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An inner approximation method to compute the weight set decomposition of a triobjective mixed-integer problem

Author

Listed:
  • Pascal Halffmann

    (Technische Universität Kaiserslautern)

  • Tobias Dietz

    (Technische Universität Kaiserslautern)

  • Anthony Przybylski

    (Université de Nantes)

  • Stefan Ruzika

    (Technische Universität Kaiserslautern)

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.

Suggested Citation

  • Pascal Halffmann & Tobias Dietz & Anthony Przybylski & Stefan Ruzika, 2020. "An inner approximation method to compute the weight set decomposition of a triobjective mixed-integer problem," Journal of Global Optimization, Springer, vol. 77(4), pages 715-742, August.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:4:d:10.1007_s10898-020-00898-9
    DOI: 10.1007/s10898-020-00898-9
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    References listed on IDEAS

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    Cited by:

    1. Stephan Helfrich & Kathrin Prinz & Stefan Ruzika, 2024. "The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1187-1216, September.
    2. Stephan Helfrich & Tyler Perini & Pascal Halffmann & Natashia Boland & Stefan Ruzika, 2023. "Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 86(2), pages 417-440, June.
    3. Fritz Bökler & Sophie N. Parragh & Markus Sinnl & Fabien Tricoire, 2024. "An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 263-290, August.

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