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Efficient multicriterial optimization based on intensive reuse of search information

Author

Listed:
  • Victor Gergel

    (Lobachevsky State University of Nizhni Novgorod)

  • Evgeny Kozinov

    (Lobachevsky State University of Nizhni Novgorod)

Abstract

This paper proposes an efficient method for solving complex multicriterial optimization problems, for which the optimality criteria may be multiextremal and the calculations of the criteria values may be time-consuming. The approach involves reducing multicriterial problems to global optimization ones through minimax convolution of partial criteria, reducing dimensionality by using Peano curves and implementing efficient information-statistical methods for global optimization. To efficiently find the set of Pareto-optimal solutions, it is proposed to reuse all the search information obtained in the course of optimization. The results of computational experiments indicate that the proposed approach greatly reduces the computational complexity of solving multicriterial optimization problems.

Suggested Citation

  • Victor Gergel & Evgeny Kozinov, 2018. "Efficient multicriterial optimization based on intensive reuse of search information," Journal of Global Optimization, Springer, vol. 71(1), pages 73-90, May.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:1:d:10.1007_s10898-018-0624-3
    DOI: 10.1007/s10898-018-0624-3
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    References listed on IDEAS

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    1. Murat Köksalan & Jyrki Wallenius & Stanley Zionts, 2011. "Multiple Criteria Decision Making:From Early History to the 21st Century," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8042.
    2. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    3. Panos M. Pardalos & Antanas Žilinskas & Julius Žilinskas, 2017. "Non-Convex Multi-Objective Optimization," Springer Optimization and Its Applications, Springer, number 978-3-319-61007-8, June.
    4. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, June.
    5. Gabriele Eichfelder, 2009. "Scalarizations for adaptively solving multi-objective optimization problems," Computational Optimization and Applications, Springer, vol. 44(2), pages 249-273, November.
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    Cited by:

    1. Alberto Lovison & Kaisa Miettinen, 2021. "On the Extension of the DIRECT Algorithm to Multiple Objectives," Journal of Global Optimization, Springer, vol. 79(2), pages 387-412, February.
    2. Renato Leone & Yaroslav D. Sergeyev & Anatoly Zhigljavsky, 2018. "Guest editors’ preface to the special issue devoted to the 2nd International Conference “Numerical Computations: Theory and Algorithms”, June 19–25, 2016, Pizzo Calabro, Italy," Journal of Global Optimization, Springer, vol. 71(1), pages 1-4, May.
    3. Wenyu Wang & Taimoor Akhtar & Christine A. Shoemaker, 2022. "Integrating $$\varepsilon $$ ε -dominance and RBF surrogate optimization for solving computationally expensive many-objective optimization problems," Journal of Global Optimization, Springer, vol. 82(4), pages 965-992, April.

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