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Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders

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  • Paolo Bevilacqua
  • Gianni Bosi
  • Magalì Zuanon

Abstract

We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter-Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal elements of preorders. The possibility of reformulating the multiobjective optimization problem for determining the weak Pareto optimal solutions by means of a scalarization procedure is finally characterized.

Suggested Citation

  • Paolo Bevilacqua & Gianni Bosi & Magalì Zuanon, 2018. "Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders," Abstract and Applied Analysis, Hindawi, vol. 2018, pages 1-6, January.
    • Handle: RePEc:hin:jnlaaa:3804742
    DOI: 10.1155/2018/3804742
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    Cited by:

    1. Pedro Hack & Daniel A. Braun & Sebastian Gottwald, 2022. "Representing preorders with injective monotones," Theory and Decision, Springer, vol. 93(4), pages 663-690, November.

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