Hybrid metamodel-based design space management method for expensive problems

Metamodel-based global optimization methods have been extensively studied for their great potential in solving expensive problems. In this work, a design space management strategy is proposed to improve the accuracy and efficiency of metamodel-based optimization methods. In this strategy, the whole design space is divided into two parts: the important region constructed using several expensive points and the other region. Combined with a previously developed hybrid metamodel strategy, a hybrid metamodel-based design space management method (HMDSM) is developed. In this method, three representative metamodels are used simultaneously in the search of the global optimum in both the important region and the other region. In the search process, the important region is iteratively reduced and the global optimum is soon captured. Tests using a series of benchmark mathematical functions and a practical expensive problem demonstrate the excellent performance of the proposed method.