Visual representation of a many-objective Pareto-optimal front in four or more dimensional objective space requires a large number of data points. Moreover, choosing a single point from a large set even with certain preference information is problematic, as it imposes a large cognitive burden on the decision-makers. Therefore, many-objective optimization and decision-making practitioners have been interested in effective visualization methods to en- able them to filter down a large set to a few critical points for further analysis. Most existing visualization methods are borrowed from other data analytics domains and they are too generic to be effective for many-criterion decision making. In this dissertation, we propose a visualization method, using star-coordinate and radial visualization plots, for effectively visualizing many-objective trade-off solutions. The proposed method respects some basic topological, geometric and functional decision-making properties of high-dimensional trade- off points mapped to a three-dimensional space. We call this method Palette Visualization (PaletteViz). We demonstrate the use of PaletteViz on a number of large-dimensional multi- objective optimization test problems and three real-world multi-objective problems, where one of them has 10 objective and 16 constraint functions. We also show the uses of NIM-BUS and Pareto-Race concepts from canonical multi-criterion decision making and analysis literature and introduce them into PaletteViz to demonstrate the ease and advantage of the proposed method.
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