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Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problems

Author

Listed:
  • Stephan Helfrich

    (RPTU Kaiserslautern-Landau)

  • Tyler Perini

    (RICE University)

  • Pascal Halffmann

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Natashia Boland

    (H. Milton Stewart School of Industrial and Systems Engineering)

  • Stefan Ruzika

    (RPTU Kaiserslautern-Landau)

Abstract

Scalarization is a common technique to transform a multiobjective optimization problem into a scalar-valued optimization problem. This article deals with the weighted Tchebycheff scalarization applied to multiobjective discrete optimization problems. This scalarization consists of minimizing the weighted maximum distance of the image of a feasible solution to some desirable reference point. By choosing a suitable weight, any Pareto optimal image can be obtained. In this article, we provide a comprehensive theory of this set of eligible weights. In particular, we analyze the polyhedral and combinatorial structure of the set of all weights yielding the same Pareto optimal solution as well as the decomposition of the weight set as a whole. The structural insights are linked to properties of the set of Pareto optimal solutions, thus providing a profound understanding of the weighted Tchebycheff scalarization method and, as a consequence, also of all methods for multiobjective optimization problems using this scalarization as a building block.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:2:d:10.1007_s10898-023-01284-x
    DOI: 10.1007/s10898-023-01284-x
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    References listed on IDEAS

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