Multiobjective Optimization on a Limited Budget of Evaluations Using Model-Assisted -Metric Selection

Real-world optimization problems often require the consideration of multiple contradicting objectives. These multiobjective problems are even more challenging when facing a limited budget of evaluations due to expensive experiments or simulations. In these cases, a specific class of multiobjective optimization algorithms (MOOA) has to be applied. This paper provides a review of contemporary multiobjective approaches based on the singleobjective meta-model-assisted 'Efficient Global Optimization' (EGO) procedure and describes their main concepts. Additionally, a new EGO-based MOOA is introduced, which utilizes the $\mathcal{S}$-metric or hypervolume contribution to decide which solution is evaluated next. A benchmark on recently proposed test functions is performed allowing a budget of 130 evaluations. The results point out that the maximization of the hypervolume contribution within a real multiobjective optimization is superior to straightforward adaptations of EGO making our new approach capable of approximating the Pareto front of common problems within the allowed budget of evaluations.