How to Read Many-Objective Solution Sets in Parallel Coordinates [Educational Forum]

Rapid development of evolutionary algor ithms in handling many-objective optimization problems requires viable methods of visualizing a high-dimensional solution set. The parallel coordinates plot which scales well to high-dimensional data is such a method, and has been frequently used in evolutionary many-objective optimization. However, the parallel coordinates plot is not as straightforward as the classic scatter plot to present the information contained in a solution set. In this paper, we make some observations of the parallel coordinates plot, in terms of comparing the quality of solution sets, understanding the shape and distribution of a solution set, and reflecting the relation between objectives. We hope that these observations could provide some guidelines as to the proper use of the parallel coordinates plot in evolutionary manyobjective optimization.

I. Introduction

The classic scatter plot is a basic tool in viewing solution vectors in multiobjective optimization. It allows us to observe/perceive the quality of a solution set, the shape and distribution of a solution set, the relation between objectives (e.g., the extent of their conflict), etc. Unfortunately, the scatter plot may only be drawn readily in a 2D or 3D Cartesian coordinate space. It could be difficult for people to comprehend the scatter plot in a higher-dimensional space.