Journal of Heuristics

, Volume 22, Issue 3, pp 245–271 | Cite as

Extending quick hypervolume

  • Luís M. S. Russo
  • Alexandre P. FranciscoEmail author


We extend the functionality of the quick hypervolume (QHV) algorithm. Given a set of d-dimensional points this algorithm determines the hypervolume of the dominated space, a useful measure for multiobjective evolutionary algorithms (MOEAs). We extend QHV in two ways: adapt it to compute the exclusive hypervolume of each point, and speed it up with parallel computation, that adjusts nicely to the divide and conquer methodology of QHV. The resulting algorithms are faster and more informative sub-routines, which can be used for MOEAs with a large number of objectives.


Diversity methods Hypervolume Multiobjective optimization Performance metrics 



We would like to thank Tobias Friedrich for his interest in the original QHV algorithm and for pointing out the exclusive hypervolume problem to us. This work was partially supported by national funds through FCT – Fundação para a Ciência e Tecnologia, under Projects EXCL/EEI-ESS/0257/2012, PTDC/EEI-ELC/3246/2012 and UID/CEC/50021/2013.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.INESC-IDLisbonPortugal
  2. 2.Department of Computer Science and Engineering, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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