Multi-surrogate-assisted stochastic fractal search algorithm for high-dimensional expensive problems *

Surrogate models have been radically used in metaheuristic algorithms owing to their capacity in solving computationally expensive problems. However, despite the promising performance of surrogate-assisted metaheuristic algorithms in coping with low-dimensional problems, they failed to tackle high-dimensional problems efficiently. Thus, a multi-surrogate-assisted stochastic fractal search algorithm (MSASFS) is proposed in this paper. Several improvements are integrated into the algorithm design: (1) By combining the original coordinate system with the eigencoordinate system, an improved surrogate-assisted differential evolution (SDE) updating mechanism is proposed to ameliorate the generalization ability of the algorithm and extend the scope of exploration. (2) A new expected improvement (EI) pre-screening strategy based on the Gaussian process (GP) model is employed to select promising candidate solutions. (3) Two different surrogate models are applied to enhance the robustness of the proposed algorithm. The effectiveness of MSASFS is further demonstrated by numerical experiments on some widely used benchmark problems with dimensions ranging from 30 to 200 and parameter estimation problem of fractional-order chaotic systems. The results reveal that, compared with state-of-the-art surrogate-assisted evolutionary algorithms (SAEAs), the proposed algorithm can effectively solve high-dimensional expensive problems. Furthermore, MSASFS shows a more significant efficiency when the dimension of problems becomes higher.