Subset selection via continuous optimization with applications to network design

Choosing a subset of representative items from a set of alternatives is an important problem in many scientific fields such as environmental science and statistics. For most practical problems, however, a computationally efficient solution method is not known to exist. While this problem has attracted a significant amount of attention, the majority of specifically designed algorithms do not scale well with respect to the problem size or do not provide a usable open-source package. In this study, we show that any global continuous optimization technique can be used for solving the representative subset selection problem. The latter is achieved by designing a simple transformation which embeds the problem’s discrete space into a larger continuous space. The proposed methodology is applied to design problems in environmental and statistical domains. We evaluate the proposed method using several open-source global optimization packages, and show that this technique compares favorably with existing direct methods.