### 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 × 10°6, it takes about 21 hours using WFG, however it takes only less than 30 minutes using FHV.