Christian von Lücken
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.
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- von Lücken, C., Barán, B., Brizuela, C.: A survey on multi-objective evolutionary algorithms for many-objective problems. Comput. Optim. and Appl. 58(3), 707--756 (2014) Google ScholarDigital Library
- Saxena, D.K., Deb, K.: Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: Employing correntropy and a novel maximum variance unfolding. In: Proc. of the 4th Int. Conf. on Evol. Multi-Criterion Optim. EMO 2007. Lect. Notes in Comput. Sci., vol. 4403, pp. 772--787. Springer (2007) Google ScholarDigital Library
Index Terms
- Dimensionality Reduction in Many-objective Problems Combining PCA and Spectral Clustering
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