A tabu search with geometry‐based sparsification methods for angular traveling salesman problems

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

Networks Pub Date : 2023-08-16 DOI:10.1002/net.22180

Rossana Cavagnini, Michael Schneider, Alina Theiß

{"title":"A tabu search with geometry‐based sparsification methods for angular traveling salesman problems","authors":"Rossana Cavagnini, Michael Schneider, Alina Theiß","doi":"10.1002/net.22180","DOIUrl":null,"url":null,"abstract":"The angular‐metric traveling salesman problem (AngleTSP) aims to find a tour visiting a given set of vertices in the Euclidean plane exactly once while minimizing the cost given by the sum of all turning angles. If the cost is obtained by combining the sum of all turning angles and the traveled distance, the problem is called angular‐distance‐metric traveling salesman problem (AngleDistanceTSP). In this work, we study the symmetric variants of these problems. Because both the AngleTSP and AngleDistanceTSP are NP‐hard, multiple heuristic approaches have been proposed in the literature. Nevertheless, a good tradeoff between solution quality and runtime is hard to find. We propose a granular tabu search (GTS) that considers the geometric features of the two problems in the design of starting solutions and sparsification methods. We further enrich the GTS with components that guarantee both intensification and diversification during the search. The computational results on benchmark instances from the literature show that (i) for the AngleTSP, our GTS lies on the Pareto frontier of the best performing‐heuristics, and (ii) for the AngleDistanceTSP, our GTS provides the best solution quality across all existing heuristics in competitive runtimes. In addition, new best‐known solutions are found for most benchmark instances for which an optimal solution is not available.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Networks","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1002/net.22180","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}

引用次数: 0

Abstract

The angular‐metric traveling salesman problem (AngleTSP) aims to find a tour visiting a given set of vertices in the Euclidean plane exactly once while minimizing the cost given by the sum of all turning angles. If the cost is obtained by combining the sum of all turning angles and the traveled distance, the problem is called angular‐distance‐metric traveling salesman problem (AngleDistanceTSP). In this work, we study the symmetric variants of these problems. Because both the AngleTSP and AngleDistanceTSP are NP‐hard, multiple heuristic approaches have been proposed in the literature. Nevertheless, a good tradeoff between solution quality and runtime is hard to find. We propose a granular tabu search (GTS) that considers the geometric features of the two problems in the design of starting solutions and sparsification methods. We further enrich the GTS with components that guarantee both intensification and diversification during the search. The computational results on benchmark instances from the literature show that (i) for the AngleTSP, our GTS lies on the Pareto frontier of the best performing‐heuristics, and (ii) for the AngleDistanceTSP, our GTS provides the best solution quality across all existing heuristics in competitive runtimes. In addition, new best‐known solutions are found for most benchmark instances for which an optimal solution is not available.

查看原文本刊更多论文

角旅行商问题的基于几何稀疏化方法的禁忌搜索

角度量旅行推销员问题（AngleSP）旨在找到一个恰好访问欧几里得平面中给定顶点集一次的旅行，同时最小化所有转角之和所给出的成本。如果成本是通过将所有转向角和行驶距离的总和相结合来获得的，则该问题被称为角距离度量旅行商问题（AngleDistanceTSP）。在这项工作中，我们研究了这些问题的对称变体。由于AngleTSP和AngleDistanceTSP都是NP困难的，因此文献中提出了多种启发式方法。然而，很难在解决方案质量和运行时间之间找到一个好的折衷方案。我们提出了一种粒度禁忌搜索（GTS），它在设计起始解和稀疏化方法时考虑了这两个问题的几何特征。我们进一步丰富GTS的组成部分，以保证在搜索过程中的强化和多样化。对文献中基准实例的计算结果表明，（i）对于AngleTSP，我们的GTS位于性能最佳的启发式算法的Pareto前沿，以及（ii）对于AngreDistanceTSP，我们在竞争运行时中的GTS在所有现有启发式算法中提供了最佳的解决方案质量。此外，对于大多数无法获得最佳解决方案的基准实例，都会找到新的最佳解决方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.