多时间窗车辆路径问题的智能水滴算法

研究了多时间窗车辆路径问题,考虑了车容量、多个硬时间窗限制等约束条件,以动用车辆的固定成本和车辆运行成本之和最小为目标,建立了整数线性规划模型。根据智能水滴算法的基本原理,设计了求解多时间窗车辆路径问题的快速算法,利用具体实例进行了模拟计算,并与遗传算法的计算结果进行了对比分析,结果显示,利用智能水滴算法求解多时间窗车辆路径问题,能够以很高的概率得到全局最优解,是求解多时间窗车辆路径问题的有效算法。     

A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods

Most of the research on integrated inventory and routing problems ignores the case when products are perishable. However, considering the integrated problem with perishable goods is crucial since any discrepancy between the routing and inventory cost can double down the risk of higher obsolescence costs due to the limited shelf-life of the products. In this paper, we consider a distribution problem involving a depot, a set of customers and a homogeneous fleet of capacitated vehicles. Perishable goods are transported from the depot to customers in such a way that out-of-stock situations never occur. The objective is to simultaneously determine the inventory and routing decisions over a given time horizon such that total transportation cost is minimized. We present a new “arc-based formulation” for the problem which is deemed more suitable for our new tabu search based approach for solving the problem. We perform a thorough sensitivity analysis for each of the tabu search parameters individually and use the obtained gaps to fine-tune the parameter values that are used in solving larger sized instances of the problem. We solve different sizes of randomly generated instances and compare the results obtained using the tabu search algorithm to those obtained by solving the problem using CPLEX and a recently published column generation algorithm. Our computational experiments demonstrate that the tabu search algorithm is capable of obtaining a near-optimal solution in less computational time than the time required to solve the problem to optimality using CPLEX, and outperforms the column generation algorithm for solving the “path flow formulation” of the problem in terms of solution quality in almost all of the considered instances.     

部分联合运输策略下的物流车辆路径优化问题研究

论文分析了物流车辆路径优化问题的特点,提出了企业自营物流和第三方物流协同运输的部分联合运输策略。根据客户需求节点的特点进行了节点分类,建立了以车辆调用成本、车辆运输成本、第三方物流运输成本之和最小为目标的整数线性规划模型。根据部分联合运输策略下各类客户需求点运输方式特点,构造了一种新的变维数矩阵编码结构,并对传统算法中概率选择操作方式进行修改,提出了一种新的智能优化算法并与枚举法和遗传算法的运算结果进行了算法性能对比分析。结果显示,本文提出的逆选择操作蚁群算法具有较快的运算速度和较高的稳定性,是求解此类问题的一种有效算法。     

基于两阶段启发式算法的物流配送选址-路径问题研究

为了解决配送中心选址与带时间窗的多中心车辆路径优化组合决策问题,利用双层规划法建立了配送中心选址与车辆路径安排的多目标整数规划模型,针对该模型的特点,采用两阶段启发式算法进行了求解。首先,通过基于聚集度的启发式算法对客户进行分类,确定了备选配送中心的服务范围;然后,基于双层规划法,以配送中心选址成本最小作为上层规划目标,以车辆配送成本最小作为下层规划目标,建立了多目标整数规划模型;最后,利用改进的蚁群算法进行了求解。通过分析实例数据和Barreto Benchmark算例的实验结果,验证了该模型的有效性和可行性。     

An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles

The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows.     

An adaptive insertion algorithm for the single-vehicle dial-a-ride problem with narrow time windows

The dial-a-ride problem (DARP) is a widely studied theoretical challenge related to dispatching vehicles in demand-responsive transport services, in which customers contact a vehicle operator requesting to be carried from specified origins to specified destinations. An important subproblem arising in dynamic dial-a-ride services can be identified as the single-vehicle DARP, in which the goal is to determine the optimal route for a single vehicle with respect to a generalized objective function. The main result of this work is an adaptive insertion algorithm capable of producing optimal solutions for a time constrained version of this problem, which was first studied by Psaraftis in the early 1980s. The complexity of the algorithm is analyzed and evaluated by means of computational experiments, implying that a significant advantage of the proposed method can be identified as the possibility of controlling computational work smoothly, making the algorithm applicable to any problem size.     

Combination of geographical information system and efficient routing algorithms for real life distribution operations

This paper presents a decision support system (DSS) employing a metaheuristic algorithm called BoneRoute, for solving the open vehicle routing problem (OVRP). The OVRP deals with the problem of finding a set of vehicle routes, for a fleet of capacitated vehicles to satisfy the delivery requirements of customers, without returning to the distribution centre. The computational performance of the BoneRoute algorithm for the OVRP was found to be very efficient, producing new best solutions over a set of well-known published case studies examined. Technical and managerial issues aroused from the ad hoc connections between the geographical information system (GIS), the routing technique used for calculating shortest paths and the BoneRoute algorithm for finding the optimal sequence of customers, were faced successfully.     

