Multi-depot vehicle routing problem: a one-stage approach

This paper introduces multi-depot vehicle routing problem with fixed distribution of vehicles (MDVRPFD) which is one important and useful variant of the traditional multi-depot vehicle routing problem (MDVRP) in the supply chain management and transportation studies. After modeling the MDVRPFD as a binary programming problem, we propose two solution methodologies: two-stage and one-stage approaches. The two-stage approach decomposes the MDVRPFD into two independent subproblems, assignment and routing, and solves them separately. In contrast, the one-stage approach integrates the assignment with the routing where there are two kinds of routing methods-draft routing and detail routing. Experimental results show that our new one-stage algorithm outperforms the published methods. Note to Practitioners-This work is based on several consultancy work that we have done for transportation companies in Hong Kong. The multi-depot vehicle routing problem (MDVRP) is one of the core optimization problems in transportation, logistics, and supply chain management, which minimizes the total travel distance (the major factor of total transportation cost) among a number of given depots. However, in real practice, the MDVRP is not reliable because of the assumption that there have unlimited number of vehicles available in each depot. In this paper, we propose a new useful variant of the MDVRP, namely multi-depot vehicle routing problem with fixed distribution of vehicles (MDVRPFD), to model the practicable cases in applications. Two-stage and one-stage solution algorithms are also proposed. The industry participators can apply our new one-stage algorithm to solve the MDVRPFD directly and efficiently. Moreover, our one-stage solution framework allows users to smoothly add new specified constraints or variants.     

基于深度强化学习的多配送中心车辆路径规划

多配送中心车辆路径规划(multi-depot vehicle routing problem, MDVRP)是现阶段供应链应用较为广泛的问题模型,现有算法多采用启发式方法,其求解速度慢且无法保证解的质量,因此研究快速且有效的求解算法具有重要的学术意义和应用价值.以最小化总车辆路径距离为目标,提出一种基于多智能体深度强化学习的求解模型.首先,定义多配送中心车辆路径问题的多智能体强化学习形式,包括状态、动作、回报以及状态转移函数,使模型能够利用多智能体强化学习训练;然后通过对MDVRP的节点邻居及遮掩机制的定义,基于注意力机制设计由多个智能体网络构成的策略网络模型,并利用策略梯度算法进行训练以获得能够快速求解的模型;接着,利用2-opt局部搜索策略和采样搜索策略改进解的质量;最后,通过对不同规模问题仿真实验以及与其他算法进行对比,验证所提出的多智能体深度强化学习模型及其与搜索策略的结合能够快速获得高质量的解.     

多车场车辆路径问题的遗传算法

给出了多车场车辆路径问题(MDVRP)的数学模型,提出一种基于客户的编码表示方式,可以表示出各车场出动的车辆及路径,能够有效地实现MDVRP的优化,并用计算实例进行了验证。     

Multi-phase modified shuffled frog leaping algorithm with extremal optimization for the MDVRP and the MDVRPTW

In this work, a novel multi-phase modified shuffled frog leaping algorithm (MPMSFLA) framework is presented to solve the multi-depot vehicle routing problem (MDVRP) more quickly. The presented algorithm adopts the K-means algorithm to execute the clustering analyses for all customers, generates a frog population according to the result of the clustering analyses, and then proceeds to the three-phase process. In the first phase, a cluster MSFLA local search is carried out for each cluster. In the second phase, the algorithm selects good individuals through a binary tournament to construct a new population and then performs a global optimization for all customers and depots using the global MSFLA. In the third phase, a cluster adjustment is implemented for the population to generate new clusters. These procedures continue until the convergence criterion is satisfied. The experimental results show that our algorithm can achieve a high quality solution within a short runtime for the MDVRP, the MDVRP with time windows (MDVRPTW) and the capacitated vehicle routing problem (CVRP). The proposed algorithm is suitable for solving large-scale problems.     

泰森多边形的离散蝙蝠算法求解多车场车辆路径问题

本文提出一种泰森多边形的离散蝙蝠算法求解多车场车辆路径问题(multi-depot vehicle routing problem,MDVRP).所提出算法以离散蝙蝠算法为核心,融入了一种基于多车场多车辆问题的编解码策略.所提出算法还使用基于泰森多边形的初始化策略加快算法的前期收敛速度,采用基于向量比较机制的适应度函数来控制算法收敛的方向,引入基于近邻策略和优先配送策略的局部搜索算法来提高算法的寻优能力.实验结果表明:在合理的时间耗费内,所提出的算法能有效地求解MDVRP,尤其是带配送距离约束的MDVRP;相对于对比算法,所提出的算法表现出较强的寻优能力和稳定性.     

