Asynchronous parallel hybrid optimization combining DIRECT and GSS

In this paper we explore hybrid parallel global optimization using DIRECT and asynchronous generating set search (GSS). Both DIRECT and GSS are derivative-free and so require only objective function values; this makes these methods applicable to a wide variety of science and engineering problems. DIRECT is a global search method that strategically divides the search space into ever-smaller rectangles, sampling the objective function at the center point for each rectangle. GSS is a local search method that samples the objective function at trial points around the current best point, i.e., the point with the lowest function value. Latin hypercube sampling (LHS) can be used to seed GSS with a good starting point. Using a set of global optimization test problems, we compare the parallel performance of DIRECT and GSS with hybrids that combine the two methods. Our experiments suggest that the hybrid methods are much faster than DIRECT and scale better when more processors are added. This improvement in performance is achieved without any sacrifice in the quality of the solution — the hybrid methods find the global optimum whenever DIRECT does.