A two-stage surrogate-assisted meta-heuristic algorithm for high-dimensional expensive problems

This study proposes a two-stage surrogate-assisted meta-heuristic algorithm named SDAMA-SPS to solve computationally expensive problems with high dimensions. In this algorithm, a surrogate-assisted monkey algorithm with dynamic adaptation (SDAMA) is presented to globally search for the best solution of the first stage, and a surrogate-based perturbation search (SPS) is designed to perform a more intensive local search for the final optimal solution. In the first stage, a global radial basis function (RBF) surrogate model is constructed with all historical solutions and is used to evaluate the positions of monkeys in the climb process and watch-jump process. Such global RBF model is updated with the positions of monkeys and their real objective function values after the second round of the climb process for each iteration. In the second stage, a local RBF surrogate model is built with a set of current best solutions, which can help to select the most promising sample so as to further locally improve the solution searched in the first stage. Experimental studies are conducted on eight benchmark optimization problems with the number of dimensions varying from 30 to 100, and numerical results show that the proposed algorithm achieves better performance than five other state-of-the-art surrogate-assisted algorithms with a limited budget of function evaluations.