Visualization and analysis of Pareto-optimal fronts using interpretable self-organizing map (iSOM)

Abstract

Visualizing and analyzing multiple Pareto-optimal solutions obtained using an evolutionary multi- or many-objective optimization algorithm is as important a task as the task of finding them. Besides helping to choose a single preferred solution, they provide a better understanding of the trade-off among the objectives and also reveal key insights about interactions among variables and objectives for the Pareto-optimal solutions. Existing visualization methods do not provide a comprehensive account of both visualization and analysis of Pareto-optimal solutions. In this paper, we present an interpretable self-organizing map (iSOM) method that produces a more simplistic mapping of higher-dimensional variable spaces into two dimensions. Multiple iSOM plots, one for each objective, allows an easier visual understanding of trade-off among objectives. By identifying high trade-off Pareto-optimal solutions and marking them on the iSOM plots, we also provide decision-makers a comprehensive method to locate critical and likely preferred solutions on the Pareto-optimal front. The visualization and analysis of Pareto-optimal solutions using iSOMs are demonstrated on 11 problems involving three to five objectives. As discussed, the approach is generically applicable to higher-dimensional and constrained problems.