The Alienor method coupled to the Brent algorithm

Abstract

Purpose

Classical multidimensional global optimization methods are difficult to implement in high dimensions. To show that the Alienor method coupled with the Brent algorithm can avoid this difficulty.

Design/methodology/approach

Use is made of the Alienor method and the Brent algorithm to obtain algorithms that were applied to test functions having several local minima.

Findings

Interesting results concerning the number of evaluation points were obtained. It was shown that this coupling can be improved if α‐dense curves of minimal length were used.

Research limitations/implications

Multidimensional global optimization problems have proven to be difficult to implement in high dimensions. This research continues the search for improved methods by coupling existing established methods such as Alienor with others such as the Brent algorithm.

Originality/value

A new coupled method has been developed and algorithms obtained to tackle such global optimization problems. The coupling is unique and the algorithms are tested numerically on selected functions.

Citation

Ziadi, A., Khelladi, S. and Cherruault, Y. (2005), "The Alienor method coupled to the Brent algorithm", Kybernetes, Vol. 34 No. 7/8, pp. 1059-1069. https://doi.org/10.1108/03684920510605876