Incorporating decision-maker's preferences into the automatic configuration of bi-objective optimisation algorithms

Automatic configuration (AC) methods are increasingly used to tune and design optimisation algorithms for problems with multiple objectives. Most AC methods use unary quality indicators, which assign a single scalar value to an approximation to the Pareto front, to compare the performance of different optimisers. These quality indicators, however, imply preferences beyond Pareto-optimality that may differ from those of the decision maker (DM). Although it is possible to incorporate DM's preferences into quality indicators, e.g., by means of the weighted hypervolume indicator (HV^w), expressing preferences in terms of weight function is not always intuitive nor an easy task for a DM, in particular, when comparing the stochastic outcomes of several algorithm configurations. A more visual approach to compare such outcomes is the visualisation of their empirical attainment functions (EAFs) differences. This paper proposes using such visualisations as a way of eliciting information about regions of the objective space that are preferred by the DM. We present a method to convert the information about EAF differences into a HV^w that will assign higher quality values to approximation fronts that result in EAF differences preferred by the DM. We show that the resulting HV^w may be used by an AC method to guide the configuration of multi-objective optimisers according to the preferences of the DM. We evaluate the proposed approach on a well-known benchmark problem. Finally, we apply our approach to re-configuring, according to different DM's preferences, a multi-objective optimiser tackling a real-world production planning problem arising in the manufacturing industry.