routes.append(route)

    return num_vehicle,vehicle_routes

def calRouteDistance(route,model):
    distance=0
    for i in range(len(route)-1):
        from_node=route[i]
        to_node=route[i+1]
        distance +=model.distance_matrix[from_node,to_node]
    return distance

def calObj(node_id_list,model):
    num_vehicle, vehicle_routes = splitRoutes(node_id_list, model)
    if model.opt_type==0:
        return num_vehicle,vehicle_routes
    else:
        distance = 0
        for route in vehicle_routes:
            distance += calRouteDistance(route, model)
        return distance,vehicle_routes

（5）初始解

def genInitialSol(node_id_list):
    node_id_list=copy.deepcopy(node_id_list)
    random.seed(0)
    random.shuffle(node_id_list)
    return node_id_list

（6）定义destroy算子（破坏算子）
这里实现两种destory：

• random destroy : 随机从当前解中移除一定比例的需求节点
• worst destroy：从当前解中移除一定比例引起目标函数增幅较大的需求节点

def createRandomDestory(model):
    d=random.uniform(model.rand_d_min,model.rand_d_max)
    reomve_list=random.sample(range(len(model.demand_id_list)),int(d*len(model.demand_id_list)))
    return reomve_list

def createWorseDestory(model,sol):
    deta_f=[]
    for node_id in sol.node_id_list:
        nodes_id_=copy.deepcopy(sol.node_id_list)
        nodes_id_.remove(node_id)
        obj,vehicle_routes=calObj(nodes_id_,model)
        deta_f.append(sol.obj-obj)
    sorted_id = sorted(range(len(deta_f)), key=lambda k: deta_f[k], reverse=True)
    d=random.randint(model.worst_d_min,model.worst_d_max)
    remove_list=sorted_id[:d]
    return remove_list

（7）定义repair算子（修复算子）

def createRandomRepair(remove_list,model,sol):
    unassigned_nodes_id=[]
    assigned_nodes_id = []
    # remove node from current solution
    for i in range(len(model.demand_id_list)):
        if i in remove_list:
            unassigned_nodes_id.append(sol.node_id_list[i])
        else:
            assigned_nodes_id.append(sol.node_id_list[i])
    # insert
    for node_id in unassigned_nodes_id:
        index=random.randint(0,len(assigned_nodes_id)-1)
        assigned_nodes_id.insert(index,node_id)
    new_sol=Sol()
    new_sol.node_id_list=copy.deepcopy(assigned_nodes_id)
    new_sol.obj,new_sol.routes=calObj(assigned_nodes_id,model)
    return new_sol

def findGreedyInsert(unassigned_nodes_id,assigned_nodes_id,model):
    best_insert_node_id=None
    best_insert_index = None
    best_insert_cost = float('inf')
    assigned_nodes_id_obj,_=calObj(assigned_nodes_id,model)
    for node_id in unassigned_nodes_id:
        for i in range(len(assigned_nodes_id)):
            assigned_nodes_id_ = copy.deepcopy(assigned_nodes_id)
            assigned_nodes_id_.insert(i, node_id)
            obj_, _ = calObj(assigned_nodes_id_, model)
            deta_f = obj_ - assigned_nodes_id_obj
            if deta_f<best_insert_cost:
                best_insert_index=i
                best_insert_node_id=node_id
                best_insert_cost=deta_f
    return best_insert_node_id,best_insert_index

def createGreedyRepair(remove_list,model,sol):
    unassigned_nodes_id = []
    assigned_nodes_id = []
    # remove node from current solution
    for i in range(len(model.demand_id_list)):
        if i in remove_list:
            unassigned_nodes_id.append(sol.node_id_list[i])
        else:
            assigned_nodes_id.append(sol.node_id_list[i])
    #insert
    while len(unassigned_nodes_id)>0:
        insert_node_id,insert_index=findGreedyInsert(unassigned_nodes_id,assigned_nodes_id,model)
        assigned_nodes_id.insert(insert_index,insert_node_id)
        unassigned_nodes_id.remove(insert_node_id)
    new_sol=Sol()
    new_sol.node_id_list=copy.deepcopy(assigned_nodes_id)
    new_sol.obj,new_sol.routes=calObj(assigned_nodes_id,model)
    return new_sol

