Exact separation of the rounded capacity inequalities for the capacitated vehicle routing problem

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

Networks Pub Date : 2023-09-29 DOI:10.1002/net.22183

Konstantin Pavlikov, Niels Christian Petersen, Jon Lilholt Sørensen

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Abstract

Abstract The family of Rounded Capacity (RC) inequalities is one of the most important sets of valid inequalities for the Capacitated Vehicle Routing Problem (CVRP). This paper considers the problem of separation of violated RC inequalities and develops an exact procedure employing mixed integer linear programming. The developed routine is demonstrated to be very efficient for small and medium‐sized problem instances. For larger‐scale problem instances, an iterative approach for exact separation of RC inequalities is developed, based upon a selective variable pricing strategy. The approach combines column and row generation and allows us to introduce variables only when they are needed, which is essential when dealing with large‐scale problem instances. A computational study demonstrates scalability of the proposed separation routines and provides exact RC‐based lower bounds to some of the publicly available unsolved CVRP instances. The same computational study provides RC‐based lower bounds for very large‐scale CVRP instances with more than 3000 locations obtained within appropriate computational time limits.

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有容车辆路径问题的舍入容量不等式的精确分离

舍入容量不等式族是有能力车辆路径问题(CVRP)中最重要的有效不等式集之一。本文考虑了违背RC不等式的分离问题，并利用混合整数线性规划给出了一个精确的求解方法。所开发的程序对于中小型问题实例是非常有效的。对于更大规模的问题实例，基于选择性变量定价策略，开发了精确分离RC不等式的迭代方法。该方法结合了列和行生成，并允许我们仅在需要时引入变量，这在处理大规模问题实例时是必不可少的。一项计算研究证明了所提出的分离例程的可扩展性，并为一些公开可用的未解决的CVRP实例提供了精确的基于RC的下限。同样的计算研究为在适当的计算时间限制内获得超过3000个位置的超大规模CVRP实例提供了基于RC的下限。

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.