基于end-to-end深度强化学习的多车场车辆路径优化

为提高多车场车辆路径问题（multi-depot vehicle routing problem,MDVRP）的求解效率,提出了端到端的深度强化学习框架。首先,将MDVRP建模为马尔可夫决策过程（Markov decision process,MDP）,包括对其状态、动作、收益的定义;同时,提出了改进图注意力网络（graph attention network,GAT）作为编码器对MDVRP的图表示进行特征嵌入编码,设计了基于Transformer的解码器;采用改进REINFORCE算法来训练该模型,该模型不受图的大小约束,即其一旦完成训练,就可用于求解任意车场和客户数量的算例问题。最后,通过随机生成的算例和公开的标准算例验证了所提出框架的可行性和有效性,即使在求解客户节点数为100的MDVRP上,经训练的模型平均仅需2 ms即可得到与现有方法相比更具优势的解。     

A general heuristic for vehicle routing problems

We present a unified heuristic which is able to solve five different variants of the vehicle routing problem: the vehicle routing problem with time windows (VRPTW), the capacitated vehicle routing problem (CVRP), the multi-depot vehicle routing problem (MDVRP), the site-dependent vehicle routing problem (SDVRP) and the open vehicle routing problem (OVRP).     

Two solution representations for solving multi-depot vehicle routing problem with multiple pickup and delivery requests via PSO

Two solution representations for solving the generalized multi-depot vehicle routing problem with multiple pickup and delivery requests (GVRP-MDMPDR) is presented in this paper. The representations are used in conjunction with GLNPSO, a variant of PSO with multiple social learning terms. The computational experiments are carried out using benchmark test instances for pickup and delivery problem with time windows (PDPTW) and the generalized vehicle routing problem for multi-depot with multiple pickup and delivery requests (GVRP-MDMPDR). The preliminary results illustrate that the proposed method is capable of providing good solutions for most of the test problems.     

多中心半开放式送取需求可拆分的车辆路径优化

针对多中心半开放式送取需求可拆分的车辆路径问题,构建了以车辆配送距离最短为目标的多中心半开放式送取需求可拆分的数学模型。设计大变异邻域遗传算法进行求解,采用二维染色体编码及顺序交叉策略,同时运用大变异策略和邻域搜索策略提高算法全局和局部的寻优能力,通过算例对比验证了所提模型与算法的有效性。算例实验表明,大变异邻域遗传算法在求解多中心物流配送车辆路径问题上求解质量较优、求解效率较高、求解结果较为稳定,同时验证了联合配送下多中心半开放式送取需求可拆分的配送模式优于独立配送下单中心送取需求可拆分的配送模式。研究成果不仅拓展了车辆路径问题,还可为相关快递物流企业配送优化提供决策参考。     

A hybridisation of adaptive variable neighbourhood search and large neighbourhood search: Application to the vehicle routing problem

In this paper, an adaptive variable neighbourhood search (AVNS) algorithm that incorporates large neighbourhood search (LNS) as a diversification strategy is proposed and applied to the capacitated vehicle routing problem. The AVNS consists of two stages: a learning phase and a multi-level VNS with guided local search. The adaptive aspect is integrated in the local search where a set of highly successful local searches is selected based on the intelligent selection mechanism. In addition, the hybridisation of LNS with the AVNS enables the solution to escape from the local minimum effectively. To make the algorithm more competitive in terms of the computing time, a simple and flexible data structure and a neighbourhood reduction scheme are embedded. Finally, we adapt a new local search move and an effective removal strategy for the LNS. The proposed AVNS was tested on the benchmark data sets from the literature and produced very competitive results.     

