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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Carlos Ignacio Hernández Castellanos & Oliver Schütze & Jian-Qiao Sun & Guillermo Morales-Luna & Sina Ober-Blöbaum, 2020. "Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1959-:d:440361
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    References listed on IDEAS

    as
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    3. P.J. Zufiria & T. Martínez-Marín, 2003. "Improved Optimal Control Methods Based Upon the Adjoining Cell Mapping Technique," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 657-680, September.
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