A novel global optimization algorithm based on the smoothing function

Abstract

In this paper, a new global optimization algorithm based on the smoothing function is suggested. Firstly, one of the minimizer x*1 of the smooth function F is found by employing any local minimizer finder, then the function m(x, x*1) := min{F(x); F(x*1)} is considered instead of the objective function F and the minimizer x*2 of the function m is searched. Because of the non-smooth of the function m, the smoothing function for m is used in order to make the local minimizer finding algorithms for smooth optimization available. Finally, a global optimization algorithm based on the smoothing function is presented. The implementation of the algorithm on several test problems is reported with numerical results.