 A branch and bound algorithm for Holder bi-objective optimization. Implementation to multidimensional optimizationHamadi Ammar and Bechir Naffeti Mathematics and Computers in Simulation (MATCOM), 2023, vol. 204, issue C, 181-201 Abstract: In the present paper, we put forward and explain the branch and bound method to solve Holder multidimensional bi-objective optimization problems. We start by considering the one-dimensional case and developing an optimization algorithm based on parabolic under-estimators. Those under-estimators generate a sequence of points that will contribute in the identification of the Pareto front of the problem being raised. When seeking these points, we have to solve nonlinear equations that are difficult to solve. Besides, we develop a recursive method suitable for solving such nonlinear equations. Then we widen our focus to deal with Holder multidimensional bi-objective optimization problems. We illustrate how to implement the proposed algorithm in the multidimensional case using α-dense space filling curves. In the last section, we implement the proposed algorithm to solve some numerical examples in the one-dimensional and the multidimensional cases. Keywords: Optimization algorithms; Bi-objective optimization; Branch and bound methods; Trisection methods; Holder functions; Pareto front; Alienor technical (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:204:y:2023:i:c:p:181-201 DOI: 10.1016/j.matcom.2022.08.003 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.