A hybrid approach for the vehicle routing problem with three-dimensional loading constraints

This paper addresses a recently practical combinatorial problem named Three-Dimensional Loading Capacitated Vehicle Routing Problem, which combines three-dimensional loading problem and vehicle routing problem in distribution logistics. The problem requires a combinatorial optimization of a feasible loading and successive routing of vehicles to satisfy customer demands, where all vehicles must start and finish at a central depot. The goal of this combinatorial problem is to minimize the total transportation cost while serving customers. Despite its clearly practical significance in the real world distribution management, for its high combinatorial complexity, published papers on this problem in literature are very limited.     

An effective tabu search approach with improved loading algorithms for the 3L-CVRP

In this paper, we consider the Three-Dimensional Loading Capacitated Vehicle Routing Problem(3L-CVRP) which combines the routing of a fleet of vehicles and the loading of three-dimensional shaped goods into the vehicles while minimizing the total travel distance incurred. Apparently, 3L-CVRP is a combination of capacitated vehicle routing and three-dimensional bin packing problem and thus of high complexity. Different from most of previous works, we propose an innovative approach, called improved least waste heuristic for solving the loading subproblem, which is iteratively invoked by a simple tabu search algorithm for the routing. The good performance in terms of the solution quality and computational efficiency of our approach is shown through the numerical experiments on the benchmark instances from literature.     

基于博弈论的内河港口作业车辆协同选路方法

针对以汽车运输为主且吞吐量较大的内河港口的交通拥堵问题,提出一种基于博弈论的内河港口作业车辆协同选路方法。首先,基于港口路网特征与车辆作业特点,将同时请求路径规划的作业车辆间的交互建模为不完全信息博弈,采用满足均衡（SE）的概念来分析该博弈。假设每个车辆对选路效用都有一个预期,当所有车辆都得到满足时博弈即达到均衡。然后,提出了一种车辆协同选路算法,算法中每个车辆首先按照贪心策略初始选路,之后将所有车辆按规则分组,组内车辆根据历史选路结果进行适应性学习并完成博弈。实验结果表明,当港区同时作业车辆数为286时,协同选路算法的车辆平均行驶时间分别比Dijkstra算法和自适应学习算法（SALA）少50.8%和16.3%,系统收益分别比Dijkstra算法和SALA提高51.7%和24.5%。所提算法能够有效减少车辆平均行驶时间,提高系统收益,更适用于内河港口车辆选路问题。     

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.     

Heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem in a carrier

In this paper, we present heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem arising in a real-world situation. In this problem, customers make requests of goods, which are packed in a sortment of boxes. The objective is to find minimum cost delivery routes for a set of identical vehicles that, departing from a depot, visit all customers only once and return to the depot. Apart of the usual 3D container loading constraints which ensure that the boxes are packed completely inside the vehicles and that the boxes do not overlap each other in each vehicle, the problem also takes into account constraints related to the vertical stability of the cargo and multi-drop situations. The algorithms are based on the combination of classical heuristics from both vehicle routing and container loading literatures, as well as two metaheuristic strategies, and their use in more elaborate procedures. Although these approaches cannot assure optimal solutions for the respective problems, they are relatively simple, fast enough to solve real instances, flexible enough to include other practical considerations, and normally assure relatively good solutions in acceptable computational times in practice. The approaches are also sufficiently generic to be embedded with algorithms other than those considered in this study, as well as they can be easily adapted to consider other practical constraints, such as the load bearing strength of the boxes, time windows and pickups and deliveries. Computational tests were performed with these methods considering instances based on the vehicle routing literature and actual customers’ orders, as well as instances based on a real-world situation of a Brazilian carrier. The results show that the heuristics are able to produce relatively good solutions for real instances with hundreds of customers and thousands of boxes.     

Routing fleets with multiple driving ranges: Is it possible to use greener fleet configurations?

