| Abstract: |
In the field of evolutionary multi-criterion optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto
dominance: whenever a Pareto set approximation entirely dominates another one, then also the indicator value of the former will be better. This property is of high interest and relevance for
problems involving a large number of objective functions. However, the high computational effort required for hypervolume calculation has so far prevented to fully exploit the potential of this
indicator; current hypervolume-based search algorithms are limited to problems with only a few objectives. This paper addresses this issue and proposes a fast search algorithm that uses Monte
Carlo simulation to approximate the exact hypervolume values. The main idea is that not the actual indicator values are important, but rather the rankings of solutions induced by the hypervolume
indicator. In detail, we present \hype, a hypervolume estimation algorithm for multiobjective optimization, by which the accuracy of the estimates and the available computing resources can be
traded off; thereby, not only many-objective problems become feasible with hypervolume-based search, but also the runtime can be flexibly adapted. Moreover, we show how the same principle can be
used to statistically compare the outcomes of different multiobjective optimizers with respect to the hypervolume---so far, statistical testing has been restricted to scenarios with few
objectives. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multiobjective evolutionary algorithms. HypE is available for
download at \url{http://www.tik.ee.ethz.ch/sop/download/supplementary/hype/ |
