Enhanced pareto interpolation method to aid decision making for discontinuous pareto optimal fronts

Abstract

Multi-criteria decision making is of interest in several domains such as engineering, finance and logistics. It aims to address the key challenges of search for optimal solutions and decision making in the presence of multiple conflicting design objectives/criteria. The decision making aspect can be particularly challenging when there are too few Pareto optimal solutions available as this severely limits the understanding of the nature of the Pareto optimal front (POF) and subsequently affects the confidence on the choice of solutions. This problem is studied in this paper, wherein a decision maker is presented with a few outcomes and the aim is to identify regions of interest for further investigation. To address the problem, the contemporary approaches attempt to generate POF approximation through linear interpolation of a given set of (a few) Pareto optimal outcomes. While the process helps in gaining an understanding of the POF, it ignores the possibility of discontinuities or voids in the POF. In this study, we investigate two measures to alleviate this difficulty. First is to make use of infeasible solutions obtained during the search, along with the Pareto outcomes while constructing the interpolations. Second is to use proximity to a set of uniform reference directions to determine potential discontinuities. Consequently, the proposed approach enables approximation of both continuous and discontinuous POF more accurately. Additionally, a set of interpolated outcomes along uniformly distributed reference directions are presented to the decision maker. The errors in the given interpolations are also estimated in order to further aid decision making by establishing confidence on predictions. We illustrate the performance of the approach using four problems spanning different types of fronts, such as mixed (convex/concave), degenerate, and disconnected.