Visualization of Pareto Front Approximations in Evolutionary Multiobjective Optimization: A Critical Review and the Prosection Method

摘要

In evolutionary multiobjective optimization, it is very important to be able to visualize approximations of the Pareto front (called approximation sets) that are found by multiobjective evolutionary algorithms. While scatter plots can be used for visualizing 2-D and 3-D approximation sets, more advanced approaches are needed to handle four or more objectives. This paper presents a comprehensive review of the existing visualization methods used in evolutionary multiobjective optimization, showing their outcomes on two novel 4-D benchmark approximation sets. In addition, a visualization method that uses prosection (projection of a section) to visualize 4-D approximation sets is proposed. The method reproduces the shape, range, and distribution of vectors in the observed approximation sets well and can handle multiple large approximation sets while being robust and computationally inexpensive. Even more importantly, for some vectors, the visualization with prosections preserves the Pareto dominance relation and relative closeness to reference points. The method is analyzed theoretically and demonstrated on several approximation sets.