Hybrid simulated annealing and direct search method for nonlinear unconstrained global optimization

Abstract

In this article we give a new approach of hybrid direct search methods with meta-heuristics of simulated annealing for finding a global minimum of a nonlinear function with continuous variables. First, we suggest a Simple Direct Search (SDS) method, which comes from some ideas of other well-known direct search methods. Since our goal is to find global minima and the SDS method is still a local search method, we hybridize it with the standard simulated annealing to design a new method, called Simplex Simulated Annealing (SSA) method, which is expected to have some ability to look for a global minimum. To obtain faster convergence, we first accelerate the cooling schedule in SSA, and in the final stage, we apply Kelley's modification of the Nelder-Mead method on the best solutions found by the accelerated SSA method to improve the final results. We refer to this last method as the Direct Search Simulated Annealing (DSSA) method. The performance of SSA and DSSA is reported through extensive numerical experiments on some well-known functions. Comparing their performance with that of other meta-heuristics shows that SSA and DSSA are promising in practice. Especially, DSSA is shown to be very efficient and robust.