METAHEURISTIC APPROACH FOR THE MULTI-DEPOT VEHICLE ROUTING PROBLEM

Distribution logistics comprises all activities related to the provision of finished products and merchandise to a customer. The focal point of distribution logistics is the shipment of goods from the manufacturer to the consumer. The products can be delivered to a customer directly either from the production facility or from the trader's stock located close to the production site or, probably, via additional regional distribution warehouses. These kinds of distribution logistics are mathematically represented as a vehicle routing problem (VRP), a well-known nondeterministic polynomial time (NP)-hard problem of operations research. VRP is more suited for applications having one warehouse. In reality, however, many companies and industries possess more than one distribution warehouse. These kinds of problems can be solved with an extension of VRP called multi-depot VRP (MDVRP). MDVRP is an NP-hard and combinatorial optimization problem. MDVRP is an important and challenging problem in logistics management. It can be solved using a search algorithm or metaheuristic and can be viewed as searching for the best element in a set of discrete items. In this article, cluster first and route second methodology is adapted and metaheuristics genetic algorithms (GA) and particle swarm optimization (PSO) are used to solve MDVRP. A hybrid particle swarm optimization (HPSO) for solving MDVRP is also proposed. In HPSO, the initial particles are generated based on the k-means clustering and nearest neighbor heuristic (NNH). The particles are decoded into clusters and multiple routes are generated within the clusters. The 2-opt local search heuristic is used for optimizing the routes obtained; then the results are compared with GA and PSO for randomly generated problem instances. The home delivery pharmacy program and waste-collection problem are considered as case studies in this paper. The algorithm is implemented using MATLAB 7.0.1.     

GRASP/VND and multi-start evolutionary local search for the single truck and trailer routing problem with satellite depots

In the single truck and trailer routing problem with satellite depots (STTRPSD) a vehicle composed of a truck with a detachable trailer serves the demand of a set of customers reachable only by the truck without the trailer. This accessibility constraint implies the selection of locations to park the trailer before performing the trips to the customers. We propose two metaheuristics based on greedy randomized adaptive search procedures (GRASP), variable neighborhood descent (VND) and evolutionary local search (ELS) to solve this problem. To evaluate these metaheuristics we test them on a set of 32 randomly generated problems. The computational experiment shows that a multi-start evolutionary local search outperforms a GRASP/VND. Moreover, it obtains competitive results when applied to the multi-depot vehicle routing problem (MDVRP), that can be seen as a special case of the STTRPSD.     

Solving fuzzy capacitated location routing problem using hybrid variable neighborhood search and evolutionary local search

A fuzzy capacitated location routing problem (FCLRP) is solved by using a heuristic method that combines variable neighborhood search (VNS) and evolutionary local search (ELS). Demands of the customer and travel times between customers and depots are considered as fuzzy and deterministic variables, respectively in FCLRP. Heterogeneous and homogeneous fleet sizes are performed together to reach the least multi-objective cost in a case study. The multi-objective cost consists of transportation cost, additional cost, vehicle waiting cost and delay cost. A fuzzy chance constrained programming model is added by using credibility theory. The proposed method reaches the solution by performing four stages. In the first stage, initial solutions are obtained by using a greedy heuristic method, and then VNS heuristic, which consists of seven different neighborhood structures, is performed to improve the solution quality in the second stage. In the third stage, a perturbation procedure is applied to the improved solution using ELS algorithm, and then VNS heuristic is applied again in the last stage. The combination of VNS and ELS is called VNSxELS algorithm and applied to a case study, which has fifty-seven customers and five distributing points, effectively in a reasonable time.     

Variable neighborhood search for the inventory routing and scheduling problem in a supply chain

The inventory, routing and scheduling decisions are three major driving factors for supply chain performance. Since they are related to one another in a supply chain, they should be determined simultaneously to improve the decision quality. In the past, the inventory policy, vehicle routing and vehicle scheduling are determined sequentially and separately. Hence, the total cost (inventory, routing and vehicle costs) would increase. In this paper, an integrated model for the inventory routing and scheduling problem (IRSP) is proposed. Since searching for the optimal solution for this model is a non-polynomial (NP) problem, a metaheuristic, variable neighborhood search (VNS), is proposed. The proposed method was compared with other existing methods. The experimental results indicate that the proposed method is better than other methods in terms of average cost per day.     

Variable neighborhood search for location routing

In this paper we propose various neighborhood search heuristics (VNS) for solving the location routing problem with multiple capacitated depots and one uncapacitated vehicle per depot. The objective is to find depot locations and to design least cost routes for vehicles. We integrate a variable neighborhood descent as the local search in the general variable neighborhood heuristic framework to solve this problem. We propose five neighborhood structures which are either of routing or location type and use them in both shaking and local search steps. The proposed three VNS methods are tested on benchmark instances and successfully compared with other two state-of-the-art heuristics.     

