[基因遗传算法]进阶之六:VRP的进阶经典问题的解码如何写

一、CVRP

见博文《[基因遗传算法]进阶之三:实践CVRP》

二、MDCVRP

参考资料:《Python实现MDCVRP常见求解算法——遗传算法（GA）》
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

2.1 解的编码分析

可以看到第3个图(左下)与第4个图(右下). 每段route的路径是相同的, 区别在于depot不同.只有一个仓库的时候,不需要做选择.而多个仓库的时候,需要对一段route就近选择合适的depot.因此需要定义两个函数:

• splitRoutes(node_id_list,model) :根据车容量限制要求,分割为多个route.
  例如:node_id_list=[3,4,2,0,1,9,8,7,6,5],分割为[ [3,4],[2,0,1,9,8],[7,6,5]]

• selectDepot(route,depot_dict,model): 对每个route选择合适的depot,要求该仓库进出该route的距离最小,且depot可以容纳该车辆(即depot的库存为满).

2.2 代码

1. 对route选择合适的depot(多中选一)

## MDCVRP
def selectDepot(route,depot_dict,model):
    # 假设route=[2,0,1,9,8],前后都没有depot,只有需求节点的一段序列
    # 我们要给这段距离选择一个合适depot
    min_in_out_distance=float('inf')#进出route的最小距离
    index=None
    for _,depot in depot_dict.items():
        # 如果depot能够容纳的车的数目>0
        if depot.depot_capacity>0:
            #当前(选择的)depot到route[0](起点)的距离+routed[-1](终点)到depot的距离
            in_out_distance=model.distance_matrix[depot.id,route[0]]+model.distance_matrix[route[-1],depot.id]
            # 是否更新 ‘进出route的最小距离'
            if in_out_distance<min_in_out_distance:
                index=depot.id #记录使(当前)‘距离’的depot的ID号
                min_in_out_distance=in_out_distance
    if index is None:
        print("there is no vehicle to dispatch")#没有车辆去分配
    # 在route的首尾插入depot的ID号
    route.insert(0,index)
    route.append(index)
    #对于(已定的)depot,其可容纳的车辆数目减少1个
    depot_dict[index].depot_capacity=depot_dict[index].depot_capacity-1
    return route,depot_dict

2. 对node_id_list(需求节点列表)分割路径

## MDCVRP的分割路径的方法.
def splitRoutes(node_id_list,model):
    num_vehicle = 0#存储车的数量,初始为0
    vehicle_routes = []#车辆的总路径
    route = []#单条路径,如果只有一个depot,直接放入即可.现在是多个,要选择depot
    remained_cap = model.vehicle_cap#车的当前容量,初始为满值
    depot_dict=copy.deepcopy(model.depot_dict)#depot们的深复制
    #设node_id_list=[3,4,2,0,1,9,8,7,6,5]
    for node_id in node_id_list:
        #当前需求节点:node_id.
        if remained_cap - model.demand_dict[node_id].demand >= 0:
            # 如果车的当前存货>=节点需求.则路径选择当前节点(放入route中),并完成需求任务
            route.append(node_id)
            remained_cap = remained_cap - model.demand_dict[node_id].demand
        else:
            # 如果车不能完成当前节点的任务,则对当前的一段路径就近选择depot
            route,depot_dict=selectDepot(route,depot_dict,model)
            # 当前路径route已结束,放入总轨迹vehicle_routes中.
            vehicle_routes.append(route)
            #当前节点作为新route的起点
            route = [node_id]
            num_vehicle = num_vehicle + 1#数量加1
            #新车的当前存货=满货-当前节点的需求
            remained_cap =model.vehicle_cap - model.demand_dict[node_id].demand
    #对于这段route就近选择合适(可容车)的depot
    route, depot_dict = selectDepot(route, depot_dict, model)
    vehicle_routes.append(route) 
    return num_vehicle,vehicle_routes

