Delorme, M., Garcia, S., Gondzio, J., Kalcsics, J., Manlove, D. and Pettersson, W. (2019) Mathematical models for stable matching problems with ties and incomplete lists. European Journal of Operational Research, 277(2), pp. 426-441. (doi: 10.1016/j.ejor.2019.03.017)
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Abstract
We present new integer linear programming (ILP) models for N P-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals/Residents problem with Ties (HRT). These models can be used to efficiently solve these optimisation problems when applied to (i) instances derived from real-world applications, and (ii) larger instances that are randomly-generated. In the case of SMTI, we consider instances arising from the pairing of children with adoptive families, where preferences are obtained from a quality measure of each possible pairing of child to family. In this case, we seek a maximum weight stable matching. We present new algorithms for preprocessing instances of SMTI with ties on both sides, as well as new ILP models. Algorithms based on existing state-of-the-art models only solve 6 of our 22 real-world instances within an hour per instance, and our new models incorporating dummy variables and constraint merging, together with preprocessing and a warm start, solve all 22 instances within a mean runtime of a minute. For HRT, we consider instances derived from the problem of assigning junior doctors to foundation posts in Scottish hospitals. Here, we seek a maximum size stable matching. We show how to extend our models for SMTI to HRT and reduce the average running time for real-world HRT instances by two orders of magnitude. We also show that our models outperform by a wide margin all known state-of-the-art models on larger randomly-generated instances of SMTI and HRT.
| Item Type: | Articles |
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| Additional Information: | This research was supported by the Engineering and Physical Science Research Council through grant nos. EP/P029825/1 (first four authors) and EP/P028306/1 (fifth and sixth authors). |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Manlove, Professor David and Pettersson, Dr William |
| Authors: | Delorme, M., Garcia, S., Gondzio, J., Kalcsics, J., Manlove, D., and Pettersson, W. |
| College/School: | College of Science and Engineering > School of Computing Science |
| Journal Name: | European Journal of Operational Research |
| Publisher: | Elsevier BV |
| ISSN: | 0377-2217 |
| ISSN (Online): | 0377-2217 |
| Published Online: | 18 March 2019 |
| Copyright Holders: | Copyright © 2019 The Authors |
| First Published: | First published in European Journal of Operational Research 277(2):426-441 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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