Estimation of Multi-Objective Pareto Frontier using Hyperspace Diagonal Counting

The Hyper-Space Diagonal Counting (HSDC) method was previously proposed for generating representations of n-dimensional data in 2or 3-dimensions. Since its inception, the HSDC has been used to visualize the n-dimensional performance space in an intuitive fashion for Multiobjective Optimization Applications, through the incorporation of the HSDC into the Hyperspace Pareto Frontier (HPF) visualization approach. This paper presents a newer application of the HSDC method that enables estimation of the Pareto frontier without performing a formal optimization. Further, it is demonstrated that this estimated Pareto frontier can be represented in the design space, with a different representation associated with each objective. This very different type of visualization provides designers with a means of investigating the trade-offs for both objectives as well as design points using only the design space.