Heuristics and memetic algorithm for the two-dimensional loading capacitated vehicle routing problem with time windows

This work deals with a new combinatorial optimization problem, the two-dimensional loading capacitated vehicle routing problem with time windows which is a realistic extension of the well known vehicle routing problem. The studied problem consists in determining vehicle trips to deliver rectangular objects to a set of customers with known time windows, using a homogeneous fleet of vehicles, while ensuring a feasible loading of each vehicle used. Since it includes NP-hard routing and packing sub-problems, six heuristics are firstly designed to quickly compute good solutions for realistic instances. They are obtained by combining algorithms for the vehicle routing problem with time windows with heuristics for packing rectangles. Then, a Memetic algorithm is developed to improve the heuristic solutions. The quality and the efficiency of the proposed heuristics and metaheuristic are evaluated by adding time windows to a set of 144 instances with 15–255 customers and 15–786 items, designed by Iori et al. (Transport Sci 41:253–264, 2007) for the case without time windows.     

带时间窗分车运输同时收发车辆路径问题及其启发式算法

本文结合汽车零部件第三方物流的实际背景,提出了带时间窗的可分车运输同时收发车辆路径问题(简称SVRPSPDTW),并给出了问题的数学模型,同时提出两个求解该问题的启发式算法,最后进行了数值试验.由于没有可以利用的算例,本文在Solomn测试基准库的基础上构建了针对新问题的算例.计算结果表明,所有算例计算时间均不超过1秒,且算法1无论是从车辆的使用数还是从车辆行驶的路径总长度上都明显优于算法2,从而说明算法1是寻找SVRPSPDTW问题初始可行解的较为有效的算法.     

一种带时间窗和容量约束的车辆路线问题及其Tabu Search算法

本文提出一种带时间窗和容量约束的车辆路线问题（CVRPTW），并利用Tabu Search快速启式算法，针对Solomon提出的几个标准问题，快捷地得到了优良的数值结果。     

一种带时间窗和车辆数目限制的车辆路线问题及其算法

本文提出了带时间窗和车辆数目限制的车辆路线问题的数学模型,针对该问题的特征构造了一种路线生成算法和禁忌搜索算法,并对Solomon提出的C1、R1、RC1类数据集给出了数值运算的结果,实验结果表明算法是有效的.     

A vehicle routing problem with multi-trips and time windows for circular items

This article presents a vehicle routing problem with time windows, multiple trips, a limited number of vehicles and loading constraints for circular objects. This is a real problem experienced by a home delivery service company. A linear model is proposed to handle small problems and a two-step heuristic method to solve real size instances: the first step builds an initial solution through the modification of the Solomon I1 sequential insertion heuristic, and the second step improves the initial solution through the Tabu search algorithm proposed; in both steps, the problems related to circle packing with different sizes and bin packing are solved jointly with the use of heuristics. Finally, the computing results for two different sets of instances are presented.     

The vehicle routing problem with coupled time windows

In this article we introduce the vehicle routing problem with coupled time windows (VRPCTW), which is an extension of the vehicle routing problem with time windows (VRPTW), where additional coupling constraints on the time windows are imposed. VRPCTW is applied to model a real-world planning problem concerning the integrated optimization of school starting times and public bus services. A mixed-integer programming formulation for the VRPCTW within this context is given. It is solved using a new meta-heuristic that combines classical construction aspects with mixed-integer preprocessing techniques, and improving hit-and-run, a randomized search strategy from global optimization. Solutions for several randomly generated and real-world instances are presented.     

一类新的车辆路径问题及其两阶段算法

本文结合汽车零部件第三方物流业的实际背景,提出了一类新的车辆路径问题,它是一种带时间窗约束的分车运输同时收发车辆路径问题(简称SVRPSPDTW).接着给出了问题的模型,并提出求解问题的启发式算法：两阶段算法. 最后在改进的Solomn的算例的基础上,进行了数值试验.     

