Authors: Sergio García Moratilla, Ruben Ruiz-Torrubiano and Alberto Suarez.
In this article we review several hybrid techniques that can be used to accurately and efficiently solve large optimization problems with cardinality constraints. Exact methods, such as branch-and-bound, require lengthy computations and are, for this reason, infeasible in practice. As an alternative, this study focuses on approximate techniques that can identify near-optimal solutions at a reduced computational cost. Most of the methods considered encode the candidate solutions as sets. This representation, when used in conjunction with specially devised search operators, is specially suited to problems whose solution involves the selection of optimal subsets of specified cardinality. The performance of these techniques is illustrated in optimization problems of practical interest that arise in the fields of machine learning (pruning of ensembles of classifiers), quantitative finance (portfolio selection), time-series modeling (index tracking) and statistical data analysis (sparse principal component analysis).