{"title":"A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems","authors":"Hongwei Jiao, Binbin Li, Wenqiang Yang","doi":"10.1007/s10898-023-01358-w","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate a generalized multiplicative problem (GMP) that is known to be NP-hard even with one linear product term. We first introduce some criterion-space variables to obtain an equivalent problem of the GMP. A criterion-space branch-reduction-bound algorithm is then designed, which integrates some basic operations such as the two-level linear relaxation technique, rectangle branching rule and criterion-space region reduction technologies. The global convergence of the presented algorithm is proved by means of the subsequent solutions of a series of linear relaxation problems, and its maximum number of iterations is estimated on the basis of exhaustiveness of branching rule. Finally, numerical results demonstrate the presented algorithm can efficiently find the global optimum solutions for some test instances with the robustness.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10898-023-01358-w","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate a generalized multiplicative problem (GMP) that is known to be NP-hard even with one linear product term. We first introduce some criterion-space variables to obtain an equivalent problem of the GMP. A criterion-space branch-reduction-bound algorithm is then designed, which integrates some basic operations such as the two-level linear relaxation technique, rectangle branching rule and criterion-space region reduction technologies. The global convergence of the presented algorithm is proved by means of the subsequent solutions of a series of linear relaxation problems, and its maximum number of iterations is estimated on the basis of exhaustiveness of branching rule. Finally, numerical results demonstrate the presented algorithm can efficiently find the global optimum solutions for some test instances with the robustness.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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