Multiple Surrogate-Assisted Many-Objective Optimization for Computationally Expensive Engineering Design

Abstract

Engineering design often involves problems with multiple conflicting performance criteria, commonly referred to as multi-objective optimization problems (MOP). MOPs are known to be particularly challenging if the number of objectives is more than three. This has motivated recent attempts to solve MOPs with more than three objectives, which are now more specifically referred to as “many-objective” optimization problems (MaOPs). Evolutionary algorithms (EAs) used to solve such problems require numerous design evaluations prior to convergence. This is not practical for engineering applications involving computationally expensive evaluations such as computational fluid dynamics and finite element analysis. While the use of surrogates has been commonly studied for single-objective optimization, there is scarce literature on its use for MOPs/MaOPs. This paper attempts to bridge this research gap by introducing a surrogate-assisted optimization algorithm for solving MOP/MaOP within a limited computing budget. The algorithm relies on principles of decomposition and adaptation of reference vectors for effective search. The flexibility of function representation is offered through the use of multiple types of surrogate models. Furthermore, to efficiently deal with constrained MaOPs, marginally infeasible solutions are promoted during initial phases of the search. The performance of the proposed algorithm is benchmarked with the state-of-the-art approaches using a range of problems with up to ten objective problems. Thereafter, a case study involving vehicle design is presented to demonstrate the utility of the approach.