  Subset selection is a popular topic in recent years and a number of subset
selection methods have been proposed. Among those methods, hypervolume subset
selection is widely used. Greedy hypervolume subset selection algorithms can
achieve good approximations to the optimal subset. However, when the candidate
set is large (e.g., an unbounded external archive with a large number of
solutions), the algorithm is very time-consuming. In this paper, we propose a
new lazy greedy algorithm exploiting the submodular property of the hypervolume
indicator. The core idea is to avoid unnecessary hypervolume contribution
calculation when finding the solution with the largest contribution.
Experimental results show that the proposed algorithm is hundreds of times
faster than the original greedy inclusion algorithm and several times faster
than the fastest known greedy inclusion algorithm on many test problems.
