Hybrid Coupled Local Minimizers

This paper proposes an improved global optimization technique, named Hybrid Coupled Local Minimizers (HCLM), which is inspired on the method of coupled local minimizers (CLM). The HCLM method uses a set of search points, called “particles”, initially spread over the search space, that are occasionally impulsively coupled, instead of permanently coupled. This approach leads to a much better optimization efficiency, because it combines the fast convergence (due to a Newton-based method that is used for each particle) with the capability of global optimization (resulting from the hybrid interaction which enables a parallel strategy). Such parallel and distributed computing process embedded with a trust region strategy relies on the hybrid interconnections of particles rather than individual particles, which is able to fully exploit the parallel nature of the computation and produce results which are more globally optimal. It is worth mentioning that the stability of each particle and the synchronization of all particles are also derived and proved by means of the contraction theory. The HCLM method is illustrated on several test functions with many local minima and applied to a problem of static nonlinear regression with multilayer perceptrons (MLPs) from given noisy measurement data.