A comparison of different algorithms for the calculation of dominated hypervolumes

• Authors: Christopher Priester;Kaname Narukawa;Tobias Rodemann
• Venue: Proceedings of the 15th annual conference on Genetic and evolutionary computation
• Year: 2013

In the fields of multi- and many-objective optimization methods, the hypervolume of a set of solutions is a very useful measure for assessing the current state of the optimization process. It is also the fundamental quality criterion for the well-known SMS-EMOA (S-metric selection evolutionary multi-objective optimization), which is one of the best many objective optimization algorithms known at the moment. Unfortunately, the computation of the hypervolume for a given set of solutions is a time-consuming effort which scales unfavorably with the number of objectives and the size of the population. In this work we analyzed a number of algorithms for hypervolume computation and systematically measured their computational effort for different numbers of objectives and population size. We compared three established standard algorithms that are used in the Shark optimization library and a recent approach by While et al. We also included an approximation computation algorithm proposed by Ishibuchi et al., where we additionally evaluated the precision of the approximation computation and its impact on the selection process within an optimization run. Our findings indicate that the algorithm by While et al. outperforms the three other exact algorithms for a wide range of settings. The Ishibuchi algorithm was shown to have a slightly negative effect on the selection process, but for very large population sizes or number of objectives, the approximation method might be the only viable alternative.