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

Abstract

PurposeTo 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/approachThe 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.FindingsIt 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/implicationsThe results depend on the use of a computer system or “micro‐calculator”.Practical implicationsThis 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/valueThe method is innovative and shown to be accurate and fast even with a function of a large number of variables.