2.3 分割展示

# 构造初始解
genInitialSol(model)
# 查看个体的基因
print(model.sol_list[0].node_no_seq  )

结果:
[4, 71, 10, 31, 75, 89, 19, 32, 70, 92, 54, 90, 80, 13, 41, 74, 21, 37, 99, 85, 16, 30, 50, 3, 52, 0, 34, 29, 11, 60, 49, 1, 91, 69, 24, 57, 81, 26, 46, 79, 38, 2, 72, 97, 27, 35, 28, 94, 62, 56, 20, 7, 51, 88, 67, 47, 66, 64, 63, 83, 36, 95, 45, 40, 44, 58, 5, 6, 86, 39, 14, 53, 96, 77, 73, 33, 48, 87, 9, 76, 12, 55, 59, 68, 65, 22, 93, 82, 61, 23, 84, 43, 15, 42, 18, 98, 25, 8, 17, 78]

node_id_list=model.sol_list[0].node_no_seq #个体的基因的id序列
num_vehicle,vehicle_routes=splitRoutes(node_id_list,model)
print(num_vehicle)
print(vehicle_routes) 

结果:
23
[[‘d1’, 4, 71, 10, 31, 75, 89, ‘d1’], [‘d1’, 19, 32, 70, ‘d1’], [‘d1’, 92, 54, 90, ‘d1’], [‘d2’, 80, 13, 41, 74, ‘d2’], [‘d1’, 21, 37, 99, 85, ‘d1’], [‘d1’, 16, 30, 50, 3, 52, ‘d1’], [‘d1’, 0, 34, 29, 11, 60, 49, ‘d1’], [‘d2’, 1, 91, 69, ‘d2’], [‘d1’, 24, 57, ‘d1’], [‘d1’, 81, 26, 46, 79, 38, 2, ‘d1’], [‘d2’, 72, 97, 27, 35, 28, ‘d2’], [‘d2’, 94, 62, ‘d2’], [‘d1’, 56, 20, 7, ‘d1’], [‘d2’, 51, 88, 67, 47, 66, 64, 63, ‘d2’], [‘d2’, 83, 36, 95, 45, ‘d2’], [‘d1’, 40, 44, 58, 5, 6, ‘d1’], [‘d2’, 86, 39, 14, ‘d2’], [‘d2’, 53, 96, ‘d2’], [‘d2’, 77, 73, ‘d2’], [‘d2’, 33, 48, 87, 9, 76, ‘d2’], [‘d2’, 12, 55, 59, ‘d2’], [‘d2’, 68, 65, 22, 93, 82, 61, 23, ‘d2’], [‘d2’, 84, 43, 15, ‘d2’], [‘d2’, 42, 18, 98, 25, 8, 17, 78, ‘d2’]]

三、VRPTW

见参考博文《[基因遗传算法]进阶之四:实践VRPTW》

四、MDVRPTW

这里是对车辆进行了限制?与VRPTW相比,其结构上的变化,应该只是解码过程的变化. 解码后的route_list结构不变,所以后续的求距离时间成本,和计算适应度方法,都是几乎不改变的. 因此,这里重点讨论 如何对MDVRPTW进行解码.
本文参考了《Python实现(MD)VRPTW常见求解算法——遗传算法（GA）》

• 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

4. 1 解的编码分析

4.2 解的代码

1. 先计算任意两点间的距离,因为序列的分割需要用到距离和时间距离

# 计算任意两点间的距离
def calDistanceTimeMatrix(model):
    # 节点有demand_id_list中的需求节点,有
    for i in range(len(model.demand_id_list)):
        from_node_id = model.demand_id_list[i]#需求节点1
        for j in range(i + 1, len(model.demand_id_list)):
            to_node_id = model.demand_id_list[j]#需求节点2
            # 求两个节点之间的距离,并保存到矩阵
            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
            # 求两个节点之间的时间距离=距离/速度,并保存到时间矩阵
            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():
            # depot_dict: d1, d2,..分别计算from_node_id与depot的距离
            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)

2. 因为多仓库,在route确定仓库的时候需要选择. 注意,同MDCVRP的没有改变

## MDVRPTW的depot的选择.完全没有改变
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

3. 路径的提取

## MDVRPTW的根据Pred提取路径问题.
# 在VRPTW中只有一个depot,直接加入depot的ID号即可.
#但是现在多个depot,所以要增加一个选择depot的环节.
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

