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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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    1. Nguyen, Cuong M. & Pathirana, Pubudu N. & Trinh, Hieu, 2019. "Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 42-53.
    2. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
    3. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    4. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    5. Soltani, Roya & Safari, Jalal & Sadjadi, Seyed Jafar, 2015. "Robust counterpart optimization for the redundancy allocation problem in series-parallel systems with component mixing under uncertainty," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 80-88.
    6. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    7. Johannes Jahn & Truong Xuan Duc Ha, 2011. "New Order Relations in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 209-236, February.
    8. Zhou, Weijun & Wang, Fei, 2015. "A PRP-based residual method for large-scale monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 1-7.
    9. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
    10. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "A Unified Characterization of Multiobjective Robustness via Separation," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 86-102, October.
    11. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    12. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    13. Li, Ruoxia & Gao, Xingbao & Cao, Jinde, 2019. "Non-fragile state estimation for delayed fractional-order memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 221-233.
    14. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    15. Jonas Ide & Elisabeth Köbis, 2014. "Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 99-127, August.
    16. H. Yu & H. M. Liu, 2013. "Robust Multiple Objective Game Theory," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 272-280, October.
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    2. 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).
    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.

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