Intuitive visualization of Pareto Frontier for multi-objective optimization in n-dimensional performance space

A visualization methodology is presented in which a Pareto Frontier can be visualized in an intuitive and straightforward manner for an n-dimensional performance space. Based on this visualization, it is possible to quickly identify 'good' regions of the performance and optimal design spaces for a multi-objective optimization application, regardless of space complexity. Visualizing Pareto solutions for more than three objectives has long been a significant challenge to the multi-objective optimization community. The Hyper-space Diagonal Counting (HSDC) method described here enables the lossless visualization to be implemented. The proposed method requires no dimension fixing. In this paper, we demonstrate the usefulness of visualizing n-f space (i.e. for more than three objective functions in a multiobjective optimization problem). The visualization is shown to aid in the final decision of what potential optimal design point should be chosen amongst all possible Pareto solutions.