Title: A covering method for continuous global optimisation

Authors: Raouf Ziadi; Abdelatif Becherif-Madani

Addresses: Department of Mathematics, Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, 19000, Setif, Algeria ' Department of Mathematics, Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, 19000, Setif, Algeria

Abstract: In this paper, we improve the reducing transformation method for solving a large class of global optimisation problems. The reducing transformation method allows us to transform a multidimensional problem into a one-dimensional one of the same type, and then use the one-dimensional Evtushenko algorithm to obtain the global minimum. To accelerate the corresponding mixed algorithm (Reducing transformation-Evtushenko), we have incorporated the Hook-Jeeves algorithm to explore promising regions. Our approach is suitable for solving a large class of global optimisation problems on a rectangle of ℝⁿ where the objective function is only continuous. This method converges in a finite number of iterations to the global minimum within a prescribed accuracy δ > 0. Numerical experiments are achieved on some typical test problems and a comparison with well known methods is carried out to show the performance of our algorithm.

Keywords: global optimisation; covering algorithm; reducing transformation method; α-dense curves; Evtushenko's algorithm; Hooke-Jeeves algorithm.

DOI: 10.1504/IJCSM.2021.117599

International Journal of Computing Science and Mathematics, 2021 Vol.13 No.4, pp.369 - 390

Received: 25 Nov 2019
Accepted: 06 Jan 2020
Published online: 15 Sep 2021 *

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