Globally-biased Disimpl algorithm for expensive global optimization


Direct-type global optimization algorithms often spend an excessive number of function evaluations on problems with many local optima exploring suboptimal local minima, thereby delaying discovery of the global minimum. In this paper, a globally-biased simplicial partition Disimpl algorithm for global optimization of expensive Lipschitz continuous functions with an unknown Lipschitz constant is proposed. A scheme for an adaptive balancing of local and global information during the search is introduced, implemented, experimentally investigated, and compared with the well-known Direct and Direct l methods. Extensive numerical experiments executed on 800 multidimensional multiextremal test functions show a promising performance of the new acceleration technique with respect to competitors.

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The authors would like to thank anonymous referees for their careful reading of the paper and insightful comments that helped us to improve the paper. Postdoctoral fellowship of R. Paulavičius is being funded by European Union Structural Funds project “Postdoctoral Fellowship Implementation in Lithuania” within the framework of the Measure for Enhancing Mobility of Scholars and Other Researchers and the Promotion of Student Research (VP1-3.1-ŠMM-01) of the Program of Human Resources Development Action Plan. The research work of Ya. D. Sergeyev and D. E. Kvasov was partially supported by the INdAM–GNCS 2014 Research Project of the Italian National Group for Scientific Computation of the National Institute for Advanced Mathematics “F. Severi”. The closing part of this research has been done in the framework of the project “Multiextremal optimization: Efficient global search algorithms and supercomputing” submitted to the Russian Scientific Fund.

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Correspondence to Yaroslav D. Sergeyev.

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Dedicated to Panos M. Pardalos on the occasion of his 60th birthday.

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Paulavičius, R., Sergeyev, Y.D., Kvasov, D.E. et al. Globally-biased Disimpl algorithm for expensive global optimization. J Glob Optim 59, 545–567 (2014).

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  • Global optimization
  • Lipschitz condition
  • Direct algorithm
  • Two-phase approach
  • Globally-biased Disimpl algorithm