def findRegretInsert(unassigned_nodes_id,assigned_nodes_id,model):
    opt_insert_node_id = None
    opt_insert_index = None
    opt_insert_cost = -float('inf')
    for node_id in unassigned_nodes_id:
        n_insert_cost=np.zeros((len(assigned_nodes_id),3))
        for i in range(len(assigned_nodes_id)):
            assigned_nodes_id_=copy.deepcopy(assigned_nodes_id)
            assigned_nodes_id_.insert(i,node_id)
            obj_,_=calObj(assigned_nodes_id_,model)
            n_insert_cost[i,0]=node_id
            n_insert_cost[i,1]=i
            n_insert_cost[i,2]=obj_
        n_insert_cost= n_insert_cost[n_insert_cost[:, 2].argsort()]
        deta_f=0
        for i in range(1,model.regret_n):
            deta_f=deta_f+n_insert_cost[i,2]-n_insert_cost[0,2]
        if deta_f>opt_insert_cost:
            opt_insert_node_id = int(n_insert_cost[0, 0])
            opt_insert_index=int(n_insert_cost[0,1])
            opt_insert_cost=deta_f
    return opt_insert_node_id,opt_insert_index

def createRegretRepair(remove_list,model,sol):
    unassigned_nodes_id = []
    assigned_nodes_id = []
    # remove node from current solution
    for i in range(len(model.demand_id_list)):
        if i in remove_list:
            unassigned_nodes_id.append(sol.node_id_list[i])
        else:
            assigned_nodes_id.append(sol.node_id_list[i])
    # insert
    while len(unassigned_nodes_id)>0:
        insert_node_id,insert_index=findRegretInsert(unassigned_nodes_id,assigned_nodes_id,model)
        assigned_nodes_id.insert(insert_index,insert_node_id)
        unassigned_nodes_id.remove(insert_node_id)
    new_sol = Sol()
    new_sol.node_id_list = copy.deepcopy(assigned_nodes_id)
    new_sol.obj, new_sol.routes = calObj(assigned_nodes_id, model)
    return new_sol

（8）随机选择算子

def selectDestoryRepair(model):
    d_weight=model.d_weight
    d_cumsumprob = (d_weight / sum(d_weight)).cumsum()
    d_cumsumprob -= np.random.rand()
    destory_id= list(d_cumsumprob > 0).index(True)

    r_weight=model.r_weight
    r_cumsumprob = (r_weight / sum(r_weight)).cumsum()
    r_cumsumprob -= np.random.rand()
    repair_id = list(r_cumsumprob > 0).index(True)
    return destory_id,repair_id

（9）执行destory算子

def doDestory(destory_id,model,sol):
    if destory_id==0:
        reomve_list=createRandomDestory(model)
    else:
        reomve_list=createWorseDestory(model,sol)
    return reomve_list

（10）执行repair算子

def doRepair(repair_id,reomve_list,model,sol):
    if repair_id==0:
        new_sol=createRandomRepair(reomve_list,model,sol)
    elif repair_id==1:
        new_sol=createGreedyRepair(reomve_list,model,sol)
    else:
        new_sol=createRegretRepair(reomve_list,model,sol)
    return new_sol

（11）重置算子得分

def resetScore(model):

    model.d_select = np.zeros(2)
    model.d_score = np.zeros(2)

    model.r_select = np.zeros(3)
    model.r_score = np.zeros(3)

（12）更新算子权重

def updateWeight(model):

    for i in range(model.d_weight.shape[0]):
        if model.d_select[i]>0:
            model.d_weight[i]=model.d_weight[i]*(1-model.rho)+model.rho*model.d_score[i]/model.d_select[i]
        else:
            model.d_weight[i] = model.d_weight[i] * (1 - model.rho)
    for i in range(model.r_weight.shape[0]):
        if model.r_select[i]>0:
            model.r_weight[i]=model.r_weight[i]*(1-model.rho)+model.rho*model.r_score[i]/model.r_select[i]
        else:
            model.r_weight[i] = model.r_weight[i] * (1 - model.rho)
    model.d_history_select = model.d_history_select + model.d_select
    model.d_history_score = model.d_history_score + model.d_score
    model.r_history_select = model.r_history_select + model.r_select
    model.r_history_score = model.r_history_score + model.r_score

（13）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()

（14）绘制车辆路线

def plotRoutes(model):
    for route in model.best_sol.routes:
        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()

（15）输出结果

def outPut(model):
    work=xlsxwriter.Workbook('result.xlsx')
    worksheet=work.add_worksheet()
    worksheet.write(0,0,'opt_type')
    worksheet.write(1,0,'obj')
    if model.opt_type==0:
        worksheet.write(0,1,'number of vehicles')
    else:
        worksheet.write(0, 1, 'drive distance of vehicles')
    worksheet.write(1,1,model.best_sol.obj)
    for row,route in enumerate(model.best_sol.routes):
        worksheet.write(row+2,0,'v'+str(row+1))
        r=[str(i)for i in route]
        worksheet.write(row+2,1, '-'.join(r))
    work.close()

