SGOP: Surrogate-assisted global optimization using a Pareto-based sampling strategy

In this paper, we present a new global optimization algorithm SGOP for computationally intensive black-box problems. Considering that multiple surrogates concurrently used in an optimization process can have more robust performance in most cases, a Pareto-based multi-point sampling strategy is presented to improve iterative efficiency. Ideally, a group of samples having best predictive values on all the surrogates and meanwhile keeping better space-filling feature are most appropriate to be selected in each cycle. Therefore, a four-objective optimization formula is presented, where Kriging, radial basis function, quadratic response surface and a sampling density function are defined as objective functions, respectively. The non-dominated sorting strategy is used to capture the Pareto solutions of the multi-objective problem and the new promising samples are adaptively chosen from their Pareto solutions set to drive the optimization cycle. Moreover, a dynamic monitor is presented to check the premature convergence. Once the trigger is activated, the search will focus on unexplored area. SGOP can not only build a reasonable balance between global exploration and local exploitation, but also has remarkable advantages in sampling efficiency. Finally, the new algorithm is tested on 17 benchmark cases and compared with several existing algorithms. The results show SGOP's superior performance and strong robustness. Besides, SGOP is used for the shape optimization of a blended-wing-body underwater glider (BWBUG), and the lift–drag-ratio gets remarkable improvement.