Evolutionary optimization of expensive multiobjective problems with co-sub-Pareto front Gaussian process surrogates

Abstract

This paper proposes a Gaussian process (GP) based co-sub-Pareto front surrogate augmentation strategy for evolutionary optimization of computationally expensive multiobjective problems. In the proposed algorithm, a multiobjective problem is decomposed into a number of subproblems, the solution of each of which is used to approximate a portion or sector of the Pareto front (i.e., a subPF). Thereafter, a multitask GP model is incorporated to exploit the correlations across the subproblems via joint surrogate model learning. A novel criterion for the utility function is defined on the surrogate landscape to determine the next candidate solution for evaluation using the actual expensive objectives. In addition, a new management strategy for the evaluated solutions is presented for model building. The novel feature of our approach is that it infers multiple subproblems jointly by exploiting the possible dependencies between them, such that knowledge can be transferred across subPFs approximated by the subproblems. Experimental studies under several scenarios indicate that the proposed algorithm outperforms state-of-the-art multiobjective evolutionary algorithms for expensive problems. The parameter sensitivity and effectiveness of the proposed algorithm are analyzed in detail.