A quality metric for multi-objective optimization based on hierarchical clustering techniques

Authors:
Frederico G. Guimarães;Elizabeth F. Wanner;Ricardo H. C. Takahashi
Affiliations:
Department of Computer Science, Universidade Federal de Ouro Preto, Ouro Preto, Brazil;Department of Mathematics, Universidade Federal de Ouro Preto, Ouro Preto, Brazil;Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
Venue:
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Year:
2009

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Abstract

This paper presents the Hierarchical Cluster Counting (HCC), a new quality metric for nondominated sets generated by multi-objective optimizers that is based on hierarchical clustering techniques. In the computation of the HCC, the samples in the estimate set are sequentially grouped into clusters. The nearest clusters in a given iteration are joined together until all the data is grouped in only one class. The distances of fusion used at each iteration of the hierarchical agglomerative clustering process are integrated into one value, which is the value of the HCC for that estimate set. The examples show that the HCC metric is able to evaluate both the extension and uniformity of the samples in the estimate set, making it suitable as a unary diversity metric for multi-objective optimization.