This paper discusses the vehicle routing problem with multiple driving ranges (VRPMDR), an extension of the classical routing problem where the total distance each vehicle can travel is limited and is not necessarily the same for all vehicles – heterogeneous fleet with respect to maximum route lengths. The VRPMDR finds applications in routing electric and hybrid-electric vehicles, which can only cover limited distances depending on the running time of their batteries. Also, these vehicles require from long charging times, which in practice makes it difficult to consider en route recharging. The paper formally introduces the problem, describes an integer programming formulation and a multi-round heuristic algorithm that iteratively constructs a solution for the problem. Using a set of benchmarks adapted from the literature, the algorithm is then employed to analyze how distance-based costs are increased when considering ‘greener’ fleet configurations – i.e., when using electric vehicles with different degrees of autonomy.     

随机需求多车辆路径问题的神经网络算法

目前国内外对随机需求多车辆路径问题的研究还很少,本文针对标准hopfield神经网络容易陷入局部极值点等问题,以总路程最短和总使用车辆数最少为目标,提出了一种基于退火策略的混沌神经网络的求解随机需求多车辆路径问题的算法,该算法既可以使混沌运动有足够长的进程以提高粗搜索性能,又可以随混沌动态的减弱使收敛速度加快。实验结果表明,该算法优化车辆路径更佳,是解决随机需求多车辆路径问题的有效方法。     

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.     

三维装载与CVRP 联合多目标优化问题的模型及算法

提出三维装载与CVRP联合多目标优化问题(3LCVRPMO)模型,该模型在三维装载约束下的CVRP问题(3LCVRP)的基础上,考虑了配送车辆数目及路径总距离两个目标函数.在权衡装箱和路径优化两个优化过程的基础上,构建了多阶段/两层混合算法架构(MSOTLH)及其算法,并对路径优化偏好的3LCVRPMO问题进行求解.基于3LCVRP问题相关算例的数据实验结果表明,所提出的3LCVRPMO模型及MSOTLH算法是有效的.     

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.     

混合最大最小蚁群算法在VRPTW中的应用

为解决有时间窗车辆路径问题,采用两个最大最小蚁群系统,一个蚁群最小化车辆数量,另一个蚁群最小化旅行距离。通过分析有时间窗车辆路径问题和旅行商问题的区别,改进了最大最小蚁群算法中状态转移策略,并增加与可用车辆相同数量的虚拟仓库,使这两个蚁群使用独立的信息素但通过分享全局最优解来协作,算法还结合了2-opt局部搜索,从而减少了算法的计算时间并避免过早收敛。仿真实验结果表明,该算法性能优良,能有效地求解有时间窗车辆路径问题。     

面向不同目标偏好的CVRP多目标模型及其求解方法*

为了更有效地求解车辆路径问题、全方位地评估物流运输成本,本文提出了面向不同目标偏好的车载能力约束车辆路径问题(CVRP)的多目标优化模型(MOCVRPFDTP),其包括三种不同的偏好结构：装载与CVRP联合优化、绝对最小车辆数偏好及路径优化偏好。为了求解该模型,本文设计了算法架构及具体算法。在实验中,该模型及其求解方法对CVRP国际标准算例VRPLIB的测试结果,显示了令人满意的性能,并且它更适用于实际CVRP问题的求解。     

考虑随机旅行时间与二维装载约束的越库配送车辆路径优化

面向越库配送模式下二维装载和车辆路径联合优化,考虑现实配送过程的不确定性因素,提出考虑随机旅行时间和二维装载约束的越库配送车辆路径问题.基于蒙特卡洛模拟与场景分析方法,建立以运输成本、车辆固定成本以及时间窗期望惩罚成本之和最小化为目标的带修正随机规划模型.继而根据问题特征,设计改进的自适应禁忌搜索算法和基于禁忌搜索的多重排序最佳适应装箱算法进行求解.其中,改进的自适应禁忌搜索算法在禁忌搜索算法的基础上引入自适应机制,对不同邻域算子进行动态选择,并提出基于移除-修复策略的多样性机制以增强算法的寻优能力.数值实验表明,所提出的模型与方法能够有效求解考虑随机旅行时间和二维装载约束的越库配送车辆路径问题,自适应与多样性机制能一定程度上增强算法的全局搜索能力.     

