A Hierarchical and Ensemble Surrogate-Assisted Evolutionary Algorithm With Model Reduction for Expensive Many-Objective Optimization

The Kriging model has been widely used in regression-based surrogate-assisted evolutionary algorithms (SAEAs) for expensive multiobjective optimization by using one model to approximate one objective, and the fusion of all the models forms the fitness surrogate. However, when tackling expensive many-objective optimization problems, too many models are required to construct such a fitness surrogate, which incurs cumulative prediction uncertainty and higher computational cost. Considering that the fitness surrogate works to predict different objective values to help select promising solutions with good convergence and diversity, this article proposes a novel model reduction idea to change the many-models-based fitness surrogate to a two-models-based indicator surrogate (TIS) that directly approximates convergence and diversity indicators. Based on TIS, a hierarchical and ensemble surrogate-assisted evolutionary algorithm (HES-EA) is proposed with three stages. Firstly, the HES-EA transforms the many objectives of the real-evaluated solutions into two indicators (i.e., the convergence and diversity indicators) and divides these solutions into different clusters. Secondly, a HES consisting of a cluster surrogate and different TISs is trained through these clustered solutions and their indicators. Thirdly, during the optimization process, the HES can predict the candidate solutions’ cluster information via the cluster surrogate and indicator information via the TISs. Promising solutions can thus be selected based on the predicted information via a clustering-based sequential selection strategy without real fitness evaluation consumption. Compared with state-of-the-art SAEAs on three widely used benchmark suites up to 184 instances and one real-world application, HES-EA shows its superiority in both optimization performance and computational cost.