Quality Indicators for Preference-based Evolutionary Multi-objective Optimization Using a Reference Point: A Review and Analysis

Some quality indicators have been proposed for benchmarking preference-based evolutionary multiobjective optimization (EMO) algorithms using a reference point. Although a systematic review and analysis of the quality indicators are helpful for both benchmarking and practical decision making, neither has been conducted. In this context, first, this article reviews existing regions of interest and quality indicators for preference-based EMO using the reference point. We point out that each quality indicator was designed for a different region of interest. Then, this article investigates the properties of the quality indicators. We demonstrate that an achievement scalarizing function value is not always consistent with the distance from a solution to the reference point in the objective space. We observe that the regions of interest can be significantly different depending on the position of the reference point and the shape of the Pareto front. We identify undesirable properties of some quality indicators. We also show that the ranking of preference-based EMO algorithms depends on the choice of quality indicators.