Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping

Carlos Ignacio Hernández Castellanos, Oliver Schütze, Jian-Qiao Sun, Guillermo Morales-Luna and Sina Ober-Blöbaum
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Carlos Ignacio Hernández Castellanos: Department of Computer Science, CINVESTAV-IPN, Av. IPN 2508, Gustavo A. Madero, San Pedro Zacatenco, Mexico City 07360, Mexico
Oliver Schütze: Department of Computer Science, CINVESTAV-IPN, Av. IPN 2508, Gustavo A. Madero, San Pedro Zacatenco, Mexico City 07360, Mexico
Jian-Qiao Sun: School of Engineering, University of California Merced, Merced, CA 95343, USA
Guillermo Morales-Luna: Department of Computer Science, CINVESTAV-IPN, Av. IPN 2508, Gustavo A. Madero, San Pedro Zacatenco, Mexico City 07360, Mexico
Sina Ober-Blöbaum: Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, 33098 Paderborn, Germany

Mathematics, 2020, vol. 8, issue 11, 1-18

Abstract: In this paper, we present a novel algorithm for the computation of lightly robust optimal solutions for multi-objective optimization problems. To this end, we adapt the generalized cell mapping, originally designed for the global analysis of dynamical systems, to the current context. This is the first time that a set-based method is developed for such kinds of problems. We demonstrate the strength of the novel algorithms on several benchmark problems as well as on one feed-back control design problem where the objectives are given by the peak time, the overshoot, and the absolute tracking error for the linear control system, which has a control time delay. The numerical results indicate that the new algorithm is well-suited for the reliable treatment of low dimensional problems.

Keywords: cell mapping techniques; multi-objective optimization; robustness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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