Surrogate-assisted operator-repeated evolutionary algorithm for computationally expensive multi-objective problems

Abstract

Surrogate-assisted strategies work differently in surrogate-assisted multi-objective evolutionary algorithms. How to select suitable surrogate-assisted strategies to balance global and local search and diversity of Pareto optimal solutions is usually difficult for efficient optimization of computationally expensive multi-objective problems, which only allow limited time costs in the optimization process. Therefore, to further improve the optimization efficiency for expensive multi-objective problems, a surrogate-assisted operator-repeated multi-objective evolutionary algorithm is proposed by reasonably integrating several surrogate-assisted strategies in this study. Specifically, the proposed algorithm is based on a operator-repeated offspring creation strategy, which can produce many diverse candidate offspring individuals and thus make the proposed algorithm search globally and efficiently. In addition, a novel infill criterion termed as reference-vector-guided surrogate-assisted penalty-based boundary intersection is proposed and combined with a common Kriging-based expected improvement matrix infill criterion for complementary prescreening over the candidate offspring individuals. These two infill criteria can make a good balance between global search and diversity of Pareto optimal solutions. In addition, to fasten convergence speed, an improved surrogate-based multi-objective local search method with minimum distance-angle sampling is also proposed and embedded in the proposed algorithm. Several benchmark problems with dimensions varying from 8 to 50 and a practical two-objective airfoil design optimization problem with 14 design variables are tested to validate efficiency of the proposed algorithm. The experimental results demonstrate that the proposed algorithm significantly outperforms some state-of-the-art surrogate-assisted multi-objective optimization algorithms on most of problems.