Additive chaotic forcing scheme for determination of the global minimum of functions

Abstract

The problem of determination of the global minimum of a continuous unconstrained or bound-constrained cost function is studied in a discrete dynamical systems framework. An additive chaotic forcing scheme is developed and shown to be able to locate the global minimum of difficult unconstrained optimization test functions. The key role of crisis-like bifurcations, which are essential to (i) enable regular jumps across different minima, and (ii) permit access into the vicinity of the global minimum, is highlighted.