Does Preference Always Help? A Holistic Study on Preference-Based Evolutionary Multi-Objective Optimisation Using Reference Points

The ultimate goal of multi-objective optimisation is to help a decision maker (DM) identify solution(s) of interest (SOI) achieving satisfactory trade-offs among multiple conflicting criteria. This can be realised by leveraging DM's preference information in evolutionary multi-objective optimisation (EMO). No consensus has been reached on the effectiveness brought by incorporating preference in EMO (either a priori or interactively) versus a posteriori decision making after a complete run of an EMO algorithm. Bearing this consideration in mind, this paper i) provides a pragmatic overview of the existing developments of preference-based EMO; and ii) conducts a series of experiments to investigate the effectiveness brought by preference incorporation in EMO for approximating various SOI. In particular, the DM's preference information is elicited as a reference point, which represents her/his aspirations for different objectives. Experimental results demonstrate that preference incorporation in EMO does not always lead to a desirable approximation of SOI if the DM's preference information is not well utilised, nor does the DM elicit invalid preference information, which is not uncommon when encountering a black-box system. To a certain extent, this issue can be remedied through an interactive preference elicitation. Last but not the least, we find that a preference-based EMO algorithm is able to be generalised to approximate the whole PF given an appropriate setup of preference information.