Surrogate strategies for scalarisation-based multi-objective Bayesian optimizers

Scalarisation-based approaches to multi-objective Bayesian optimization, such as the seminal ParEGO algorithm, may be either single-surrogate or multi-surrogate. In the former case, a single surrogate model is built of the scalarised function; in the latter case, separate surrogates are built for each objective function. A recent study argued that the multi-surrogate approach should be preferred and presented empirical findings supportive of this case. However, these findings were based on an outdated approach to benchmarking algorithm performance and were limited to low-dimensional problems. In this study, we use the modern COCO benchmarking framework to analyse the performance of single-surrogate and multi-surrogate ParEGO algorithms and compare these to random sampling, Sobol space-filling, and the high performing optimizer known as TPB. Our findings broadly support the original findings for low-dimensional problems, but we find that multisurrogate ParEGO performs comparatively poorly in higher dimensions. TPB tends to outperform both ParEGOs, suggesting that initial budget investment in ideal and nadir point identification is a favourable strategy.