An inner approximation method to compute the weight set decomposition of a triobjective mixed-integer problem
This article is dedicated to the weight set decomposition of a multiobjective (mixed-)integer linear problem with three objectives. We propose an algorithm that returns a decomposition of the parameter set of the weighted sum scalarization by solving biobjective subproblems via Dichotomic Search whi...
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| Veröffentlicht in: | Journal of global optimization Jg. 77; H. 4; S. 715 - 742 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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New York, NY
Springer US
01.08.2020
Springer Springer Nature B.V Springer Verlag |
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| ISSN: | 1573-2916, 0925-5001, 1573-2916 |
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| Abstract | This article is dedicated to the weight set decomposition of a multiobjective (mixed-)integer linear problem with three objectives. We propose an algorithm that returns a decomposition of the parameter set of the weighted sum scalarization by solving biobjective subproblems via Dichotomic Search which corresponds to a line exploration in the weight set. Additionally, we present theoretical results regarding the boundary of the weight set components that direct the line exploration. The resulting algorithm runs in output polynomial time, i.e. its running time is polynomial in the encoding length of both the input and output. Also, the proposed approach can be used for each weight set component individually and is able to give intermediate results, which can be seen as an “approximation” of the weight set component. We compare the running time of our method with the one of an existing algorithm and conduct a computational study that shows the competitiveness of our algorithm. Further, we give a state-of-the-art survey of algorithms in the literature. |
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| AbstractList | This article is dedicated to the weight set decomposition of a multiobjective (mixed-)integer linear problem with three objectives. We propose an algorithm that returns a decomposition of the parameter set of the weighted sum scalarization by solving biobjective subproblems via Dichotomic Search which corresponds to a line exploration in the weight set. Additionally, we present theoretical results regarding the boundary of the weight set components that direct the line exploration. The resulting algorithm runs in output polynomial time, i.e. its running time is polynomial in the encoding length of both the input and output. Also, the proposed approach can be used for each weight set component individually and is able to give intermediate results, which can be seen as an “approximation” of the weight set component. We compare the running time of our method with the one of an existing algorithm and conduct a computational study that shows the competitiveness of our algorithm. Further, we give a state-of-the-art survey of algorithms in the literature. This article is dedicated to the weight set decomposition of a multiobjective (mixed-)integer linear problem with three objectives. We propose an algorithm that returns a decomposition of the parameter set of the weighted sum scalarization by solving biobjective subproblems via Dichotomic Search which corresponds to a line exploration in the weight set. Additionally, we present theoretical results regarding the boundary of the weight set components that direct the line exploration. The resulting algorithm runs in output polynomial time, i.e. its running time is polynomial in the encoding length of both the input and output. Also, the proposed approach can be used for each weight set component individually and is able to give intermediate results, which can be seen as an “approximation” of the weight set component. We compare the running time of our method with the one of an existing algorithm and conduct a computational study that shows the competitiveness of our algorithm. Further, we give a state-of-the-art survey of algorithms in the literature. |
| Audience | Academic |
| Author | Ruzika, Stefan Halffmann, Pascal Dietz, Tobias Przybylski, Anthony |
| Author_xml | – sequence: 1 givenname: Pascal surname: Halffmann fullname: Halffmann, Pascal – sequence: 2 givenname: Tobias surname: Dietz fullname: Dietz, Tobias – sequence: 3 givenname: Anthony surname: Przybylski fullname: Przybylski, Anthony – sequence: 4 givenname: Stefan surname: Ruzika fullname: Ruzika, Stefan |
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| CitedBy_id | crossref_primary_10_1007_s10957_024_02481_8 crossref_primary_10_1109_TEVC_2024_3374519 crossref_primary_10_1007_s10898_025_01512_6 crossref_primary_10_1007_s10586_023_04227_z crossref_primary_10_1007_s10898_023_01284_x crossref_primary_10_1287_ijoc_2023_0220 crossref_primary_10_1007_s00186_023_00847_8 crossref_primary_10_1002_mcda_1829 |
| Cites_doi | 10.1007/s10957-011-9849-8 10.1007/s10898-011-9709-y 10.1137/060674831 10.1007/BF02712873 10.1007/s10479-006-0072-1 10.1287/mnsc.1100.1248 10.1109/TAC.1963.1105511 10.1287/mnsc.25.1.73 10.1002/nav.3800020109 10.1016/0020-0190(88)90065-8 10.1017/CBO9780511804090 10.1002/mcda.1574 10.1016/j.disopt.2010.03.005 10.1287/ijoc.1090.0342 10.1016/j.ejor.2015.06.072 10.1007/s10898-013-0098-2 10.1002/mcda.1603.Mcda.1603 10.1016/0022-247X(68)90201-1 10.1007/978-3-662-48350-3_25 10.1007/978-3-642-13962-8_20 |
| ContentType | Journal Article |
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| Keywords | Scalarization Weight set decomposition Weighted sum method Multiobjective optimization |
| Language | English |
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| PublicationSubtitle | An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering |
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| SubjectTerms | Algorithms Analysis Approximation Computer Science Decomposition Exploration Integers Mathematical analysis Mathematics Mathematics and Statistics Methods Multiobjective optimization Multiple objective analysis Operations Research Operations Research/Decision Theory Optimization Polynomials Real Functions Scalarization Weight Weight set decomposition Weighted sum method |
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| Title | An inner approximation method to compute the weight set decomposition of a triobjective mixed-integer problem |
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