A branch-and-price-and-check model for the vehicle routing problem with location congestion

This paper considers a vehicle routing problem with pickup and delivery, time windows and location congestion. Locations provide a number of cumulative resources that are utilized by vehicles either during service (e.g., forklifts) or for the entirety of their visit (e.g., parking bays). Locations can become congested if insufficient resources are available, upon which vehicles must wait until a resource becomes available before proceeding. The problem is challenging from a computational standpoint since it incorporates the vehicle routing problem and the resource-constrained project scheduling problem. The main contribution of this paper is a branch-and-price-and-check model that uses a branch-and-price algorithm that solves the underlying vehicle routing problem, and a constraint programming subproblem that checks the feasibility of the location resource constraints, and then adds combinatorial nogood cuts to the master problem if the resource constraints are violated. Experimental results show the benefits of the branch-and-price-and-check approach.     

改进变邻域搜索算法求解动态车辆路径问题

针对动态车辆路径问题DVRP(Dynamic Vehicle Routing Problem)的优化问题,提出一种改进算法。该算法在分析路径寻优问题的局部特性的基础上,利用变邻域搜索算法VNS(Variable Neighbourhood Search)对路径空间进行"局部探索",结合变异机制对路径空间进行"全局开采",最后根据近邻优先原则将动态路径片段安插到适宜的路径中。实验结果验证了算法的有效性。     

Vehicle routing with pick-up and delivery: tour-partitioning heuristics

Many applications of the classical vehicle routing problem involve pick-up and delivery services between the depot and peripheral locations (warehouses, stores, stations). This paper studies an important version of the vehicle routing problem with pick-up and delivery (the so-called delivery and backhaul problem): delivery in our case refers to transportation of goods from the depot to customers, and pick-up (backhaul) refers to shipment from customers to the depot. The objective is to find a set of vehicle routes that service customers such that vehicle capacity is not violated and the total distance traveled is minimized. Tour partitioning heuristics for solving the capacitated vehicle routing problem are based on breaking a basic tour into disjoint segments served by different vehicles. This idea is adapted for solving the delivery and backhaul problem. Two heuristics that focus on efficient utilization of vehicles’ capacities are introduced, analyzed and tested numerically.     

A Java™ universal vehicle router for routing unmanned aerial vehicles

We consider vehicle routing problems in the context of the Air Force operational problem of routing unmanned aerial vehicles from base locations to various reconnaissance sites. The unmanned aerial vehicle routing problem requires consideration of heterogeneous vehicles, vehicle endurance limits, time windows, and time walls for some of the sites requiring coverage, site priorities, and asymmetric travel distances. We propose a general architecture for operational research problems, specified for vehicle routing problems, that encourages object‐oriented programming and code reuse. We create an instance of this architecture for the unmanned aerial vehicle routing problem and describe the components of this architecture to include the general user interface created for the operational users of the system. We employ route building heuristics and tabu search in a symbiotic fashion to provide a user‐defined level‐of‐effort solver interface. Empirical tests of solution algorithms parameterized for solution speed reveal reasonable solution quality is attained.     

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASP×ELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASP×ELS approach outperforms all previously published methods.     

平衡装载约束下的车辆路径问题研究

针对车辆三维装载约束下的车辆路径问题（3L-VRP）进行研究,引进车辆的平衡装载约束,综合考虑传统的先进后出、局部支撑、脆弱性等约束,构建平衡装载约束下的车辆路径问题（BL-VRP）模型。针对模型中的平衡约束,提出一种接触面积的装载算法。在此基础上,构建以回溯遗传算法（B-GA）为骨架的多阶段算法框架,对车辆路径优化进行求解。研究结果表明,多阶段算法不仅在解决3L-VRP上好于目前已有算法,同时对BL-VRP表现优秀。提出的多阶段算法为解决BL-VRP问题提供一条参考思路,但在时效性上需要进一步完善。     

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。