Multi-surrogate-based global optimization using a score-based infill criterion

Abstract

This paper presents a new global optimization algorithm named MGOSIC to solve unconstrained expensive black-box optimization problems. In MGOSIC, three surrogate models Kriging, Radial Basis Function (RBF), and Quadratic Response Surfaces (QRS) are dynamically constructed, respectively. Additionally, a multi-point infill criterion is proposed to obtain new points in each cycle, where a score-based strategy is presented to mark cheap points generated by Latin hypercube sampling. According to their predictive values from the three surrogate models, the promising cheap points are assigned with different scores. In order to obtain the samples with diversity, a Max-Min approach is proposed to select promising sample points from the cheap point sets with higher scores. Simultaneously, the best solutions predicted by Kriging, RBF, and QRS are also recorded as supplementary samples, respectively. Once MGOSIC gets stuck in a local valley, the estimated mean square error of Kriging will be maximized to explore the sparsely sampled regions. Moreover, the whole optimization algorithm is carried out alternately in the global space and a reduced space. In summary, MGOSIC not only brings a new idea for multi-point sampling, but also builds a reasonable balance between exploitation and exploration. Finally, 19 mathematical benchmark cases and an engineering application of hydrofoil optimization are used to test MGOSIC. Furthermore, seven existing global optimization algorithms are also tested as contrast. The final results show that MGOSIC has high efficiency, strong stability, and better multi-point sampling capability in dealing with expensive black-box optimization problems.