A Multiple Surrogate Assisted Decomposition-Based Evolutionary Algorithm for Expensive Multi/Many-Objective Optimization

Many-objective optimization problems (MaOPs) contain four or more conflicting objectives to be optimized. A number of efficient decomposition-based evolutionary algorithms have been developed in the recent years to solve them. However, computationally expensive MaOPs have been scarcely investigated. Typically, surrogate-assisted methods have been used in the literature to tackle computationally expensive problems, but such studies have largely focused on problems with 1-3 objectives. In this paper, we present an approach called hybrid surrogate-assisted many-objective evolutionary algorithm to solve computationally expensive MaOPs. The key features of the approach include: 1) the use of multiple surrogates to effectively approximate a wide range of objective functions; 2) use of two sets of reference vectors for improved performance on irregular Pareto fronts (PFs); 3) effective use of archive solutions during offspring generation; and 4) a local improvement scheme for generating high quality infill solutions. Furthermore, the approach includes constraint handling which is often overlooked in contemporary algorithms. The performance of the approach is benchmarked extensively on a set of unconstrained and constrained problems with regular and irregular PFs. A statistical comparison with the existing techniques highlights the efficacy and potential of the approach.