Metamodel-based prediction of performance metrics for bilevel parameter tuning in MOEAs

We consider a bilevel parameter tuning problem where the goal is to maximize the performance of a given multi-objective evolutionary optimizer on a given problem. The search for optimal algorithmic parameters requires the assessment of several sets of parameters, through multiple optimization runs, in order to mitigate the effect of noise that is inherent to evolutionary algorithms. This task is computationally expensive and therefore, in this paper, we propose to use sampling and metamodeling to approximate the performance of the optimizer as a function of its parameters. While such an approach is not unheard of, the choice of the metamodel to be used still remains unclear. The aim of this paper is to empirically compare 11 different metamodeling techniques with respect to their accuracy and training times in predicting two popular multi-objective performance metrics, namely, the hypervolume and the inverted generational distance. For the experiments in this pilot study, NSGA-II is used as the multi-objective optimizer for solving ZDT problems, 1 through 4.