A new reducing transformation for global optimization (with Alienor method)

Abstract

Purpose

To propose a new reducing transformation that allows the calculation of the absolute minimum of a function that depends on a large number of variables to be performed quickly.

Design/methodology/approach

The methodology depends on the building of α‐dense curve in a compact of Rⁿ that allows the approximate at any point of this compact with a desired precision. This approach allows global optimization problems that depend on a large number of variables, be tackled quickly and precisely.

Findings

It was found that this new method for densifying a space Rⁿ (compact) by means of simple parametric curve (a space filling curve) could be used to deal with global optimization problems of some several hundreds or thousands of variables in some seconds or minutes. The technique is being based on the cosine function.

Research limitations/implications

The results depend on the use of a computer system or “micro‐calculator”.

Practical implications

This is an “economic” method and the technique which uses the cosine function allows the reduction of the calculation time and avoids calculus errors. It has the practical advantages that coupled with a transformation eliminating local minima, it permits the solution of global optimization problems of more than 1,000 variables in less than 1 min.

Originality/value

The method is innovative and shown to be accurate and fast even with a function of a large number of variables.

Citation

Cherruault, Y. (2005), "A new reducing transformation for global optimization (with Alienor method)", Kybernetes, Vol. 34 No. 7/8, pp. 1084-1089. https://doi.org/10.1108/03684920510605894