Multi-Objective Bayesian Optimisation Using an Exploitative Attainment Front Acquisition Function

Abstract

Efficient methods for optimising expensive black-box problems with multiple objectives can often themselves become prohibitively expensive as the number of objectives is increased. We propose an infill criterion based on the distance to the summary attainment front which does not rely on the expensive hypervolume or expected improvement computations, which are the principal causes of poor dimensional scaling in current stateof-the-art approaches. By evaluating performance on the wellknown Walking Fish Group problem set, we show that our method delivers similar performance to the current state-of-theart. We further show that methods based on surrogate mean predictions are more often than not superior to the widely used expected improvement, suggesting that the additional exploration produced by accounting for the uncertainty in the surrogate's prediction of the optimisation landscape is often unnecessary and does not aid convergence towards the Pareto front.