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
Hauptverfasser: Halffmann, Pascal, Dietz, Tobias, Przybylski, Anthony, Ruzika, Stefan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY Springer US 01.08.2020
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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.
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
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  surname: Przybylski
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CitedBy_id crossref_primary_10_1007_s10957_024_02481_8
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ISSN 1573-2916
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Issue 4
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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Snippet This article is dedicated to the weight set decomposition of a multiobjective (mixed-)integer linear problem with three objectives. We propose an algorithm...
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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
URI https://www.econstor.eu/handle/10419/288277
https://link.springer.com/article/10.1007/s10898-020-00898-9
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https://hal.science/hal-02523885
Volume 77
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