An Extension of DIRECT Algorithm Using Kriging Metamodel for Global Optimization

As a very well-known non-gradient global optimization method, DIviding RECTangles (DIRECT) algorithm has been proven to be an effective and efficient search method for many global optimization problems. However, computation of the algorithm could be costly and slow in solving problems involving computation intensive, Expensive Black Box (EBB) function due to the high number of objective function evolution required. This work proposes a new strategy which integrates meta-modeling techniques with DIRECT for solving EBB problems. The principal idea of the new approach is to use meta-modeling techniques, such as Kriging, to assist DIRECT to identify the optimum with less number of function evolutions. Specifically, the new approach starts with DIRECT search with a number of iterations and then uses the resulting points in Kriging to construct the meta-model. The best point predicted by Kriging search will then be used by DIRECT as new initial point. As a result, the entire search domain will gradually shrink to the region enclosing the possible optimum. Several runs are carried out to avoid high number of function evaluations to obtain the approximation solution at each stage. The newly proposed method has been tested using ten commonly used benchmark functions. All these tests showed significant improvements over the original DIRECT for EBB design problems.