An exact algorithm for a single-vehicle routing problem with time windows and multiple routes

This paper describes an exact algorithm for solving a problem where the same vehicle performs several routes to serve a set of customers with time windows. The motivation comes from the home delivery of perishable goods, where vehicle routes are short and must be combined to form a working day. A method based on an elementary shortest path algorithm with resource constraints is proposed to solve this problem. The method is divided into two phases: in the first phase, all non-dominated feasible routes are generated; in the second phase, some routes are selected and sequenced to form the vehicle workday. Computational results are reported on Euclidean problems derived from benchmark instances of the classical vehicle routing problem with time windows.     

有时间窗的车辆路径问题的局部下降搜索算法

介绍了一个求解有时间窗的车辆路径问题(vehicle routing problem with time windows,VRPTW)的启发式算法——基于λ-交换的局部下降搜索算法(Local search descent method based on λ-interchange).VRPTW是指合理安排车辆行驶路线,为一组预先设定有时间限制的客户运送货物,在不违反时间要求和车辆容量限制的条件下使得成本最小.它是一个典型的NP-难题,可以通过启发式算法获得近优解来解决.通过两个实验验证,显示了局部下降搜索算法的优良性能,取得了很好的效果,可以作为进一步研究复杂算法的基础.     

Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation

This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as time windows and vehicle capacity. To solve such a multiobjective and multi-modal combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A new way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions for the VRPSD and the solutions are robust to the stochastic nature of the problem. The developed algorithm is further validated on a few VRPSD instances adapted from Solomon’s vehicle routing problem with time windows (VRPTW) benchmark problems.     

Vehicle routing with multiple deliverymen: Modeling and heuristic approaches for the VRPTW

In real life distribution of goods, relatively long service times may make it difficult to serve all requests during regular working hours. These difficulties are even greater if the beginning of the service in each demand site must occur within a time window and violations of routing time restrictions are particularly undesirable. We address this situation by considering a variant of the vehicle routing problem with time windows for which, besides routing and scheduling decisions, a number of extra deliverymen can be assigned to each route in order to reduce service times. This problem appears, for example, in the distribution of beverage and tobacco in highly dense Brazilian urban areas. We present a mathematical programming formulation for the problem, as well as a tabu search and an ant colony optimization heuristics for obtaining minimum cost routes. The performance of the model and the heuristic approaches are evaluated using instances generated from a set of classic examples from the literature.     

A self-tuning heuristic for a multi-objective vehicle routing problem

In this study, a heuristic free from parameter tuning is introduced to solve the vehicle routing problem (VRP) with two conflicting objectives. The problem which has been presented is the designing of optimal routes: minimizing both the number of vehicles and the maximum route length. This problem, even in the case of its single objective form, is NP-hard. The proposed self-tuning heuristic (STH) is based on local search and has two parameters which are updated dynamically throughout the search process. The most important advantage of the algorithm is the application convenience for the end-users. STH is tested on the instances of a multi-objective problem in school bus routing and classical vehicle routing. Computational experiments, when compared with the prior approaches proposed for the multi-objective routing of school buses problem, confirm the effectiveness of STH. STH also finds high-quality solutions for multi-objective VRPs.     

A robust optimization approach to dispatching technicians under stochastic service times

We consider the problem of dispatching technicians to service/repair geographically distributed equipment. This problem can be cast as a vehicle routing problem with time windows, where customers expect fast response and small delays. Estimates of the service time, however, can be subject to a significant amount of uncertainty due to misdiagnosis of the reason for failure or surprises during repair. It is therefore crucial to develop routes for the technicians that would be less sensitive to substantial deviations from estimated service times. In this paper we propose a robust optimization model for the vehicle routing problem with soft time windows and service time uncertainty and solve real-world instances with a branch and price method. We evaluate the efficiency of the approach through computational experiments on real industry routing data.     

