Quasi-linear time heuristic to solve the Euclidean traveling salesman problem with low gap

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science Pub Date : 2024-08-17 DOI:10.1016/j.jocs.2024.102424

Arno Formella

{"title":"Quasi-linear time heuristic to solve the Euclidean traveling salesman problem with low gap","authors":"Arno Formella","doi":"10.1016/j.jocs.2024.102424","DOIUrl":null,"url":null,"abstract":"<div><p>The traveling salesman problem (TSP) is a well studied NP-hard optimization problem. We present a novel heuristic to find approximate solutions for the case of the TSP with Euclidean metric. Our pair-center algorithm runs in quasi-linear time and on linear space. In practical experiments on a variety of well known benchmarks the algorithm shows linearithmic (i.e., <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><mo>log</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span>) runtime. The solutions found by the pair-center algorithm are very good on smaller problem instances, and better than those generated by any other heuristic with at most quadratic runtime. Eventually, the average gap of the pair-center algorithm on all benchmark instances with less than 1001 points is 0.94% and for all instances with more than 1000 points up to 100 million points is 4.57%.</p></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"82 ","pages":"Article 102424"},"PeriodicalIF":3.1000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1877750324002175/pdfft?md5=f01dfeaca300fe86a8ddf250d2d1414b&pid=1-s2.0-S1877750324002175-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1877750324002175","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

Abstract

The traveling salesman problem (TSP) is a well studied NP-hard optimization problem. We present a novel heuristic to find approximate solutions for the case of the TSP with Euclidean metric. Our pair-center algorithm runs in quasi-linear time and on linear space. In practical experiments on a variety of well known benchmarks the algorithm shows linearithmic (i.e., $O (n log n)$ ) runtime. The solutions found by the pair-center algorithm are very good on smaller problem instances, and better than those generated by any other heuristic with at most quadratic runtime. Eventually, the average gap of the pair-center algorithm on all benchmark instances with less than 1 001 points is 0.94% and for all instances with more than 1000 points up to 100 million points is 4.57%.

查看原文本刊更多论文

解决低间隙欧几里得旅行推销员问题的准线性时间启发式

旅行推销员问题（TSP）是一个经过深入研究的 NP 难优化问题。我们提出了一种新颖的启发式方法，用于寻找具有欧几里得度量的 TSP 的近似解。我们的对中心算法可在准线性时间和线性空间内运行。在各种知名基准的实际实验中，该算法显示出线性的运行时间（即 O(nlogn)）。在较小的问题实例上，对中心算法找到的解非常好，比任何其他启发式算法生成的解都要好，运行时间最多为二次方。最终，在所有小于 1001 个点的基准实例上，对心算法的平均差距为 0.94%，而在所有大于 1000 个点至 1 亿个点的实例上，对心算法的平均差距为 4.57%。

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

Journal of Computational Science COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-COMPUTER SCIENCE, THEORY & METHODS

CiteScore

5.50

自引率

3.00%

发文量

227

审稿时长

41 days

期刊介绍： Computational Science is a rapidly growing multi- and interdisciplinary field that uses advanced computing and data analysis to understand and solve complex problems. It has reached a level of predictive capability that now firmly complements the traditional pillars of experimentation and theory. The recent advances in experimental techniques such as detectors, on-line sensor networks and high-resolution imaging techniques, have opened up new windows into physical and biological processes at many levels of detail. The resulting data explosion allows for detailed data driven modeling and simulation. This new discipline in science combines computational thinking, modern computational methods, devices and collateral technologies to address problems far beyond the scope of traditional numerical methods. Computational science typically unifies three distinct elements: • Modeling, Algorithms and Simulations (e.g. numerical and non-numerical, discrete and continuous); • Software developed to solve science (e.g., biological, physical, and social), engineering, medicine, and humanities problems; • Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components (e.g. problem solving environments).