A Kriging-assisted evolutionary algorithm with multiple infill sampling for expensive many-objective optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have been extensively used to solve computationally expensive multi-objective optimization problems (MOPs) as they can obtain a set of satisfyingly optimal solutions while remaining within a limited computational budget. Nevertheless, the expensive MOPs with more than three objectives have received little attention, and most existing SAEAs fail to achieve satisfactory results when solving them. Therefore, to fill this research gap, a Kriging-assisted evolutionary algorithm with multiple infill sampling for solving expensive many-objective optimization problems is proposed. In this paper, to balance exploration and exploitation, a new environmental selection operator is proposed, which is composed of three procedures conducted consecutively. In addition, a new multiple infill sampling strategy is proposed to select the most representative solutions for real function evaluations and model updates. Furthermore, to limit the computational costs of constructing/updating the surrogate model, a new archive update strategy is proposed to maneuver the training data set. In experiments, our method is verified on some benchmark problems. The experimental results demonstrate that the proposed algorithm shows promising performance when compared with four state-of-the-art SAEAs for solving expensive many-objective optimization problems.