Abstract
Surrogate-assisted evolutionary algorithms are one effective approach to handling expensive problems and have attracted increasing attention over the past decades. However, existing surrogate-assisted evolutionary algorithms pay little attention to expensive many-objective problems with irregular Pareto fronts, also called irregular problems. In this study, we propose a surrogate-assisted evolutionary algorithm for dealing with expensive irregular problems, where only a small number of expensive fitness evaluations is allowed. In the proposed algorithm, the reference vectors are adapted based on both the individuals in the current population and the non-dominated solutions that have been evaluated using the real objective functions. A surrogate management strategy is then designed to balance convergence and diversity according to the adaptive reference vectors as well as the non-dominated solutions that have been evaluated using the expensive objective functions so that the irregularity of the Pareto front can be taken into account. To reduce the computational cost for updating the Gaussian process based surrogates, a subset of training data near the adaptive reference vectors are prioritized. Experimental results on the DTLZ, WFG, DPF and MaF test suites demonstrate that the proposed algorithm is able to solve expensive many-objective optimization problems with both irregular and regular Pareto fronts. The proposed algorithm is also tested on a real-world application example to further confirm its effectiveness and competitiveness.