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Generalized multiobjective robustness and relations to set-valued optimization

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  • Jiang, Ling
  • Cao, Jinde
  • Xiong, Lianglin

Abstract

In this paper, we provide the augmented weighted Tschebyscheff scalarization to computing robust efficient solutions for uncertain multiobjective optimization problems (UMOPs). Furthermore, we propose two generalized robustness concepts called the minmax certainly nondominated ordered robustness and the certainly less ordered robustness to general spaces and cones in the context of set orderings. Some explanations for both concepts are given, as well as the relations between them and several existing robustness are clearly described. Finally, the corresponding relationships to set-valued optimization are well revealed.

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  • Jiang, Ling & Cao, Jinde & Xiong, Lianglin, 2019. "Generalized multiobjective robustness and relations to set-valued optimization," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 599-608.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:599-608
    DOI: 10.1016/j.amc.2019.06.006
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    2. Eichfelder, Gabriele & Quintana, Ernest, 2024. "Set-based robust optimization of uncertain multiobjective problems via epigraphical reformulations," European Journal of Operational Research, Elsevier, vol. 313(3), pages 871-882.
    3. Miaadi, Foued & Li, Xiaodi, 2021. "Impulse-dependent settling-time for finite time stabilization of uncertain impulsive static neural networks with leakage delay and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 259-276.
    4. Shi, Zhicheng & Yang, Yongqing & Chang, Qi & Xu, Xianyun, 2020. "The optimal state estimation for competitive neural network with time-varying delay using Local Search Algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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