A deterministic method for continuous global optimization using a dense curve

Raouf Ziadi, Abdelatif Bencherif-Madani and Rachid Ellaia

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 178, issue C, 62-91

Abstract: In this paper, we develop a new approach for solving a large class of global optimization problems for objective functions which are only continuous on a rectangle of Rn. This method is based on the reducing transformation technique by running in the feasible domain a single parametrized Lissajous curve, which becomes increasingly denser and progressively fills the feasible domain. By means of the one-dimensional Evtushenko algorithm, we realize a mixed method which explores the feasible domain. To speed up the mixed exploration algorithm, we have incorporated a DIRECT local search type algorithm to explore promising regions. This method converges in a finite number of iterations to the global minimum within a prescribed accuracy ε>0. Simulations on some typical test problems with diverse properties and different dimensions indicate that the algorithm is promising and competitive.

Keywords: Global optimization; Reducing transformation method; Evtushenko’s algorithm; Generalized pattern search algorithm; Lissajous parametrized curve (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:178:y:2020:i:c:p:62-91

DOI: 10.1016/j.matcom.2020.05.029

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