A hypervolume-based optimizer for high-dimensional objective spaces

Abstract

In the field of evolutionary multiobjective optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance. This property is of high interest and relevance for multi objective search involving a large number of objective functions. However, the high computational effort required for calculating the indicator values has so far prevented to fully exploit the potential of hyper volume-based multi objective optimization. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo sampling to approximate the exact hyper volume values. In detail, we present HypE (Hyper volume Estimation Algorithm for Multi objective 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 hyper volume-based search, but also the runtime can be flexibly adapted. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multi objective evolutionary algorithms. © Springer-Verlag Berlin Heidelberg 2010.