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International Conference on Network Analysis

NET 2016: Models, Algorithms, and Technologies for Network Analysis pp 27–45Cite as

Efficient Methods of Multicriterial Optimization Based on the Intensive Use of Search Information

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 197))

Abstract

In this paper, an efficient approach for solving complex multicriterial optimization problems is proposed. For the problems being solved, the optimality criteria may be multiextremal ones, and calculating the criteria values may require a large amount of computations. The proposed approach is based on reducing multicriterial problems to nonlinear programming problems via the minimax convolution of the partial criteria, reducing dimensionality by using Peano evolvents, and applying efficient information-statistical global optimization methods. The new contribution is that all the search information obtained in the course of optimization is used to find each current Pareto-optimal solution. The results of the computational experiments show that the proposed approach essentially reduces the computational costs of solving multicriterial optimization problems (by tens and hundreds of times).

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Notes

  1. 1.

    More precisely, the minimization of \(F(\lambda ,y)\) can lead to obtaining weakly efficient solutions (the set of weakly efficient solutions includes the Pareto domain). The situation can be corrected by adding an additional correcting element into (4)—see, for example, [21].

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Acknowledgements

This work has been supported by Russian Science Foundation, project No 16-11-10150 “Novel efficient methods and software tools for time-consuming decision making problems using supercomputers of superior performance.”

Author information

Authors and Affiliations

  1. Nizhni Novgorod State University, 23, Gagarin av., Nizhny Novgorod, Russia

    Victor Gergel & Evgeny Kozinov

Authors
  1. Victor Gergel
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  2. Evgeny Kozinov
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Corresponding author

Correspondence to Victor Gergel .

Editor information

Editors and Affiliations

  1. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A. Kalyagin

  2. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Alexey I. Nikolaev

  3. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  4. Department of Industrial Engineering, University of Pittsburgh , Pittsburgh, Pennsylvania, USA

    Oleg A. Prokopyev

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Gergel, V., Kozinov, E. (2017). Efficient Methods of Multicriterial Optimization Based on the Intensive Use of Search Information. In: Kalyagin, V., Nikolaev, A., Pardalos, P., Prokopyev, O. (eds) Models, Algorithms, and Technologies for Network Analysis. NET 2016. Springer Proceedings in Mathematics & Statistics, vol 197. Springer, Cham. https://doi.org/10.1007/978-3-319-56829-4_3

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