PaletteViz: A Visualization Method for Functional Understanding of High-Dimensional Pareto-Optimal Data-Sets to Aid Multi-Criteria Decision Making

Abstract

To represent a many-objective Pareto-optimal front having four or more dimensions of the objective space, a large number of points are necessary. However, for choosing a single preferred point from a large set is problematic and time-consuming, as they provide a large cognitive burden on the part of the decision-makers (DMs). Hence, many-objective optimization and decision-making researchers and practitioners have been interested in effective visualization methods to filter down a few critical points for further analysis. While some ideas are borrowed from data analytics and visualization literature, they are generic and do not exploit the functionalities that DMs are usually interested. In this paper, we outline some such functionalities: a point's trade-off among conflicting objectives in its neighborhood, closeness of a point to the boundary or core of the high-dimensional Pareto set, specific desired geometric properties of points, spatial distance of one point to another, closeness of a point to constraint boundary, and others, in developing a new visualization technique. We propose a novel way to map a high-dimensional Pareto-optimal front (points or data-set) into two-and-half dimensions by revealing functional features of points that may be of great interest to DMs. As a proof-of-principle demonstration, we apply our proposed palette visualization (PaletteViz) technique to a number of different structures of Pareto-optimal data-sets and discuss how the proposed technique is different from a few popularly used visualization techniques.