4. 序列的分割

##MDVRPTW的路径分割
def splitRoutes(node_id_list,model):
    depot=model.depot_id_list[0]#选择depot_id_list中的第一个,作为初始值
    V={id:float('inf') for id in model.demand_id_list}
    #同VRPTW一样的值函数,初始之设为正无穷
    V[depot]=0#初始情况:第一个depot的值函数为0
    # 这里设为0,是不区分depotde.只是分割序列,使得某些节点处回到depot.
    # 具体选择哪一个,可以在 ‘函数selectDepot’中确定.
    Pred={id:depot for id in model.demand_id_list}
    # 初始情况:假设所有的需求节点都映射给第一个depot
    for i in range(len(node_id_list)):
        n_1=node_id_list[i]#序列中的当前节点
        demand=0#depot的初始需求
        departure=0#depot的初始离开时间
        j=i#j,j+1,...查看当前节点后的所有节点可以是后续节点
        cost=0
        while True:
            n_2 = node_id_list[j] #序列i后的某个节点或本身,我将其命名为 检测节点
            demand = demand + model.demand_dict[n_2].demand#累计需求
            if n_1 == n_2:
                # 当前节点=检测节点. 当前节点要返回仓库的时候
                #计算车从(当前节点n_1, depot)的最早到达时间
                arrival= max(model.demand_dict[n_2].start_time,model.depot_dict[depot].start_time+model.time_matrix[depot,n_2])
                #计算从depot离开的最早时间
                departure=arrival+model.demand_dict[n_2].service_time+model.time_matrix[n_2,depot]
                # 确定优化目标,求距离最小?时间最小?
                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]#检测节点的前一个节点,n1和n2不同
                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]
                # 确定成本函数
                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:
                # 累计需求<车的当前存货 且 离开时间
                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]:
                        # 更新值函数并记录节点映射关系
                        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

可能存在的错误: Sol中保存节点ID序列的话. 所在的属性,sol.node_id-list或者是sol.node_no_seq

4.3 结果展示

node_id_list=model.sol_list[0].node_no_seq
route_num,route_list=splitRoutes(node_id_list,model)
print(route_num)
print(route_list) 

out:
58
[[‘d1’, 35, 48, ‘d1’], [‘d2’, 87, ‘d2’], [‘d2’, 60, ‘d2’], [‘d2’, 70, 72, ‘d2’], [‘d1’, 43, 33, ‘d1’], [‘d1’, 18, 1, ‘d1’], [‘d2’, 89, ‘d2’], [‘d2’, 56, 63, ‘d2’], [‘d1’, 97, 11, 0, ‘d1’], [‘d3’, 45, ‘d3’], [‘d2’, 7, 13, 79, ‘d2’], [‘d1’, 16, ‘d1’], [‘d2’, 62, ‘d2’], [‘d1’, 31, 51, ‘d1’], [‘d2’, 52, ‘d2’], [‘d2’, 66, 90, ‘d2’], [‘d3’, 95, 76, 88, ‘d3’], [‘d1’, 83, 8, ‘d1’], [‘d1’, 34, 21, ‘d1’], [‘d2’, 58, ‘d2’], [‘d2’, 55, ‘d2’], [‘d3’, 82, 99, 46, ‘d3’], [‘d2’, 59, 68, ‘d2’], [‘d2’, 71, ‘d2’], [‘d1’, 12, 69, ‘d1’], [‘d1’, 92, 22, ‘d1’], [‘d1’, 93, ‘d1’], [‘d2’, 77, 78, ‘d2’], [‘d2’, 81, ‘d2’], [‘d1’, 26, 15, ‘d1’], [‘d2’, 53, ‘d2’], [‘d3’, 64, 28, 20, ‘d3’], [‘d1’, 3, ‘d1’], [‘d1’, 50, ‘d1’], [‘d1’, 4, 49, ‘d1’], [‘d2’, 84, ‘d2’], [‘d1’, 9, ‘d1’], [‘d2’, 75, ‘d2’], [‘d1’, 19, 96, ‘d1’], [‘d1’, 86, 17, 29, ‘d1’], [‘d3’, 39, 91, ‘d3’], [‘d2’, 42, 37, 67, ‘d2’], [‘d1’, 10, ‘d1’], [‘d1’, 36, 47, ‘d1’], [‘d2’, 85, 5, 65, ‘d2’], [‘d3’, 27, ‘d3’], [‘d2’, 54, ‘d2’], [‘d3’, 23, 98, ‘d3’], [‘d3’, 32, ‘d3’], [‘d2’, 80, 61, ‘d2’], [‘d3’, 41, 44, ‘d3’], [‘d2’, 73, 38, ‘d2’], [‘d3’, 14, ‘d3’], [‘d3’, 6, ‘d3’], [‘d3’, 30, 74, ‘d3’], [‘d3’, 40, 57, 25, ‘d3’], [‘d3’, 2, 24, ‘d3’], [‘d3’, 94, ‘d3’]]

