{"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":15961,"journal":{"name":"Journal of Global Optimization","volume":"56 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Global Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10898-023-01358-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","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：
The Journal of Global Optimization publishes carefully refereed papers that encompass theoretical, computational, and applied aspects of global optimization. While the focus is on original research contributions dealing with the search for global optima of non-convex, multi-extremal problems, the journal’s scope covers optimization in the widest sense, including nonlinear, mixed integer, combinatorial, stochastic, robust, multi-objective optimization, computational geometry, and equilibrium problems. Relevant works on data-driven methods and optimization-based data mining are of special interest.
In addition to papers covering theory and algorithms of global optimization, the journal publishes significant papers on numerical experiments, new testbeds, and applications in engineering, management, and the sciences. Applications of particular interest include healthcare, computational biochemistry, energy systems, telecommunications, and finance. Apart from full-length articles, the journal features short communications on both open and solved global optimization problems. It also offers reviews of relevant books and publishes special issues.
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