{"title":"Facet separation for disjunctive constraints with network flow representation","authors":"Péter Dobrovoczki, Tamás Kis","doi":"10.1007/s10479-024-06264-2","DOIUrl":null,"url":null,"abstract":"<div><p>We present a novel algorithm for separating facet-inducing inequalities for the convex-hull of the union of polytopes representing a disjunctive constraint of special structure. It is required that the union of polytopes admit a certain network flow representation. The algorithm is based on a new, graph theoretic characterization of the facets of the convex-hull. Moreover, we characterize the family of polytopes that are representable by the networks under consideration. We demonstrate the effectiveness of our approach by computational results on a set of benchmark problems.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"341 2-3","pages":"825 - 857"},"PeriodicalIF":4.4000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10479-024-06264-2.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-024-06264-2","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We present a novel algorithm for separating facet-inducing inequalities for the convex-hull of the union of polytopes representing a disjunctive constraint of special structure. It is required that the union of polytopes admit a certain network flow representation. The algorithm is based on a new, graph theoretic characterization of the facets of the convex-hull. Moreover, we characterize the family of polytopes that are representable by the networks under consideration. We demonstrate the effectiveness of our approach by computational results on a set of benchmark problems.
期刊介绍：
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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