Visualization and Performance Metric in Many-Objective Optimization


Visualization of population in a high-dimensional objective space throughout the evolution process presents an attractive feature that could be well exploited in designing many-objective evolutionary algorithms (MaOEAs). In this paper, a new visualization method is proposed. It maps individuals from a high-dimensional objective space into a 2-D polar coordinate plot while preserving Pareto dominance relationship, retaining shape and location of the Pareto front, and maintaining distribution of individuals. From it, a decision-maker can observe the evolution process, estimate location, range, and distribution of Pareto front, assess quality of the approximated front and tradeoff between objectives, and easily select preferred solutions. Furthermore, its applications can be scalable to any dimensions, handle a large number of individuals on front, and simultaneously visualize multiple fronts for comparison. Based on this visualization tool, a performance metric, named polar-metric, is designed. The convergence of the approximate front is measured by radial values of all population members on that front. Meanwhile, the diversity performance is mainly determined by niche count of each subregion in a high-dimensional objective space. Experimental results show that it can provide a comprehensive and reliable comparison among MaOEAs.