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This work was supported in part by the grant PID2021-124908NB-I00 founded by MCIN/AEI/10.13039/501100011033/and by "ERDF A way of making Europe"; by grant PRE2019-087579 funded by MCIN/AEI/10.13039/501100011033 and by "ESF Investing in your future"; and by the Generalitat Valenciana regional government through project CIAICO/2021/064. Funding for open access charge: CRUE-Universitat Politecnica de Valencia.

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Strategy for obtaining robust solutions in multi-objective design with uncertainties

Publicado en:Applied Mathematical Modelling. 138 115767- - 2025-02-01 138(), DOI: 10.1016/j.apm.2024.115767

Autores: Veyna, U; Blasco, X; Herrero, J M; Pajares, A

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Resumen

This paper proposes a novel definition of robustness for multi-objective optimization problems. This definition underpins an innovative strategy for obtaining robust solutions in the presence of uncertainty; it involves formulating the cost function under uncertainties as conflicting objectives during optimization. This approach aims to define the decision vectors that are not dominated in all scenarios simultaneously by any other. These solutions exhibit both optimality and robustness properties, aligning with conventional and unconventional multi-objective methods. This approach enables the implicit definition of the Pareto-optimal solutions for each scenario and robust solutions that optimize performance in worst-case scenarios. Additionally, the set of robust solutions that optimize the global performance concerning the utopian points of all uncertainty scenarios is also defined. To demonstrate the effectiveness of this method, this paper addresses two control design problems. The first example, a first-order process, illustrates the advantages and aspects of the optimization strategy. The second problem, multi-loop temperature control design of a proton exchange membrane fuel cell stack, is a more complex engineering problem involving results from previous research.

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