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simplicial Lipschitz optimization without the Lipschitz constant

JOURNAL OF GLOBAL OPTIMIZATION 2014年第1期59卷 23-40页

作者： Paulavicius, Remigijus Zilinskas, Julius Vilnius State Univ Inst Math & Informat LT-08663 Vilnius Lithuania

In this paper we propose a new simplicial partition-based deterministic algorithm for global optimization of Lipschitz-continuous functions without requiring any knowledge of the Lipschitz constant. Our algorithm is motivated by the well-known direct algorithm which evaluates the objective function on a set of points that tries to cover the most promising subregions of the feasible region. Almost all previous modifications of direct algorithm use hyper-rectangular partitions. However, other types of partitions may be more suitable for some optimization problems. simplicial partitions may be preferable when the initial feasible region is either already a simplex or may be covered by one or a manageable number of simplices. Therefore in this paper we propose and investigate simplicial versions of the partition-based algorithm. In the case of simplicial partitions, definition of potentially optimal subregion cannot be the same as in the rectangular version. In this paper we propose and investigate two definitions of potentially optimal simplices: one involves function values at the vertices of the simplex and another uses function value at the centroid of the simplex. We use experimental investigation to compare performance of the algorithms with different definitions of potentially optimal partitions. The experimental investigation shows, that proposed simplicial algorithm gives very competitive results to direct algorithm using standard test problems and performs particularly well when the search space and the numbers of local and global optimizers may be reduced by taking into account symmetries of the objective function.

关键词： Global optimization Lipschitz optimization simplicial direct-type algorithm Potentially optimal simplex

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A Parallel DISIMPL for Pile Placement Optimization in Grillage-type Foundations

A Parallel DISIMPL for Pile Placement Optimization in Grilla...

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8th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC)

作者： Paulavicius, Remigijus Zilinskas, Julius Herrera, Juan F. R. Casado, Leocadio G. Vilnius State Univ Inst Math & Informat Vilnius Lithuania

ISBN: (纸本)9780769550947

Recently it was shown, that proposed simplicial partition based DISIMPL algorithm gives very competitive results to well known direct algorithm for standard test functions and performs particularly well when the search space and the numbers of local and global optimizers may be reduced by avoiding symmetries. However, the simplicial partition has a cost (except for the case where the original feasible region is a simplex): in order to use simplicial partitions hyper-rectangular feasible region should be covered by simplices. After initial covering 2(n) objective function evaluations is performed for DISIMPL-V and n! for DISIMPL-C. This limits DISIMPL method to rather small dimensional problems. To increase the applicability of the DISIMPL algorithm to higher dimensional problems a parallel DISIMPL for multicore computers was created and investigated in this paper. The efficiency of the developed parallel algorithm is investigated solving up to 55 dimensional optimal design of grillage-type foundations "black-box" optimization problem.

关键词： Lipschitz optimization simplicial direct-type algorithm Parallel DISIMPL

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