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Subset selection via continuous optimization with applications to network design

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Abstract

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.

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Acknowledgments

I am thoroughly grateful to the anonymous reviewers and the editor for their valuable and constructive remarks and suggestions.

Funding

This work was supported by the Australian Research Council Centre of Excellence for Mathematical & Statistical Frontiers, under CE140100049 grant number.

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  1. School of Mathematics and Physics, The University of Queensland, Brisbane, 4072, Australia

    Radislav Vaisman

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  1. Radislav Vaisman
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Correspondence to Radislav Vaisman.

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Vaisman, R. Subset selection via continuous optimization with applications to network design. Environ Monit Assess 192, 361 (2020). https://doi.org/10.1007/s10661-019-7938-6

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