A Study on Performance Metrics to Identify Solutions of Interest from a Trade-Off Set

Optimization algorithms typically deliver a set of trade-off solutions for problems involving multi/many-objectives in conflict. The number of such solutions could be in hundreds, thousands or even more. A decision maker typically identifies a handful of preferred trade-off solutions (solutions of interest (SOI)) from the above set based on secondary indicators e.g. expected marginal utility, convex bulge, hypervolume contribution, bend angle, reflex angle etc. In this paper, we first highlight that members of SOI could be significantly different depending on the choice of the secondary indicator. This leads to an important question "what metrics should a decision maker use to choose a solution over another ?" and more importantly "how to identify a handful of solutions ?" from a potentially large set of solutions. In this paper we introduce an approach based on local curvature to select such solutions of interest. The performance of the approach is illustrated using a bi-objective test problem, and two many-objective engineering optimization problems.