A Comparison of Benson’s Outer Approximation Algorithm with an Extended Version of Multiobjective Simplex Algorithm
The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and...
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| Vydané v: | Advances in Operations Research Ročník 2021; s. 1 - 11 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Hindawi
05.07.2021
John Wiley & Sons, Inc |
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| ISSN: | 1687-9147, 1687-9155 |
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| Abstract | The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and also return the corresponding objective values (nondominated points). This paper presents an extension of the multiobjective simplex algorithm (MSA) to generate the set of all nondominated points and no redundant ones. This extended version is compared to Benson’s outer approximation (BOA) algorithm that also computes the set of all nondominated points of the problem. Numerical results on nontrivial MOLP problems show that the total number of nondominated points returned by the extended MSA is the same as that returned by BOA for most of the problems considered. |
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| AbstractList | The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and also return the corresponding objective values (nondominated points). This paper presents an extension of the multiobjective simplex algorithm (MSA) to generate the set of all nondominated points and no redundant ones. This extended version is compared to Benson’s outer approximation (BOA) algorithm that also computes the set of all nondominated points of the problem. Numerical results on nontrivial MOLP problems show that the total number of nondominated points returned by the extended MSA is the same as that returned by BOA for most of the problems considered. |
| Audience | Academic |
| Author | Nyiam, Paschal B. Salhi, Abdellah |
| Author_xml | – sequence: 1 givenname: Paschal B. orcidid: 0000-0003-2535-3526 surname: Nyiam fullname: Nyiam, Paschal B. organization: Department of Mathematical SciencesUniversity of EssexColchesterUKessex.ac.uk – sequence: 2 givenname: Abdellah surname: Salhi fullname: Salhi, Abdellah organization: Department of Mathematical SciencesUniversity of EssexColchesterUKessex.ac.uk |
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| Cites_doi | 10.1057/palgrave.jors.2602589 10.1007/bf01584543 10.1023/a:1022614814789 10.1007/s10898-013-0098-2 10.1007/s10898-013-0136-0 10.1007/bf00941298 10.1016/0377-2217(90)90010-9 10.1016/0022-247x(75)90189-4 10.2307/3008921 10.1007/bf01584348 10.1016/0377-2217(77)90063-7 10.1023/a:1022628612489 10.1016/j.ejor.2016.02.039 10.1016/j.jmaa.2008.11.063 10.1007/s00186-008-0220-2 10.1007/s10898-010-9588-7 10.1007/s10107-016-1061-z 10.1007/bf01588968 10.1007/s00186-007-0194-5 10.1051/ro/197408v300511 10.1287/mnsc.23.2.159 10.1023/A:1022614814789 10.1007/bf01580111 10.1177/1748302619870424 10.1007/978-3-642-80808-1 10.1007/s10898-011-9709-y 10.1002/cae.21601 10.1007/978-3-642-18351-5 10.1007/s10589-015-9760-6 10.1016/0022-247x(87)90065-5 10.1007/bf00935493 |
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| Copyright | Copyright © 2021 Paschal B. Nyiam and Abdellah Salhi. COPYRIGHT 2021 John Wiley & Sons, Inc. Copyright © 2021 Paschal B. Nyiam and Abdellah Salhi. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| References_xml | – volume-title: Multiple Criteria Decision Making year: 1982 ident: 39 – year: 2015 ident: 41 article-title: Bensolve: VLP solver, version 2.0.x – ident: 37 doi: 10.1057/palgrave.jors.2602589 – volume: 30 start-page: 351 issue: 4 year: 2005 ident: 32 article-title: A correction to the connectedness of the Evans-Steuer algorithm of multiple objective linear programming publication-title: Foundations of Computing and Decision Sciences – ident: 4 doi: 10.1007/bf01584543 – ident: 8 doi: 10.1023/a:1022614814789 – ident: 36 doi: 10.1007/s10898-013-0098-2 – ident: 14 doi: 10.1007/s10898-013-0136-0 – volume-title: Operating Manual for the EFFACET Multiple Objective Linear Programming Package year: 1984 ident: 24 – volume-title: Multicriteria Optimization year: 2006 ident: 7 – ident: 29 doi: 10.1007/bf00941298 – ident: 12 doi: 10.1016/0377-2217(90)90010-9 – ident: 21 doi: 10.1016/0022-247x(75)90189-4 – volume-title: Linear Programming and its Applications year: 2007 ident: 2 – ident: 23 doi: 10.2307/3008921 – year: 2012 ident: 34 article-title: Bensolve: VLP solver – ident: 18 doi: 10.1007/bf01584348 – ident: 25 doi: 10.1016/0377-2217(77)90063-7 – ident: 10 doi: 10.1023/a:1022628612489 – volume-title: Adbase: A Multiple Objective Linear Programming Solver for All Efficient Extreme Points and All Unbounded Efficient Edges year: 2003 ident: 19 – ident: 42 doi: 10.1016/j.ejor.2016.02.039 – ident: 33 article-title: A finite algorithm for minimizing a concave function under linear constraints and its applications – ident: 17 doi: 10.1016/j.jmaa.2008.11.063 – ident: 15 doi: 10.1007/s00186-008-0220-2 – volume-title: Multiple Criteria Optimization: Theory, Computation, and Applications year: 1986 ident: 26 – ident: 6 doi: 10.1007/s10898-010-9588-7 – ident: 30 doi: 10.1007/s10107-016-1061-z – ident: 27 doi: 10.1007/bf01588968 – ident: 16 doi: 10.1007/s00186-007-0194-5 – ident: 20 doi: 10.1051/ro/197408v300511 – volume: 23 start-page: 159 issue: 2 year: 1976 ident: 22 article-title: Linear multiparametric programming by multicriteria simplex method publication-title: Management Science doi: 10.1287/mnsc.23.2.159 – ident: 9 doi: 10.1023/A:1022614814789 – ident: 3 doi: 10.1007/bf01580111 – ident: 1 doi: 10.1177/1748302619870424 – volume-title: Linear Multiobjective Programming year: 1974 ident: 5 doi: 10.1007/978-3-642-80808-1 – ident: 13 doi: 10.1007/s10898-011-9709-y – ident: 40 doi: 10.1002/cae.21601 – volume-title: Vector Optimization with Infimum and Supremum year: 2011 ident: 31 doi: 10.1007/978-3-642-18351-5 – year: 2015 ident: 38 article-title: MOPLIB: multi-objective problem library – ident: 35 doi: 10.1007/s10589-015-9760-6 – ident: 11 doi: 10.1016/0022-247x(87)90065-5 – ident: 28 doi: 10.1007/bf00935493 |
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| SubjectTerms | Algorithms Approximation Comparative analysis Decision making Decomposition Efficiency Linear programming Operations research Simplex method |
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| Title | A Comparison of Benson’s Outer Approximation Algorithm with an Extended Version of Multiobjective Simplex Algorithm |
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