A multi-strategy optimizer for arbitrary generic functions in multidimensional space

Abstract

An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior, irregular and noisy, with steep variations and exhibiting a lot of local sub-optimal points. The complications of having to deal with a finite domain, as this is usually the case, are taken into account. The method is composed of a number of cascaded stages, each employing a different strategy to improve over the results of the previous stage. Many ideas and concepts employed in known methods are re-elaborated in a coherent scheme, plus several new ideas are introduced. Line minimization plays an important role in most stages, for this purpose a new and powerful algorithm for line minimization is used as well.