Nonlinear biobjective optimization: improvements to interval branch & bound algorithms
Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing...
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| Vydáno v: | Journal of global optimization Ročník 75; číslo 1; s. 91 - 110 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.09.2019
Springer Springer Nature B.V |
| Témata: | |
| ISSN: | 0925-5001, 1573-2916 |
| On-line přístup: | Získat plný text |
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| Abstract | Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing with nonlinear optimization problems, when they consider multiple objectives. In this paper, we propose a new interval branch & bound algorithm for solving nonlinear constrained biobjective optimization problems. Although the general strategy is based on other works, we propose some improvements related to the termination criteria, node selection, upperbounding and discarding boxes using the non-dominated set. Most of these techniques use and/or adapt components of IbexOpt, a state-of-the-art interval-based single-objective optimization algorithm. The code of our plugin can be found in our git repository (
https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop
). |
|---|---|
| AbstractList | Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing with nonlinear optimization problems, when they consider multiple objectives. In this paper, we propose a new interval branch & bound algorithm for solving nonlinear constrained biobjective optimization problems. Although the general strategy is based on other works, we propose some improvements related to the termination criteria, node selection, upperbounding and discarding boxes using the non-dominated set. Most of these techniques use and/or adapt components of IbexOpt, a state-of-the-art interval-based single-objective optimization algorithm. The code of our plugin can be found in our git repository (
https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop
). Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing with nonlinear optimization problems, when they consider multiple objectives. In this paper, we propose a new interval branch & bound algorithm for solving nonlinear constrained biobjective optimization problems. Although the general strategy is based on other works, we propose some improvements related to the termination criteria, node selection, upperbounding and discarding boxes using the non-dominated set. Most of these techniques use and/or adapt components of IbexOpt, a state-of-the-art interval-based single-objective optimization algorithm. The code of our plugin can be found in our git repository ( Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing with nonlinear optimization problems, when they consider multiple objectives. In this paper, we propose a new interval branch & bound algorithm for solving nonlinear constrained biobjective optimization problems. Although the general strategy is based on other works, we propose some improvements related to the termination criteria, node selection, upperbounding and discarding boxes using the non-dominated set. Most of these techniques use and/or adapt components of IbexOpt, a state-of-the-art interval-based single-objective optimization algorithm. The code of our plugin can be found in our git repository (https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop). |
| Audience | Academic |
| Author | Campusano, Jose Aliquintui, Damir Araya, Ignacio |
| Author_xml | – sequence: 1 givenname: Ignacio orcidid: 0000-0001-5882-6217 surname: Araya fullname: Araya, Ignacio email: ignacio.araya@pucv.cl organization: Pontificia Universidad Católica de Valparaíso – sequence: 2 givenname: Jose surname: Campusano fullname: Campusano, Jose organization: Pontificia Universidad Católica de Valparaíso – sequence: 3 givenname: Damir surname: Aliquintui fullname: Aliquintui, Damir organization: Pontificia Universidad Católica de Valparaíso |
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| Cites_doi | 10.1007/s10589-007-9135-8 10.1016/j.ejor.2017.01.032 10.1007/s10898-014-0201-3 10.1007/s10898-013-0066-x 10.1007/s10898-014-0145-7 10.1016/j.ejor.2016.05.045 10.1007/s00186-016-0560-2 10.1007/s10898-017-0569-y 10.1016/j.artint.2009.03.002 10.1007/s10288-014-0269-0 10.1007/s00158-004-0496-7 10.1007/s00158-003-0368-6 10.1137/S0036142995281528 10.1007/s10898-006-9132-y 10.1007/s10898-015-0375-3 10.1007/BFb0056872 10.1137/18M1169680 10.1007/978-3-642-36803-5_38 10.1109/ICTAI.2013.138 10.1007/978-3-642-29828-8_1 10.1007/978-3-540-74970-7_45 10.1609/aaai.v25i1.7817 10.1007/978-1-4614-6940-7_15 |