Optimised crossover genetic algorithm for capacitated vehicle routing problem

This paper presents a genetic algorithm for solving capacitated vehicle routing problem, which is mainly characterised by using vehicles of the same capacity based at a central depot that will be optimally routed to supply customers with known demands. The proposed algorithm uses an optimised crossover operator designed by a complete undirected bipartite graph to find an optimal set of delivery routes satisfying the requirements and giving minimal total cost. We tested our algorithm with benchmark instances and compared it with some other heuristics in the literature. Computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found.     

Using clustering analysis in a capacitated location-routing problem

The location routing problem (LRP) appears as a combination of two difficult problems: the facility location problem (FLP) and the vehicle routing problem (VRP). In this work, we consider a discrete LRP with two levels: a set of potential capacitated distribution centres (DC) and a set of ordered customers. In our problem we intend to determine the set of installed DCs as well as the distribution routes (starting and ending at the DC). The problem is also constrained with capacities on the vehicles. Moreover, there is a homogeneous fleet of vehicles, carrying a single product and each customer is visited just once. As an objective we intend to minimize the routing and location costs.     

第三方库存-路线问题的模型及混合遗传算法设计

根据第三方库存-路线问题的特点,以车辆租赁费用和运行费用之和为目标函数,不限制客户每次的配送量小于车辆容量,建立了满载运输和非满载运输混合的整数规划模型.针对第三方库存-路线问题的复杂性,本文设计嵌入禁忌搜索的遗传算法来同时决策库存和路线问题.首先对配送间隔进行编码,然后用禁忌搜索法计算每天需要配送的车辆路线问题.最后与其下界值进行比较,结果表明该算法是一个有效的算法,不但第三方能取得较低的运营总成本和较高的车辆利用率,而且也能为客户节约库存空间.     

Multi-ant colony system (MACS) for a vehicle routing problem with backhauls

The vehicle routing problem with backhaul (VRPB) is an extension of the capacitated vehicle routing problem (CVRP). In VRPB, there are linehaul as well as backhaul customers. The number of vehicles is considered to be fixed and deliveries for linehaul customers must be made before any pickups from backhaul customers. The objective is to design routes for the vehicles so that the total distance traveled is minimized. We use multi-ant colony system (MACS) to solve VRPB which is a combinatorial optimization problem. Ant colony system (ACS) is an algorithmic approach inspired by foraging behavior of real ants. Artificial ants are used to construct a solution by using pheromone information from previously generated solutions. The proposed MACS algorithm uses a new construction rule as well as two multi-route local search schemes. An extensive numerical experiment is performed on benchmark problems available in the literature.     

Finished-vehicle transporter routing problem solved by loading pattern discovery

This work addresses a new transportation problem in outbound logistics in the automobile industry: the finished-vehicle transporter routing problem (FVTRP). The FVTRP is a practical routing problem with loading constraints, and it assumes that dealers have deterministic demands for finished vehicles that have three-dimensional irregular shapes. The problem solution will identify optimal routes while satisfying demands. In terms of complex packing, finished vehicles are not directly loaded into the spaces of transporters; instead, loading patterns matching finished vehicles with transporters are identified first by mining successful loading records through virtual and manual loading test procedures, such that the packing problem is practically solved with the help of a procedure to discover loading patterns. This work proposes a mixed-integer linear programming (MILP) model for the FVTRP considering loading patterns. As a special class of routing models, the FVTRP is typically difficult to solve within a manageable computing time. Thus, an evolutionary algorithm is designed to solve the FVTRP. Comparisons of the proposed algorithm and a commercial MILP solver demonstrate that the proposed algorithm is more effective in solving medium- and large-scale problems. The proposed scheme for addressing the FVTRP is illustrated with an example and tested with benchmark instances that are derived from well-studied vehicle routing datasets.     

A branch-and-price algorithm for a vehicle routing with demand allocation problem

We investigate the vehicle routing with demand allocation problem where the decision-maker jointly optimizes the location of delivery sites, the assignment of customers to (preferably convenient) delivery sites, and the routing of vehicles operated from a central depot to serve customers at their designated sites. We propose an effective branch-and-price (B&P) algorithm that is demonstrated to greatly outperform the use of commercial branch-and-bound/cut solvers such as CPLEX. Central to the efficacy of the proposed B&P algorithm is the development of a specialized dynamic programming procedure that extends works on elementary shortest path problems with resource constraints in order to solve the more complex column generation pricing subproblem. Our computational study demonstrates the efficacy of the proposed approach using a set of 60 problem instances. Moreover, the proposed methodology has the merit of providing optimal solutions in run times that are significantly shorter than those reported for decomposition-based heuristics in the literature.     

A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows

Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize the objectives of traveling distance and number of vehicles. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW. The proposed HMOEA is featured with specialized genetic operators and variable-length chromosome representation to accommodate the sequence-oriented optimization in VRPTW. Unlike existing VRPTW approaches that often aggregate multiple criteria and constraints into a compromise function, the proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace. The HMOEA is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, which yields 20 routing solutions better than or competitive as compared to the best solutions published in literature.     