A parallel iterated tabu search heuristic for vehicle routing problems

This paper introduces a parallel iterated tabu search heuristic for solving four different routing problems: the classical vehicle routing problem (VRP), the periodic VRP, the multi-depot VRP, and the site-dependent VRP. In addition, it is applicable to the time-window constrained variant of these problems. Using the iterated local search framework, the heuristic combines tabu search with a simple perturbation mechanism to ensure a broad exploration of the search space. We also describe a parallel implementation of the heuristic to take advantage of multiple-core processors. Extensive computational results show that the proposed heuristic outperforms tabu search alone and is competitive with recent heuristics designed for each particular problem.     

带软时间窗的开放式满载车辆路径问题研究

为满足某些生产制造企业的满载运输需求,针对运输任务对车辆具有独占性的特点,分析得到总运输费用的大小取决于车辆的空车行驶费用,在此基础上,将带软时间窗的开放式满载车辆路径问题转化为带软时间窗的多车场开放式车辆路径问题,在非对称图上建立了相应的数学模型,并设计了近邻粒子群算法对模型进行求解。设计算例对算法进行了验证,实验结果表明：该算法可以快速求得软时间窗的开放式满载车辆路径问题的满意解。     

Heuristic solutions to multi-depot location-routing problems

This paper presents a method for solving the multi-depot location-routing problem (MDLRP). Since several unrealistic assumptions, such as homogeneous fleet type and unlimited number of available vehicles, are typically made concerning this problem, a mathematical formulation is given in which these assumptions are relaxed. Since the inherent complexity of the LRP problem makes it impossible to solve the problem on a larger scale, the original problem is divided into two sub-problems, i.e., the location-allocation problem, and the general vehicle routing problem, respectively. Each sub-problem is then solved in a sequential and iterative manner by the simulated annealing algorithm embedded in the general framework for the problem-solving procedure. Test problems from the literature and newly created problems are used to test the proposed method. The results indicate that this method performs well in terms of the solution quality and run time consumed. In addition, the setting of parameters throughout the solution procedure for obtaining quick and favorable solutions is also suggested.Scope and purposeIn many logistic environments managers must make decisions such as location for distribution centers (DC), allocation of customers to each service area, and transportation plans connecting customers. The location-routing problems (LRPs) are, hence, defined to find the optimal number and locations of the DCs, simultaneously with the vehicle schedules and distribution routes so as to minimize the total system costs. This paper proposes a decomposition-based method for solving the LRP with multiple depots, multiple fleet types, and limited number of vehicles for each different vehicle type. The solution procedure developed is very straightforward conceptually, and the results obtained are comparable with other heuristic methods. In addition, the setting of parameters throughout the solution procedure for obtaining quick and favorable solutions is also suggested.     

A heuristic method for the vehicle routing problem with backhauls and inventory

The purpose of this paper is to determine the route of the vehicle routing problem with backhauls (VRPB), delivering new items and picking up the reused items or wastes, and resolve the inventory control decision problem simultaneously since the regular VRPB does not. Both the vehicle routing decision for delivery and pickup, and the inventory control decision affect each other and must be considered together. Hence, a mathematical model of vehicle routing problem with backhauls and inventory (VRPBI) is proposed. Since finding the optimal solution(s) for VRPBI is a NP-hard problem, this paper proposes a heuristic method, variable neighborhood tabu search (VNTS), adopting six neighborhood searching approaches to obtain the optimal solution. Moreover, this paper compares the proposed heuristic method with two other existing heuristic methods. The experimental results indicate that the proposed method is better than the two other methods in terms of average logistic cost (transportation cost and inventory cost).     

多配送中心车辆路径问题的狼群算法

针对多配送中心动态启用和车辆的合理分配,文章首先建立了以总路径长度最小为目标函数的多配送中心车辆路径问题的数学模型;其次,根据多配送中心车辆路径问题的具体特征,模拟狼群捕食行为设计了求解该问题的狼群算法;最后,应用狼群算法求解测试算例,并将其计算结果与几种常见智能优化算法的计算结果进行比较,验证了狼群算法求解多配送中心车辆路径问题的可行性与有效性。