10.3929/ETHZ-A-005703480
Bader, Johannes
Zitzler, Eckart
HypE: An algorithm for fast hypervolume-based many-objective optimization
ETH Zurich
2008
Report
MEHRZIELOPTIMIERUNG (OPERATIONS RESEARCH)
MULTIOBJECTIVE PROGRAMMING (OPERATIONS RESEARCH)
PROGRAMS AND ALGORITHMS FOR THE SOLUTION OF SPECIAL PROBLEMS
PROGRAMME UND ALGORITHMEN ZUR LÖSUNG SPEZIELLER PROBLEME
info:eu-repo/classification/ddc/510
info:eu-repo/classification/ddc/004
Mathematics
Data processing, computer science
2008
en
25 p.
application/pdf
http://rightsstatements.org/page/InC-NC/1.0/
info:eu-repo/semantics/openAccess
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 hypervolumebased 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.
TIK Report, 286 (286)