On-line Quick Hypervolume Algorithm
[ 1 ] Instytut Informatyki, Wydział Informatyki i Telekomunikacji, Politechnika Poznańska | [ P ] employee
2023
chapter in monograph / paper
english
- hypervolume
- multiobjective optimization
EN Hypervolume is most likely the most often used quality indicator in EMO because of its compatibility with the dominance relation. In the context of EMO one is quite often interested not only in the hypervolume of the final solutions set but also in the evolution of hypervolume during the run of the algorithm. Such evolution of hypervolume may allow for a more detailed analysis of a given EMO algorithm or may be used for on-line convergence detection and on-line stopping criteria. Of course, full recalculation of hypervolume after addition of each new solution would be extremely inefficient. However, one may update hypervolume after generation of a new solution(s) which can be achieved by calculating hypervolume contribution of the new solution. In this paper we evaluate the performance of the quick hypervolume (QHV) and WFG algorithms in on-line hypervolume update using benchmark datasets. We show that especially QHV performs very well in such context with the time needed to process the whole set of solutions in on-line manner being only moderately longer than static calculation of the final hypervolume. Finally, we illustrate how on-line QHV could be used to monitor evolution of hypervolume during runs of a hybrid multiobjective evolutionary algorithm.
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