Integration of AI and OR Techniques for Computer-Aided Algorithmic Design in the Vehicle Routing Domain

This paper shows how tools and techniques of artificial intelligence can be successfully integrated into a computer system working in the vehicle routing domain. The aim of this system, called ALTO, is to facilitate the development of routing algorithms for transportation vehicles. In this paper, we describe the general algorithmic framework and the rich interface provided by the system to the expert algorithm designer. We also introduce a methodology for acquiring useful knowledge in the domain, based on examples of successful and unsuccessful problem-solving strategies. With such knowledge, ALTO would then be capable of actively supporting the algorithm designer by suggesting good candidate algorithms for solving new problems.     

The open vehicle routing problem with time windows

In this paper, we consider the open vehicle routing problem with time windows (OVRPTW). The OVRPTW seeks to find a set of non-depot returning vehicle routes, for a fleet of capacitated vehicles, to satisfy customers’ requirements, within fixed time intervals that represent the earliest and latest times during the day that customers’ service can take place. We formulate a comprehensive mathematical model to capture all aspects of the problem, and incorporate in the model all critical practical concerns. The model is solved using a greedy look-ahead route construction heuristic algorithm, which utilizes time windows related information via composite customer selection and route-insertion criteria. These criteria exploit the interrelationships between customers, introduced by time windows, that dictate the sequence in which vehicles must visit customers. Computational results on a set of benchmark problems from the literature provide very good results and indicate the applicability of the methodology in real-life routing applications.     

An adaptive memory algorithm for the split delivery vehicle routing problem

The split delivery vehicle routing problem (SDVRP) relaxes routing restrictions forcing unique deliveries to customers and allows multiple vehicles to satisfy customer demand. Split deliveries are used to reduce total fleet cost to meet those customer demands. We provide a detailed survey of the SDVRP literature and define a new constructive algorithm for the SDVRP based on a novel concept called the route angle control measure. We extend this constructive approach to an iterative approach using adaptive memory concepts, and then add a variable neighborhood descent process. These three new approaches are compared to exact and heuristic approaches by solving the available SDVRP benchmark problem sets. Our approaches are found to compare favorably with existing approaches and we find 16 new best solutions for a recent 21 problem benchmark set.     

Designing vehicle routes for a mix of different request types,under time windows and loading constraints

This article introduces and solves a new rich routing problem integrated with practical operational constraints. The problem examined calls for the determination of the optimal routes for a vehicle fleet to satisfy a mix of two different request types. Firstly, vehicles must transport three-dimensional, rectangular and stackable boxes from a depot to a set of predetermined customers. In addition, vehicles must also transfer products between pairs of pick-up and delivery locations. Service of both request types is subject to hard time window constraints. In addition, feasible palletization patterns must be identified for the transported products. A practical application of the problem arises in the transportation systems of chain stores, where vehicles replenish the retail points by delivering products stored at a central depot, while they are also responsible for transferring stock between pairs of the retailer network. To solve this very complex combinatorial optimization problem, our major objective was to develop an efficient methodology whose required computational effort is kept within reasonable limits. To this end, we propose a local search-based framework for optimizing vehicle routes, in which feasible loading arrangements are identified via a simple-structured packing heuristic. The algorithmic framework is enhanced with various memory components which store and retrieve useful information gathered through the search process, in order to avoid any duplicate unnecessary calculations. The proposed solution approach is assessed on newly introduced benchmark instances.     

车辆路径问题的混合优化算法

讨论了一类车辆路径调度问题(VRP)及其数学模型，并且分析了以遗传算法求解该类问题时的染色体表示和有关遗传操作，然后结合2-opt局部优化算法提出了GA with2-opt算法来求解VRP问题，试验结果说明了该算法的有效性和可行性。     

基于Voronoi划分的同城即时配送优化策略研究

近年来经济社会发展及新零售业强势崛起使得平台或商家对大规模即时配送需求日益增加,在求解大规模车辆路径问题时仅使用启发式算法或其融合算法已无法满足实际需求。本文针对基于分众级的同城即时配送模式及现阶段存在的问题,确定了基于Voronoi划分算法的即时配送分区方法和对基础蚁群算法的三个改进策略;并以全程配送产生的总成本最少为目标函数,构建了带用户需求软时间窗的车辆路径问题数学模型;最后选取客户、车辆以及门店共计一百二十个真实地理位置数据,验证了本文提出的求解策略的有效性,并分析最终结果。结果显示,①使用Voronoi分区-改进蚁群算法的两阶段方法求解大规模车辆路径问题能显著减少配送总成本,同时提升客户满意度;②在多门店的条件假设下,采用改进蚁群算法求解得到的超时时间比基础蚁群算法少36%,配送总成本低17%。