Diagonal Partitioning Strategy Using Bisection of Rectangles and a Novel Sampling Scheme

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dc.contributor.authorGuessoum, Nabila
dc.contributor.authorChiter, Lakhdar
dc.coverage.issue2cs
dc.coverage.volume29cs
dc.date.accessioned2024-01-11T09:48:08Z
dc.date.available2024-01-11T09:48:08Z
dc.date.issued2023-12-31cs
dc.description.abstractIn this paper, we consider a global optimization problem where the objective function is assumed to be Lipschitz-continuous with an unknown Lipschitz constant. Building upon the recently introduced BIRECT (BIsection of RECTangles) algorithm, we propose a new diagonal partitioning and sampling scheme. Our framework, named BIRECT-V (V for vertices), combines bisection with the sampling of two points. In the initial hyper-rectangle, these points are located at 1/3 and 1 along the main diagonal. Unlike most DIRECT-type algorithms, where evaluating the objective function at vertices is not suitable for bisection, our strategy, when combined with bisection, provides more comprehensive information about the objective function. However, the creation of new sampling points may coincide with existing ones at shared vertices, resulting in additional evaluations of the objective function and increasing the number of function evaluations per iteration. To overcome this issue, we propose modifying the original optimization domain to obtain a good approximation of the global solution. Experimental investigations demonstrate that this modification positively impacts the performance of the BIRECT-V algorithm. Our proposal shows promise as a global optimization algorithm compared to the original BIRECT and two popular DIRECT-type algorithms on a set of test problems. It particularly excels at high-dimensional problems.en
dc.formattextcs
dc.format.extent131-146cs
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMendel. 2023 vol. 29, č. 2, s. 131-146. ISSN 1803-3814cs
dc.identifier.doi10.13164/mendel.2023.2.131en
dc.identifier.issn2571-3701
dc.identifier.issn1803-3814
dc.identifier.urihttps://hdl.handle.net/11012/244262
dc.language.isoencs
dc.publisherInstitute of Automation and Computer Science, Brno University of Technologycs
dc.relation.ispartofMendelcs
dc.relation.urihttps://mendel-journal.org/index.php/mendel/article/view/248cs
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International licenseen
dc.rights.accessopenAccessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0en
dc.subjectGlobal Optimizationen
dc.subjectBIRECT Algorithmen
dc.subjectDiagonal Partitioning Strategyen
dc.subjectSampling Schemeen
dc.titleDiagonal Partitioning Strategy Using Bisection of Rectangles and a Novel Sampling Schemeen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
eprints.affiliatedInstitution.facultyFakulta strojního inženýrstvícs
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Vol. 29, No. 2