Rm-saea: Regularity model based surrogate-assisted evolutionary algorithms for expensive multi-objective optimization

Due to computationally and/or financially costly evaluation, tackling expensive multi-objective optimization problems is quite challenging for evolutionary algorithms. One popular approach to these problems is building cheap surrogate models to replace the expensive real function evaluations. To this end, various kinds of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed, building surrogate models which predict the fitness values, classifications, or relation of the candidate solutions. However, off-spring generation, despite its important role in evolutionary optimization, has not received enough attention in these SAEAs. In this paper, a regularity model based framework, namely RM-SAEA, is proposed for better offspring generation in expensive multi-objective optimization. To be specific, RM-SAEA is featured with a heterogeneous offspring generation module, which is composed of a regularity model and a general genetic operator. Moreover, in order to alleviate the data deficiency issue in the expensive optimization scenario, a data augmentation strategy is employed while training the regularity model. Finally, two representative SAEAs are embedded into RM-SAEA in order to instantiate the proposed framework. Experimental results on benchmark multi-objective problems with up to 10 objectives demonstrate that RM-SAEA achieves the best overall performance compared with 6 state-of-the-art algorithms.