4. 4 MDVRPTW的计算适应度

1. 计算路径的行驶成本(距离和时间)

def calTravelCost(route_list,model):
    timetable_list=[]#每个route的时间列表?
    cost_of_distance=0# 距离成本初始设为0
    cost_of_time=0# 时间成本初始设为0
    # route_list:[[d1,3,4,d1],[d3,2,0,1,9,8,d3],[d2,7,6,5,d2]]
    for route in route_list:
        timetable=[]
        for i in range(len(route)):
            if i == 0:
                # 节点为起始depot
                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)
                #计算depot的离开时间
                timetable.append((departure,departure))#起始depot的(到达,离开)时间点
            elif 1<= i <= len(route)-2:
                #中间的需求节点
                last_node_id=route[i-1]#上一个节点的id
                current_node_id=route[i]#当前节点的id
                current_node = model.demand_dict[current_node_id]#当前节点
                travel_time=model.time_matrix[last_node_id,current_node_id]#行驶时间
                arrival=max(timetable[-1][1]+travel_time,current_node.start_time)#当前节点的最早到达时间
                departure=arrival+current_node.service_time#当前节点的离开时间
                timetable.append((arrival,departure))
                #累计距离成本
                cost_of_distance = cost_of_distance + model.distance_matrix[last_node_id,current_node_id]
                #累计时间成本
                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)
                ## (上个节点到当前节点)移动时间+当前节点的服务时间+等待时间
            else:
                #为终点depot
                last_node_id = route[i - 1]#最后一个需求节点
                depot_id=route[i]#终点depot
                travel_time = model.time_matrix[last_node_id,depot_id]#行驶时间
                departure = timetable[-1][1]+travel_time#离开时间
                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

2. 计算种群的适应度
   在这里主要选择以距离成本或者时间成本作为目标函数.

def calFitness(model):
    max_obj=-float('inf')
    best_sol=Sol()
    best_sol.obj=float('inf')

    # calculate travel distance and travel time
    for sol in model.sol_list:
        node_id_list=copy.deepcopy(sol.node_id_list)
        num_vehicle, route_list = splitRoutes(node_id_list, model)
        # travel cost
        timetable_list,cost_of_time,cost_of_distance =calTravelCost(route_list,model)
        if model.opt_type == 0:
            sol.obj=cost_of_distance
        else:
            sol.obj=cost_of_time
        sol.route_list = route_list
        sol.timetable_list = timetable_list
        sol.cost_of_distance=cost_of_distance
        sol.cost_of_time=cost_of_time
        if sol.obj > max_obj:
            max_obj=sol.obj
        if sol.obj < best_sol.obj:
            best_sol=copy.deepcopy(sol)

    # calculate fitness
    for sol in model.sol_list:
        sol.fitness=max_obj-sol.obj
    if best_sol.obj<model.best_sol.obj:
        model.best_sol=copy.deepcopy(best_sol)

4.5 MDVRPTWd的结果展示图