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| DOI | 10.1007/s10898-019-00768-z |
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| Keywords | Interval methods Multiobjective optimization Branch & bound |
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| References | Redondo, Fernández, Ortigosa (CR4) 2017; 85 Coello, Lamont, Van Veldhuizen (CR5) 2007 Martin, Goldsztejn, Granvilliers, Jermann (CR10) 2016; 64 CR18 CR17 CR15 Przybylski, Gandibleux (CR3) 2017; 260 Araya, Trombettoni, Neveu, Chabert (CR14) 2014; 60 Neveu, Trombettoni, Araya (CR28) 2016; 64 CR12 Tóth, Fernández (CR22) 2010 Fernández, Tóth (CR7) 2007; 38 Chabert, Jaulin (CR23) 2009; 173 Csendes, Ratz (CR25) 1997; 34 Ninin, Messine, Hansen (CR19) 2015; 13 Araya, Neveu (CR16) 2018; 71 CR2 Goldsztejn, Domes, Chevalier (CR13) 2014; 58 Ruetsch (CR6) 2005; 30 CR9 CR27 Marler, Arora (CR1) 2004; 26 CR24 CR21 CR20 Fernández, Tóth (CR8) 2009; 42 Moore (CR26) 1966 Martin, Goldsztejn, Granvilliers, Jermann (CR11) 2017; 260 768_CR2 JL Redondo (768_CR4) 2017; 85 768_CR17 768_CR15 768_CR18 B Martin (768_CR10) 2016; 64 I Araya (768_CR16) 2018; 71 768_CR12 J Fernández (768_CR8) 2009; 42 RE Moore (768_CR26) 1966 B Tóth (768_CR22) 2010 CAC Coello (768_CR5) 2007 G Ruetsch (768_CR6) 2005; 30 A Goldsztejn (768_CR13) 2014; 58 768_CR27 B Martin (768_CR11) 2017; 260 RT Marler (768_CR1) 2004; 26 768_CR20 G Chabert (768_CR23) 2009; 173 I Araya (768_CR14) 2014; 60 768_CR24 768_CR21 J Fernández (768_CR7) 2007; 38 T Csendes (768_CR25) 1997; 34 A Przybylski (768_CR3) 2017; 260 768_CR9 J Ninin (768_CR19) 2015; 13 B Neveu (768_CR28) 2016; 64 |
| References_xml | – ident: CR18 – year: 2010 ident: CR22 publication-title: Interval Methods for Single and Bi-objective Optimization Problems-Applied to Competitive Facility Location Problems – volume: 42 start-page: 393 issue: 3 year: 2009 end-page: 419 ident: CR8 article-title: Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-007-9135-8 – volume: 260 start-page: 856 issue: 3 year: 2017 end-page: 872 ident: CR3 article-title: Multi-objective branch and bound publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2017.01.032 – ident: CR2 – ident: CR12 – volume: 64 start-page: 3 issue: 1 year: 2016 end-page: 16 ident: CR10 article-title: On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach publication-title: J. Glob. 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Optim. doi: 10.1007/s10898-014-0201-3 – volume: 85 start-page: 113 issue: 1 year: 2017 ident: 768_CR4 publication-title: Math. Methods Oper. Res. doi: 10.1007/s00186-016-0560-2 – ident: 768_CR17 – volume: 58 start-page: 653 issue: 4 year: 2014 ident: 768_CR13 publication-title: J. Glob. Optim. doi: 10.1007/s10898-013-0066-x – volume: 38 start-page: 315 issue: 2 year: 2007 ident: 768_CR7 publication-title: J. Glob. Optim. doi: 10.1007/s10898-006-9132-y – volume: 42 start-page: 393 issue: 3 year: 2009 ident: 768_CR8 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-007-9135-8 – volume: 13 start-page: 247 issue: 3 year: 2015 ident: 768_CR19 publication-title: 4OR doi: 10.1007/s10288-014-0269-0 – ident: 768_CR24 doi: 10.1007/978-3-540-74970-7_45 – volume: 173 start-page: 1079 year: 2009 ident: 768_CR23 publication-title: Artif. Intell. doi: 10.1016/j.artint.2009.03.002 – ident: 768_CR15 doi: 10.1609/aaai.v25i1.7817 – volume-title: Evolutionary Algorithms for Solving Multi-objective Problems year: 2007 ident: 768_CR5 – ident: 768_CR2 doi: 10.1007/978-1-4614-6940-7_15 – volume: 34 start-page: 922 issue: 3 year: 1997 ident: 768_CR25 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142995281528 – volume: 71 start-page: 483 issue: 3 year: 2018 ident: 768_CR16 publication-title: J. Glob. Optim. doi: 10.1007/s10898-017-0569-y – volume-title: Interval Analysis year: 1966 ident: 768_CR26 |
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| SubjectTerms | Algorithms Computer Science Mathematical optimization Mathematics Mathematics and Statistics Nonlinear programming Operations Research/Decision Theory Optimization Real Functions Solvers |
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| Title | Nonlinear biobjective optimization: improvements to interval branch & bound algorithms |
| URI | https://link.springer.com/article/10.1007/s10898-019-00768-z https://www.proquest.com/docview/2205097168 |
| Volume | 75 |
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