A Pareto Corner Search Evolutionary Algorithm and Principal Component Analysis for Objective Dimensionality Reduction

Many-objective optimisation problems (MaOPs) cause serious difficulties for existing multi-objective evolutionary algorithms (MOEAs). One common way to alleviate these difficulties is to use objective dimensionality reduction. Most existing objective reduction methods are time-consuming because they require MOEAs to run numerous generations. Pareto corner search evolutionary algorithm (PCSEA) was proposed in [18] to speed up objective reduction methods by only seeking corner solutions instead of whole solutions. However, the PCSEA-based objective reduction method in [18] needs to predefine a threshold to select objectives which strongly depends on problems and is not straightforward to obtain. This paper proposes a new objective dimensionality reduction method by integrating PCSEA and principal component analysis (PCA). Thanks to combining advantages of PCSEA and PCA, the proposed method not only can be efficient to eliminate redundant objectives, but also not require to define any parameter in advanced. The experimental results also show that the proposed method can perform objective reduction more successfully than the PCSEA-based objective reduction method. The results further strengthen the links between evolutionary computation and machine learning to address optimization problems.