{"title":"Node selection through upper bounding local search methods in branch & bound solvers for NCOPs","authors":"Victor Reyes, Ignacio Araya","doi":"10.1007/s10898-024-01403-2","DOIUrl":null,"url":null,"abstract":"<p>Interval-based branch & bound solvers are commonly used for solving Nonlinear Continuous global Optimization Problems (NCOPs). In each iteration, the solver strategically chooses and processes a node within the search tree. The node is bisected and the two generated offspring nodes are processed by filtering methods. For each of these nodes, the solver also searches for new feasible solutions in order to update the best candidate solution. The cost of this solution is used for pruning non-optimal branches of the search tree. Thus, node selection and finding new solutions, stands as pivotal aspects in the functionality of these kind of solvers. The ability to find close-to-optimal solutions early in the search process may discard extensive non-optimal search space regions, thereby effectively reducing the overall size of the search tree. In this work, we propose three novel node selection algorithms that use the feasible solutions obtained through a cost-effective iterative method. Upon updating the best candidate solution, these algorithms strategically choose the node containing this solution for subsequent processing. The newly introduced strategies have been incorporated as node selection methods in a state-of-the-art branch & bound solver, showing promising results in a set of 57 benchmark instances.\n</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-25","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/s10898-024-01403-2","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
Interval-based branch & bound solvers are commonly used for solving Nonlinear Continuous global Optimization Problems (NCOPs). In each iteration, the solver strategically chooses and processes a node within the search tree. The node is bisected and the two generated offspring nodes are processed by filtering methods. For each of these nodes, the solver also searches for new feasible solutions in order to update the best candidate solution. The cost of this solution is used for pruning non-optimal branches of the search tree. Thus, node selection and finding new solutions, stands as pivotal aspects in the functionality of these kind of solvers. The ability to find close-to-optimal solutions early in the search process may discard extensive non-optimal search space regions, thereby effectively reducing the overall size of the search tree. In this work, we propose three novel node selection algorithms that use the feasible solutions obtained through a cost-effective iterative method. Upon updating the best candidate solution, these algorithms strategically choose the node containing this solution for subsequent processing. The newly introduced strategies have been incorporated as node selection methods in a state-of-the-art branch & bound solver, showing promising results in a set of 57 benchmark instances.
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.