A variable neighborhood search for the multi-depot vehicle routing problem with loading cost

The purpose of this paper is to propose a variable neighbourhood search (VNS) for solving the multi-depot vehicle routing problem with loading cost (MDVRPLC). The MDVRPLC is the combination of multi-depot vehicle routing problem (MDVRP) and vehicle routing problem with loading cost (VRPLC) which are both variations of the vehicle routing problem (VRP) and occur only rarely in the literature. In fact, an extensive literature search failed to find any literature related specifically to the MDVRPLC. The proposed VNS comprises three phases. First, a stochastic method is used for initial solution generation. Second, four operators are randomly selected to search neighbourhood solutions. Third, a criterion similar to simulated annealing (SA) is used for neighbourhood solution acceptance. The proposed VNS has been test on 23 MDVRP benchmark problems. The experimental results show that the proposed method provides an average 23.77% improvement in total transportation cost over the best known results based on minimizing transportation distance. The results show that the proposed method is efficient and effective in solving problems.     

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.     

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).     

A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem

This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the demands of customers are fulfilled by a fleet of fixed number of vehicles with various capacities and related costs. Moreover, the vehicles start at the depot and terminate at one of the customers. This problem is an important variant of the classical vehicle routing problem and can cover more practical situations in transportation and logistics. We propose a multistart adaptive memory programming metaheuristic with modified tabu search algorithm to solve this new vehicle routing problem. The algorithmic efficiency and effectiveness are experimentally evaluated on a set of generated instances.     

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.     

The multi-depot split delivery vehicle routing problem: An integer programming-based heuristic, new test problems, and computational results

The multi-depot split delivery vehicle routing problem combines the split delivery vehicle routing problem and the multiple depot vehicle routing problem. We define this new problem and develop an integer programming-based heuristic for it. We apply our heuristic to 30 instances to determine the reduction in distance traveled that can be achieved by allowing split deliveries among vehicles based at the same depot and vehicles based at different depots. We generate new test instances with high-quality, visually estimated solutions and report results on these instances.     

战时备件配送的MDVRP问题及其遗传算法求解

战时备件配送的车辆调度是提高装备保障效率的关键因素。以装备战斗效能损失最小化为车辆调度的目标,建立了多仓库车辆路径问题MDVRP（Multi—Depot Vehicle Routing Problem）模型,并应用混合遗传算法对问题进行了求解。算法中,设计了串行、并行及半并行三种交叉算子,并应用局部搜索模块对子个体进行改进。对算例的计算实验表明,半并行交叉算子在精度方面优于另外两种交叉算子。     

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.     

A new approach on auxiliary vehicle assignment in capacitated location routing problem

The location routing problem (LRP) considers locating depots and vehicle routing decisions simultaneously. In classic LRP the number of customers in each route depends on the capacity of the vehicle. In this paper a capacitated LRP model with auxiliary vehicle assignment is presented in which the length of each route is not restricted by main vehicle capacity. Two kinds of vehicles are considered: main vehicles with higher capacity and fixed cost and auxiliary vehicles with lower capacity and fixed cost. The auxiliary vehicles can be added to the transportation system as an alternative strategy to cover the capacity limitations and they are just used to transfer goods from depots to vehicles and cannot serve the customers by themselves. To show the applicability of the proposed model, some numerical examples derived from the well-known instances are used. Moreover the model has been solved by some meta-heuristics for large sized instances. The results show the efficiency of the proposed model and the solution approach, considering the classic model and the exact solution approach, respectively.     

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.     

An integrated local search method for inventory and routing decisions

The present article studies an inventory routing model which integrates two important components of the supply chain: transportation logistics and inventory control. The distribution system examined consists of customers that face product demand at a deterministic and constant rate. Customer demand is satisfied by a fixed vehicle fleet located at the central depot. The aim of the problem is to determine the timing and size of the replenishment services together with the vehicle routes, so that the total transportation and inventory holding cost of the system is minimized. In methodological terms, we propose a solution approach applying two innovative local search operators for jointly dealing with the inventory and routing aspects of the examined problem, and Tabu Search for further reducing the transportation costs. The proposed algorithmic framework was tested on a set of new benchmark instances of various scales. It produced satisfactory results both in terms of effectiveness and robustness.     

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。     

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。     

Discrete firefly algorithm with compound neighborhoods for asymmetric multi-depot vehicle routing problem in the maintenance of farm machinery

We introduce a new variant of the vehicle routing problem, that is, the asymmetric multi-depot vehicle routing problem in the maintenance of farm machinery. When providing door-to-door service for farm machinery maintenance, there exists not only node service, (e.g., part replacement), but also directed arc service, (e.g., pulling the breakdown farm machinery from the farm location to the specified maintenance station). In the problem, there are multiple constraints, including the customer’s time window, maximum repairman working duration, fleet size, and vehicle capacity, etc. A mathematical programming model is formulated with the minimum total costs by transforming the problem into the asymmetric multi-depot vehicle routing problem with time windows. Discrete firefly algorithm with compound neighborhoods, presenting new neighborhood methods, is proposed to solve it. New procedures to evaluate the duration infeasibility are suggested with the reduced additional computational complexity. Computational results demonstrate that the proposed approach performs better than CPLEX solver, especially for large designed instances. Moreover, the proposed approach is superior to the other algorithms on solving benchmark instances of multi-depot vehicle routing problem with time windows. This study can provide decision support to door-to-door service for the maintenance of farm machinery.     

Fleet-sizing for multi-depot and periodic vehicle routing problems using a modular heuristic algorithm

In this paper, we address the problem of determining the optimal fleet size for three vehicle routing problems, i.e., multi-depot VRP, periodic VRP and multi-depot periodic VRP. In each of these problems, we consider three kinds of constraints that are often found in reality, i.e., vehicle capacity, route duration and budget constraints. To tackle the problems, we propose a new Modular Heuristic Algorithm (MHA) whose exploration and exploitation strategies enable the algorithm to produce promising results. Extensive computational experiments show that MHA performs impressively well, in terms of solution quality and computational time, for the three problem classes.     

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。     

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。     

带软时间窗的多车场开放式车辆调度

带软时间窗的多车场开放式车辆调度问题是在开放式车辆路径问题的基础上,考虑了多车场和客户服务时间的约束,是一类典型的NP难解问题。针对该问题,提出了一种改进的蚁群算法求解方案,并建立了相应的数学模型。首先通过设置一个虚拟车场将多车场VRP转化为单车场VRP,然后利用参数控制的改进蚁群算法与2-opt算法结合来对模型求解。算法先利用K-means与细菌觅食算法相结合的聚类技术判断蚁群状态,进而动态调整算法参数,使其快速收敛到全局最优解附近,再依据混沌理论的特点来调整参数,使其跳出局部最优。最后,再利用2-opt算法对最优解进行优化。实验结果验证了该算法求解MDOVRPSTW问题的有效性。