Dimensionality Reduction in Many-objective Problems Combining PCA and Spectral Clustering

Christian von Lücken, Hugo Monzón, Carlos A. Brizuela, Benjamín Barán

Abstract: In general, multi-objective optimization problems (MOPs) with up to three objectives can be solved using multi-objecti-ve evolutionary algorithms (MOEAs). However, for MOPs with four or more objectives, current algorithms show some limitations. To address these limitations, dimensionality reduction approaches try to transform the problem by eliminating not essential objectives in such a way that afterward a standard MOEA can be used. To reduce the size of the objective set, Deb and Saxena proposed a method that combines Principal Component Analysis (PCA) with the NSGA-II, called PCA-NSGA-II. Using PCA-NSGA-II as a reference, this work proposes to combine PCA and a clustering procedure for improving the dimensionality reduction process. Experimental runs were conducted with test problems DTLZ2(M) and DTLZ5(I,M) obtaining better results with the proposed method than the obtained with the PCA-NSGA-II.