{"title":"The Solution of some 100-city Travelling Salesman Problems","authors":"A. Land","doi":"10.1016/j.ejco.2021.100017","DOIUrl":null,"url":null,"abstract":"<div><p>A simplex-based <span>FORTRAN</span> code, working entirely in integer arithmetic, has been developed for the exact solution of travelling-salesman problems. The code adds tour-barring constraints as they are found to be violated. It deals with fractional solutions by adding two-matching constraints and as a last resort by ‘Gomory’ cutting plane constraints of the Method of Integer Forms. Most of the calculations are carried out on only a subset of the variables, with only occasional passes through the whole set of possible variables. Computational experience on some 100-city problems is reported.</p></div>","PeriodicalId":51880,"journal":{"name":"EURO Journal on Computational Optimization","volume":"9 ","pages":"Article 100017"},"PeriodicalIF":2.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2192440621001441/pdfft?md5=a52a3c9bdab27e0da82eb05946357c1d&pid=1-s2.0-S2192440621001441-main.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EURO Journal on Computational Optimization","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2192440621001441","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 1
Abstract
A simplex-based FORTRAN code, working entirely in integer arithmetic, has been developed for the exact solution of travelling-salesman problems. The code adds tour-barring constraints as they are found to be violated. It deals with fractional solutions by adding two-matching constraints and as a last resort by ‘Gomory’ cutting plane constraints of the Method of Integer Forms. Most of the calculations are carried out on only a subset of the variables, with only occasional passes through the whole set of possible variables. Computational experience on some 100-city problems is reported.
期刊介绍：
The aim of this journal is to contribute to the many areas in which Operations Research and Computer Science are tightly connected with each other. More precisely, the common element in all contributions to this journal is the use of computers for the solution of optimization problems. Both methodological contributions and innovative applications are considered, but validation through convincing computational experiments is desirable. The journal publishes three types of articles (i) research articles, (ii) tutorials, and (iii) surveys. A research article presents original methodological contributions. A tutorial provides an introduction to an advanced topic designed to ease the use of the relevant methodology. A survey provides a wide overview of a given subject by summarizing and organizing research results.
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