Guiding Surrogate-Assisted Multi-Objective Optimisation with Decision Maker Preferences

We present a new algorithm for efficiently solving expensive multiand many-objective, black-box optimisation problems by interactively incorporating the preferences of an external decision maker. We define a novel acquisition function which combines the maximin distance to the summary attainment front with a set of aspirational objective-space target points chosen by the decision maker. This drives an exploitative multi-surrogate model to quickly converge to solutions favourable to the decision maker, without relying on surrogate posterior uncertainty estimates or arbitrary objective weighting. The performance of the algorithm is quantified through measurement of the hypervolume of interest to the decision maker which is dominated by the set of found solutions. This measure is used to compare the performance of our algorithm to one similar, which does not involve the decision maker. We demonstrate over a range ofWalking Fish Group test problems, that incorporating preference in this way improves convergence in the vast majority of cases. Empirical evaluation further shows that preference inclusion is of increasing importance as the number of objectives increases, and that the greatest benefit is obtained when the targets dominate or are dominated by a small region of the Pareto front.