Multigranularity Surrogate Modeling for Evolutionary Multiobjective Optimization With Expensive Constraints.

Multiobjective optimization problems (MOPs) with expensive constraints pose stiff challenges to existing surrogate-assisted evolutionary algorithms (SAEAs) in a very limited computational cost, due to the fact that the number of expensive constraints for an MOP is often large. For existing SAEAs, they always approximate constraint functions in a single granularity, namely, approximating the constraint violation (CV, coarse-grained) or each constraint (fine-grained). However, the landscape of CV is often too complex to be accurately approximated by a surrogate model. Although the modeling of each constraint function may be simpler than that of CV, approximating all the constraint functions independently may result in tremendous cumulative errors and high computational costs. To address this issue, in this article, we develop a multigranularity surrogate modeling framework for evolutionary algorithms (EAs), where the approximation granularity of constraint surrogates is adaptively determined by the position of the population in the fitness landscape. Moreover, a dedicated model management strategy is also developed to reduce the impact resulting from the errors introduced by constraint surrogates and prevent the population from trapping into local optima. To evaluate the performance of the proposed framework, an implementation called K-MGSAEA is proposed, and the experimental results on a large number of test problems show that the proposed framework is superior to seven state-of-the-art competitors.