Visualisation of Pareto Front Approximation: A Short Survey and Empirical Comparisons

Abstract: Visualisation is an effective way to facilitate the analysis and understanding of multivariate data. In the context of multi-objective optimisation, comparing to quantitative performance metrics, visualisation is, in principle, able to provide a decision maker better insights about Pareto front approximation sets (e.g. the distribution of solutions, the geometric characteristics of Pareto front approximation) thus to facilitate the decision-making (e.g. the exploration of trade-off relationship, the knee region or region of interest). In this paper, we overview some currently prevalent visualisation techniques according to the way how data is represented. To have a better understanding of the pros and cons of different visualisation techniques, we empirically compare six representative visualisation techniques for the exploratory analysis of different Pareto front approximation sets obtained by four state-of-the-art evolutionary multi-objective optimisation algorithms on the classic DTLZ benchmark test problems. From the empirical results, we find that visual comparisons also follow the \textit{No-Free-Lunch} theorem where no single visualisation technique is able to provide a comprehensive understanding of the characteristics of a Pareto front approximation set. In other words, a specific type of visualisation technique is only good at exploring a particular aspect of the data.