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.     

Solving the truck and trailer routing problem based on a simulated annealing heuristic

In this study, we consider the application of a simulated annealing (SA) heuristic to the truck and trailer routing problem (TTRP), a variant of the vehicle routing problem (VRP). In the TTRP, some customers can be serviced by either a complete vehicle (that is, a truck pulling a trailer) or a single truck, while others can only be serviced by a single truck for various reasons. SA has seen widespread applications to various combinatorial optimization problems, including the VRP. However, to our best knowledge, it has not been applied to the TTRP. So far, all the best known results for benchmark TTRP instances were obtained using tabu search (TS). We applied SA to the TTRP and obtained 17 best solutions to the 21 benchmark TTRP benchmark problems, including 11 new best solutions. Moreover, the computational time required by the proposed SA heuristic is less than those reported in prior studies. The results suggest that SA is competitive with TS on solving the TTRP.     

A two-stage heuristic method for vehicle routing problem with split deliveries and pickups

The vehicle routing problem （VRP） is a well-known combinatorial optimization issue in transportation and logistics network systems. There exist several limitations associated with the traditional VRP. Releasing the restricted conditions of traditional VRP has become a research focus in the past few decades. The vehicle routing problem with split deliveries and pickups （VRPSPDP） is particularly proposed to release the constraints on the visiting times per customer and vehicle capacity, that is, to allow the deliveries and pickups for each customer to be simultaneously split more than once. Few studies have focused on the VRPSPDP problem. In this paper we propose a two-stage heuristic method integrating the initial heuristic algorithm and hybrid heuristic algorithm to study the VRPSPDP problem. To validate the proposed algorithm, Solomon benchmark datasets and extended Solomon benchmark datasets were modified to compare with three other popular algorithms. A total of 18 datasets were used to evaluate the effectiveness of the proposed method. The computational results indicated that the proposed algorithm is superior to these three algorithms for VRPSPDP in terms of total travel cost and average loading rate.     

易腐生鲜货品车辆路径问题的改进混合蝙蝠算法

针对配送易腐生鲜货品的车辆其配送路径的选择不仅受货品类型、制冷环境变化、车辆容量限制、交货时间等多种因素的影响,而且需要达到一定的目标（如：费用最少、客户满意度最高）,构建了易腐生鲜货品车辆路径问题（VRP）的多目标模型,并提出了求解该模型的改进混合蝙蝠算法。首先,采用时间窗模糊化处理方法定义客户满意度函数,细分易腐生鲜货品类型并定义制冷成本,建立了最优路径选择的多目标模型;然后,在分析蝙蝠算法求解离散问题易陷入局部最优、过早收敛等问题的基础上,精简经典蝙蝠算法的速度更新公式,并对混合蝙蝠算法的单多点变异设定选择机制,提高算法性能;最后,对改进混合蝙蝠算法进行性能测试。实验结果表明,与基本蝙蝠算法和已有混合蝙蝠算法相比,所提算法在求解VRP时能够提高客户满意度1.6%~4.2%,且减小平均总成本0.68%~2.91%。该算法具有计算效率高、计算性能好和较高的稳定性等优势。     

基于自适应蚁群算法的车辆路径问题研究

车辆路径问题(VRP)是物流研究领域中一个具有重要理论和现实意义的问题．蚁群算法是一种新型的模拟进化算法,可以很好地解决旅行商问题(TSP)．在分析VRP与TSP区别的基础上,构造了求解VRP的自适应蚁群算法．指出可行解问题是蚁群算法的关键问题,并重点对该问题进行了研究,提出了近似解可行化等解决策略．实验结果表明,自适应蚁群算法性能优良,能够有效地求解VRP问题．     

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.     

A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery

Vehicle routing problem (VRP) is an important and well-known combinatorial optimization problem encountered in many transport logistics and distribution systems. The VRP has several variants depending on tasks performed and on some restrictions, such as time windows, multiple vehicles, backhauls, simultaneous delivery and pick-up, etc. In this paper, we consider vehicle routing problem with simultaneous pickup and delivery (VRPSPD). The VRPSPD deals with optimally integrating goods distribution and collection when there are no precedence restrictions on the order in which the operations must be performed. Since the VRPSPD is an NP-hard problem, we present a heuristic solution approach based on particle swarm optimization (PSO) in which a local search is performed by variable neighborhood descent algorithm (VND). Moreover, it implements an annealing-like strategy to preserve the swarm diversity. The effectiveness of the proposed PSO is investigated by an experiment conducted on benchmark problem instances available in the literature. The computational results indicate that the proposed algorithm competes with the heuristic approaches in the literature and improves several best known solutions.     

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.     

深度强化学习求解车辆路径问题的研究综述

车辆路径问题（VRP）是组合优化问题中经典的NP难问题,广泛应用于交通、物流等领域,随着问题规模和动态因素的增多,传统算法很难快速、智能地求解复杂的VRP问题。近年来随着人工智能技术的发展,尤其是深度强化学习（DRL）在AlphaGo中的成功应用,为路径问题求解提供了全新思路。鉴于此,针对近年来利用DRL求解VRP及其变体问题的模型进行文献综述。回顾了DRL求解VRP的相关思路,并梳理基于DRL求解VRP问题的关键步骤,对基于指针网络、图神经网络、Transformer和混合模型的四类求解方法分类总结,同时对目前基于DRL求解VRP及其变体问题的模型性能进行对比分析,总结了基于DRL求解VRP问题时遇到的挑战以及未来的研究方向。     

Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem

The vehicle routing problem (VRP) has been addressed in many research papers. Only a few of them take time-dependent travel speeds into consideration. Moreover, most research related to the VRP aims to minimize total travel time or travel distance. In recent years, reducing carbon emissions has become an important issue. Therefore, fuel consumption is also an important index in the VRP. In this research a model is proposed for calculating total fuel consumption for the time-dependent vehicle routing problem (TDVRP) where speed and travel times are assumed to depend on the time of travel when planning vehicle routing. In the model, the fuel consumption not only takes loading weight into consideration but also satisfies the “non-passing” property, which is ignored in most TDVRP-related research papers. Then a simulated annealing (SA) algorithm is proposed for finding the vehicle routing with the lowest total fuel consumption. An experimental evaluation of the proposed method is performed. The results show that the proposed method provides a 24.61% improvement in fuel consumption over the method based on minimizing transportation time and a 22.69% improvement over the method based on minimizing transportation distances.