（16）主函数

def run(demand_file,depot_file,rand_d_max,rand_d_min,worst_d_min,worst_d_max,regret_n,r1,r2,r3,rho,phi,epochs,pu,v_cap,opt_type):
    """
    :param demand_file: demand file path
    :param depot_file: depot file path
    :param rand_d_max: max degree of random destruction
    :param rand_d_min: min degree of random destruction
    :param worst_d_max: max degree of worst destruction
    :param worst_d_min: min degree of worst destruction
    :param regret_n:  n next cheapest insertions
    :param r1: score if the new solution is the best one found so far.
    :param r2: score if the new solution improves the current solution.
    :param r3: score if the new solution does not improve the current solution, but is accepted.
    :param rho: reaction factor of action weight
    :param phi: the reduction factor of threshold
    :param epochs: Iterations
    :param pu: the frequency of weight adjustment
    :param v_cap: Vehicle capacity
    :param opt_type: Optimization type:0:Minimize the number of vehicles,1:Minimize travel distance
    :return:
    """
    model=Model()
    model.rand_d_max=rand_d_max
    model.rand_d_min=rand_d_min
    model.worst_d_min=worst_d_min
    model.worst_d_max=worst_d_max
    model.regret_n=regret_n
    model.r1=r1
    model.r2=r2
    model.r3=r3
    model.rho=rho
    model.vehicle_cap=v_cap
    model.opt_type=opt_type
    readCsvFile(demand_file,depot_file, model)
    calDistance(model)
    history_best_obj = []
    sol = Sol()
    sol.node_id_list = genInitialSol(model.demand_id_list)
    sol.obj, sol.routes = calObj(sol.node_id_list, model)
    model.best_sol = copy.deepcopy(sol)
    history_best_obj.append(sol.obj)
    for ep in range(epochs):
        T=sol.obj*0.2
        resetScore(model)
        for k in range(pu):
            destory_id,repair_id=selectDestoryRepair(model)
            model.d_select[destory_id]+=1
            model.r_select[repair_id]+=1
            reomve_list=doDestory(destory_id,model,sol)
            new_sol=doRepair(repair_id,reomve_list,model,sol)
            if new_sol.obj<sol.obj:
                sol=copy.deepcopy(new_sol)
                if new_sol.obj<model.best_sol.obj:
                    model.best_sol=copy.deepcopy(new_sol)
                    model.d_score[destory_id]+=model.r1
                    model.r_score[repair_id]+=model.r1
                else:
                    model.d_score[destory_id]+=model.r2
                    model.r_score[repair_id]+=model.r2
            elif new_sol.obj-sol.obj<T:
                sol=copy.deepcopy(new_sol)
                model.d_score[destory_id] += model.r3
                model.r_score[repair_id] += model.r3
            T=T*phi
            print("%s/%s:%s/%s， best obj: %s" % (ep,epochs,k,pu, model.best_sol.obj))
            history_best_obj.append(model.best_sol.obj)
        updateWeight(model)

    plotObj(history_best_obj)
    plotRoutes(model)
    outPut(model)
    print("random destory weight is {:.3f}\tselect is {}\tscore is {:.3f}".format(model.d_weight[0],
                                                                        model.d_history_select[0],
                                                                        model.d_history_score[0]))
    print("worse destory weight is {:.3f}\tselect is {}\tscore is {:.3f} ".format(model.d_weight[1],
                                                                        model.d_history_select[1],
                                                                        model.d_history_score[1]))
    print("random repair weight is {:.3f}\tselect is {}\tscore is {:.3f}".format(model.r_weight[0],
                                                                       model.r_history_select[0],
                                                                       model.r_history_score[0]))
    print("greedy repair weight is {:.3f}\tselect is {}\tscore is {:.3f}".format(model.r_weight[1],
                                                                       model.r_history_select[1],
                                                                       model.r_history_score[1]))
    print("regret repair weight is {:.3f}\tselect is {}\tscore is {:.3f}".format(model.r_weight[2],
                                                                       model.r_history_select[2],
                                                                       model.r_history_score[2]))

6. 完整代码

代码和数据文件可获取：

https://download.youkuaiyun.com/download/python_n/37365542