整数线性规划中的列生成

IF 1.8 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Rairo-Operations Research Pub Date : 2003-04-01 DOI:10.1051/RO:2003014

N. Maculan, Marcos de Mendonça Passini, Jose Brito, I. Loiseau

{"title":"整数线性规划中的列生成","authors":"N. Maculan, Marcos de Mendonça Passini, Jose Brito, I. Loiseau","doi":"10.1051/RO:2003014","DOIUrl":null,"url":null,"abstract":"We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this approach to a telecommunications network planning problem.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"441 1","pages":"67-83"},"PeriodicalIF":1.8000,"publicationDate":"2003-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"COLUMN-GENERATION IN INTEGER LINEAR PROGRAMMING\",\"authors\":\"N. Maculan, Marcos de Mendonça Passini, Jose Brito, I. Loiseau\",\"doi\":\"10.1051/RO:2003014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this approach to a telecommunications network planning problem.\",\"PeriodicalId\":54509,\"journal\":{\"name\":\"Rairo-Operations Research\",\"volume\":\"441 1\",\"pages\":\"67-83\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2003-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rairo-Operations Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://doi.org/10.1051/RO:2003014\",\"RegionNum\":4,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rairo-Operations Research","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1051/RO:2003014","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}

引用次数: 9

摘要

提出了一种求解整数线性规划问题的精确方法，该方法将分支定界与搜索树各节点的列生成相结合。对于只涉及二元列向量的模型，我们建议使用所谓的几何切割来添加到子问题中，以消除先前生成的列。该方案可以应用于一般的无特定结构的整数问题。我们报告了将该方法成功应用于电信网络规划问题的计算结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

COLUMN-GENERATION IN INTEGER LINEAR PROGRAMMING

We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this approach to a telecommunications network planning problem.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Rairo-Operations Research 管理科学-运筹学与管理科学

CiteScore

3.60

自引率

22.20%

发文量

206

审稿时长

>12 weeks

期刊介绍： RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.