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Multiextremal Optimization in Feasible Regions with Computable Boundaries on the Base of the Adaptive Nested Scheme

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Numerical Computations: Theory and Algorithms (NUMTA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

Abstract

The paper is devoted to consideration of multidimensional optimization problems with multiextremal objective functions over search domains determined by constraints, which form a special type of domain boundaries called computable ones, which, in general case, are non-linear and multiextremal. The regions of this class can be very complicated, in particular, non-convex, non-simply connected, and even disconnected. For solving such problems, a new global optimization technique based on the adaptive nested scheme developed recently for unconstrained optimization is proposed. The novelty consists in combination of the adaptive scheme with a technique for reducing the constraints to an explicit form of feasible subregions in internal subproblems of the nested scheme that allows one to evaluate the objective function at the feasible points only. For efficiency estimation of the proposed adaptive nested algorithm in comparison with the classical nested optimization and the penalty function method, a representative numerical experiment on the test classes of multidimensional multiextremal functions has been carried out. The results of the experiment demonstrate a significant advantage of the adaptive scheme over its competitors.

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Acknowledgements

The research of the first author has been supported by the Russian Science Foundation, project No 16-11-10150 “Novel efficient methods and software tools for timeconsuming decision make problems using superior-performance supercomputers.”

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Authors and Affiliations

  1. Lobachevsky State University, Gagarin Avenue 23, 603950, Nizhni Novgorod, Russia

    Victor Gergel, Vladimir Grishagin & Ruslan Israfilov

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  1. Victor Gergel
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  2. Vladimir Grishagin
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  3. Ruslan Israfilov
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Correspondence to Vladimir Grishagin .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Gergel, V., Grishagin, V., Israfilov, R. (2020). Multiextremal Optimization in Feasible Regions with Computable Boundaries on the Base of the Adaptive Nested Scheme. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_9

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  • DOI: https://doi.org/10.1007/978-3-030-40616-5_9

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