On multi-objective efficient global optimization via universal Kriging surrogate model

This paper investigates the capability of universal Kriging (UK), or Kriging with a trend, approximator enhanced with the efficient global optimization (EGO) method to solve expensive multi-objective design optimization problem. Engineering optimization problems typically can be well described with smooth and polynomial-like behavior, which is the main rationale to apply UK over the ordinary Kriging (OK) as the approximator. The UK with orthogonal polynomials and basis selection based on least-angle-regression is utilized for this purpose. Results and demonstration on three synthetic functions using expected hypervolume improvement (EHVI) and Euclidean-based expected improvement (EEI) criterions show the increased quality of the optimized non-dominated solutions when UK is coupled with EHVI criterion. On the other hand, the coupling of UK with EEI does not lead to any improvement and might produce an adverse effect. We also observed that the use of UK mainly improves the proximity to the true Pareto front, with smaller but notable effect on the diversity of the solutions when EHVI is applied as the criterion. As expected, optimization using the UK shows the greatest improvement if all objective functions can be sufficiently approximated by the UK. Based on the results, we suggest that coupling of UK and EHVI criterion is a potential approach to solve the expensive real-world multi-objective optimization problem.