Single-objective and multi-objective formulations of solution selection for hypervolume maximization

Authors:
Hisao Ishibuchi;Yuji Sakane;Noritaka Tsukamoto;Yusuke Nojima
Affiliations:
Osaka Prefecture University, Sakai, Japan;Osaka Prefecture University, Sakai, Japan;Osaka Prefecture University, Sakai, Japan;Osaka Prefecture University, Sakai, Japan
Venue:
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Year:
2009

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Abstract

A new trend in evolutionary multi-objective optimization (EMO) is the handling of a multi-objective problem as an optimization problem of an indicator function. A number of approaches have been proposed under the name of indicator-based evolutionary algorithms (IBEAs). In IBEAs, the entire population usually corresponds to a solution of the indicator optimization problem. In this paper, we show how hypervolume maximization can be handled as single-objective and multi-objective problems by coding a set of solutions of the original multi-objective problem as an individual. Our single-objective formulation maximizes the hypervolume under constraint conditions on the number of nondominated solutions. On the other hand, our multi-objective formulation minimizes the number of non-dominated solutions while maximizing their Hypervolume.