3D-RadVis: Visualization of Pareto front in many-objective optimization

In many-objective optimization, visualization of true Pareto front or obtained non-dominated solutions is difficult. A proper visualization tool must be able to show the location, range, shape, and distribution of obtained non-dominated solutions. However, existing commonly used visualization tools in many-objective optimization (e.g., parallel coordinates) fail to show the shape of the Pareto front. In this paper, we propose a simple yet powerful visualization method, called 3-dimensional radial coordinate visualization (3D-RadVis). This method is capable of mapping M-dimensional objective space to a 3-dimensional radial coordinate plot while preserving the relative location of solutions, shape of the Pareto front, distribution of solutions, and convergence trend of an optimization process. Furthermore, 3D-RadVis can be used by decision-makers to visually navigate large many-objective solution sets, observe the evolution process, visualize the relative location of a solution, evaluate trade-off among objectives, and select preferred solutions. The visual effectiveness of the proposed method is demonstrated on widely used many-objective benchmark problems containing variety of Pareto fronts (linear, concave, convex, mixed, and disconnected). In addition, we demonstrated the capability of 3D-RadVis for visual progress tracking of the NSGA-III algorithm through generations. It is worthwhile to mention that a suitable visualization is a crucial prerequisite for an effective interactive optimization.

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