Powered by OpenAIRE graph
Found an issue? Give us feedback
addClaim

On the fast hypervolume calculation method

Authors: Takeshi Watanabe; Tomoaki Tatsukawa; Akira Oyama;

On the fast hypervolume calculation method

Abstract

We propose a new algorithm FHV (Fast HyperVolume) for exact hypervolume (HV) calculation using divide and conquer algorithm. FHV divides the original set of non-dominated solutions into several fractions first, calculate the value of HV of each fraction separately, sum up the each value, and finally obtain the value of HV of the original set. Therefore there are three very strong points: 1. Calculation cost is reduced significantly because each fraction contains less number of non-dominated solutions; 2. Complete parallelism is possible because each divided fraction is independent each other; 3. An arbitrary HV calculation method such as HOY (Hypervolume by Overmars and Yap) and WFG (Walking Fish Group) can be used together with FHV. Using these features computation time of HV becomes considerably reduced. For example, in a case number of objective functions is 5 and number of solutions is 1 × 106, it takes about 21 hours using WFG, however it takes only less than 30 minutes using FHV.

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    6
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!