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.     

A methodology to solve large-scale cooperative transportation planning problems

In this paper, we suggest a methodology to solve a cooperative transportation planning problem and to assess its performance. The problem is motivated by a real-world scenario found in the German food industry. Several manufacturers with same customers but complementary food products share their vehicle fleets to deliver their customers. After an appropriate decomposition of the entire problem into sub problems, we obtain a set of rich vehicle routing problems (VRPs) with time windows for the delivery of the orders, capacity constraints, maximum operating times for the vehicles, and outsourcing options. Each of the resulting sub problems is solved by a greedy heuristic that takes the distance of the locations of customers and the time window constraints into account. The greedy heuristic is improved by an appropriate Ant Colony System (ACS). The suggested heuristics to solve the problem are assessed within a dynamic and stochastic environment in a rolling horizon setting using discrete event simulation. We describe the used simulation infrastructure. The results of extensive simulation experiments based on randomly generated problem instances and scenarios are provided and discussed. We show that the cooperative setting outperforms the non-cooperative one.     

Relation between vehicle routing problems: an insertion heuristic for the vehicle routing problem with simultaneous delivery and pick-up applied to the vehicle routing problem with backhauls

Recently, an increasing number of papers on vehicle routing problems with backhauling has been published. Different types of backhauling problems are discussed. Two of them—the vehicle routing problem with backhauls and so-called ‘mixed loads’ (VRPBM) and the vehicle routing problem with simultaneous delivery and pick-up (VRPSDP)—are closely related. In this paper, we discuss that relationship. Our findings are that previously published results for VRPSDP instances obtained by using a heuristic suggested for the VRPBM do not take into account specific properties of the VRPSDP. As a result of the analysis of the relation between both problem types the possibility of solving the VRPBM by applying an insertion heuristic based on the concept of ‘residual capacities’ originally designed for the VRPSDP is investigated. Numerical results indicate that, for certain instances, this approach is more favourable than the application of a heuristic suggested for the VRPBM in the literature.     

Solving a vehicle-routing problem arising in soft-drink distribution

The problem studied in this article arises from the distribution of soft drinks and collection of recyclable containers in a Quebec-based company. It can be modelled as a variant of the vehicle routing problem with a heterogeneous vehicle fleet, time windows, capacity and volume constraints, and an objective function combining routing costs and the revenue resulting from the sale of recyclable material. Three construction heuristics and an improvement procedure are developed for the problem. Comparative tests are performed on a real-life instance and on 10 randomly generated instances.     

An artificial bee colony algorithm for the capacitated vehicle routing problem

This paper introduces an artificial bee colony heuristic for solving the capacitated vehicle routing problem. The artificial bee colony heuristic is a swarm-based heuristic, which mimics the foraging behavior of a honey bee swarm. An enhanced version of the artificial bee colony heuristic is also proposed to improve the solution quality of the original version. The performance of the enhanced heuristic is evaluated on two sets of standard benchmark instances, and compared with the original artificial bee colony heuristic. The computational results show that the enhanced heuristic outperforms the original one, and can produce good solutions when compared with the existing heuristics. These results seem to indicate that the enhanced heuristic is an alternative to solve the capacitated vehicle routing problem.     

A powerful route minimization heuristic for the vehicle routing problem with time windows

We suggest an efficient route minimization heuristic for the vehicle routing problem with time windows. The heuristic is based on the ejection pool, powerful insertion and guided local search strategies. Experimental results on the Gehring and Homberger’s benchmarks demonstrate that our algorithm outperforms previous approaches and found 18 new best-known solutions.     

Improved tabu search algorithm for the handling of route duration constraints in vehicle routing problems with time windows

This note introduces a refinement to a previously proposed tabu search algorithm for vehicle routing problems with time windows. This refinement yields new best known solutions on a set of benchmark instances of the multi-depot, the periodic and the site-dependent vehicle routing problems with time windows.