A heuristic with a performance guarantee for the commodity constrained split delivery vehicle routing problem

IF 1.6 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Networks Pub Date : 2024-07-25 DOI:10.1002/net.22238

Matteo Petris, Claudia Archetti, Diego Cattaruzza, Maxime Ogier, Frédéric Semet

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引用次数: 0

Abstract

The commodity constrained split delivery vehicle routing problem (C‐SDVRP) is a routing problem where customer demands are composed of multiple commodities. A fleet of capacitated vehicles must serve customer demands in a way that minimizes the total routing costs. Vehicles can transport any set of commodities and customers are allowed to be visited multiple times. However, the demand for a single commodity must be delivered by one vehicle only. In this work, we developed a heuristic with a performance guarantee to solve the C‐SDVRP. The proposed heuristic is based on a set covering formulation, where the exponentially‐many variables correspond to routes. First, a subset of the variables is obtained by solving the linear relaxation of the formulation by means of a column generation approach which embeds a new pricing heuristic aimed to reduce the computational time. Solving the linear relaxation gives a valid lower bound used as a performance guarantee for the heuristic. Then, we devise a restricted master heuristic to provide good upper bounds: the formulation is restricted to the subset of variables found so far and solved as an integer program with a commercial solver. A local search based on a mathematical programming operator is applied to improve the solution. We test the heuristic algorithm on benchmark instances from the literature. The comparison with the state‐of‐the‐art heuristics for solving the C‐SDVRP shows that our approach significantly improves the solution time, while keeping a comparable solution quality and improving some best‐known solutions. In addition, our approach is able to solve large instances with 100 customers and six commodities, and also provides very good quality lower bounds. Furthermore, an instance of the C‐SDVRP can be transformed into a CVRP instance by simply duplicating each customer as many times as the requested commodities and by assigning as demand the demand of the single commodity. Hence, we compare heuristics for the C‐SDVRP against the state‐of‐the‐art heuristic for the Capacitated Vehicle Routing Problem (CVRP). The latter approach revealed to have the best performance. However, our approach provides solutions of comparable quality and has the interest of providing a performance guarantee.

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商品受限的分送车辆路由问题的性能保证启发式

商品受限分送车辆路由问题（C-SDVRP）是一个客户需求由多种商品组成的路由问题。车队必须以总路由成本最小化的方式满足客户需求。车辆可以运输任意一组商品，并允许多次访问客户。但是，对单一商品的需求必须只能由一辆车来运送。在这项工作中，我们开发了一种具有性能保证的启发式来求解 C-SDVRP。所提出的启发式基于集合覆盖公式，其中指数级变量对应于路线。首先，通过列生成方法求解公式的线性松弛，获得变量子集，该方法包含一个新的定价启发式，旨在减少计算时间。线性松弛求解给出了一个有效的下限，作为启发式的性能保证。然后，我们设计了一种受限的主启发式，以提供良好的上限：将公式限制在迄今发现的变量子集中，并使用商业求解器作为整数程序求解。我们采用基于数学编程算子的局部搜索来改进解法。我们在文献中的基准实例上测试了启发式算法。与最先进的 C-SDVRP 启发式求解算法相比，我们的方法大大缩短了求解时间，同时保持了相当的求解质量，并改进了一些最著名的求解方法。此外，我们的方法还能解决包含 100 个客户和 6 种商品的大型实例，并提供了非常优质的下限。此外，C-SDVRP 实例可以转化为 CVRP 实例，只需简单地重复每个客户所要求商品的次数，并将单个商品的需求量分配为需求量即可。因此，我们将 C-SDVRP 的启发式方法与 CVRP 最先进的启发式方法进行了比较。结果表明，后者的性能最好。然而，我们的方法提供了质量相当的解决方案，并有兴趣提供性能保证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Networks 工程技术-计算机：硬件

CiteScore

4.40

自引率

9.50%

发文量

审稿时长

12 months

期刊介绍： Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context. The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics. Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally eﬃcient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without signiﬁcant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.