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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.
Subset selection is an interesting and important topic in the field of evolutionary multi-objective optimization (EMO). Especially, in an EMO algorithm with an unbounded external archive, subset selection is an essential post-processing procedure to
Is it possible to maximize a monotone submodular function faster than the widely used lazy greedy algorithm (also known as accelerated greedy), both in theory and practice? In this paper, we develop the first linear-time algorithm for maximizing a ge
Subset selection is an important component in evolutionary multiobjective optimization (EMO) algorithms. Clustering, as a classic method to group similar data points together, has been used for subset selection in some fields. However, clustering-bas
Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems has been theoretically confirmed in cite{BCDDPW,DPW}, where it is shown
Evolution has produced an astonishing diversity of species, each filling a different niche. Algorithms like MAP-Elites mimic this divergent evolutionary process to find a set of behaviorally diverse but high-performing solutions, called the elites. O