A kind of balance between exploitation and exploration on kriging for global optimization of expensive functions

In this paper, a novel kriging-based algorithm for global optimization of computationally expensive black-box functions is presented. This algorithm utilizes a multi-start approach to find all of the local optimal values of the surrogate model and performs searches within the neighboring area around these local optimal positions. Compared with traditional surrogate-based global optimization method, this algorithm provides another kind of balance between exploitation and exploration on kriging-based model. In addition, a new search strategy is proposed and coupled into this optimization process. The local search strategy employs a kind of improved “Minimizing the predictor” method, which dynamically adjusts search direction and radius until finds the optimal value. Furthermore, the global search strategy utilizes the advantage of kriging-based model in predicting unexplored regions to guarantee the reliability of the algorithm. Finally, experiments on 13 test functions with six algorithms are set up and the results show that the proposed algorithm is very promising.