A Bi-Criteria Selection Framework for Incorporating Preference Information into Evolutionary Multi-objective Optimization

Preference-based evolutionary multi-objective optimization (PBEMO) is an effective approach for approximating the region of interest (ROI) defined by the preference information from a decision maker. An existing PBEMO algorithm is an ad-hoc extension of a conventional EMO algorithm to approximate a target ROI. However, a tedious trial-and-error process is required to extend a base EMO algorithm for a particular ROI in an ad-hoc manner. To address this issue, this paper proposes a bi-criteria selection framework (BSF) that can extend any (μ + λ)-EMO algorithm for preference-based optimization of any ROI. In environmental selection, first, the proposed BSF defines an approximation of a ROI. Then, two types of selection are performed based on the number of individuals in the approximation. We investigate the effectiveness of the proposed BSF by incorporating it into seven EMO algorithms, including NSGA-II. The results show that BSF can successfully integrate the preference information into conventional EMO algorithms. The results also show that the BSF versions of the EMO algorithms perform similarly to or better than two representative PBEMO algorithms (R-NSGA-II and g-NSGA-II) in most cases.