Abstract
The test collection problem, also known as the minimum test set problem or the minimum test cover problem, selects a minimal set of binary attributes by which it is possible to determine the state of a system. This problem commonly arises in applications such as medical diagnosis and fault detection in the design of monitoring systems. We generalize this problem by (i) allowing attributes to obtain arbitrary categorical values; (ii) allowing multiple attributes combinations to represent a single state of a system; and (iii) including a different cost for testing each attribute. The objective of the planer is to select a set of tests at a minimum cost that can determine the state of the system. To address this problem, we present an integer programming model and an effective exact solution method that uses the model’s unique structure to reduce its dimension. Using this method, large instances that could not be solved directly by a commercial solver can easily be solved. Our solution method was implemented and demonstrated to be superior to those described in previous studies when applied on two sets of benchmark instances from the literature. One dataset was adapted from the UCI repository and one was based on a realistic and large-scale sensor placement problem in urban water networks.
Similar content being viewed by others
References
Bertolazzi P, Felici G, Festa P, Fiscon G, Weitschek E (2016) Integer programming models for feature selection: new extensions and a randomized solution algorithm. Eur J Oper Res 250(2):389–399
Centre of Water Systems University of Exeter (2015). http://emps.exeter.ac.uk/engineering/research/cws/downloads/benchmarks/. Accessed 1 Aug 2019
De Bontridder KM, Halldórsson BV, Halldórsson MM, Hurkens CA, Lenstra JK, Ravi R, Stougie L (2003) Approximation algorithms for the test cover problem. Math Program 98(1–3):477–491
Garey MR, Johnson DS (1979) Computers and intractability. W. H. Freeman, New York
Halldórsson BV, Halldórsson MM, Ravi R (2001) On the approximability of the minimum test collection problem. In: auf der Heide FM (ed) European symposium on algorithms. Algorithms—ESA 2001. Lecture Notes in Computer Science, vol 2161. Heidelberg, Springer, Berlin, pp 158–169
Jolly MD, Lothes AD, Sebastian Bryson L, Ormsbee L (2014) Research database of water distribution system models. J Water Resour Plan Manage 140(4):410–416
Karwan MH, Lotfi V, Telgen J, Zionts S (1983) Redundancy in mathematical programming: a state-of-the-art survey. Springer, Berlin, Heidelberg
Krause A, Leskovec J, Guestrin C, VanBriesen J, Faloutsos C (2008) Efficient sensor placement optimization for securing large water distribution networks. J Water Resour Plan Manage 134(6):516–526
Lichman, M. (2013). UCI machine learning repository http://archive.ics.uci.edu/ml. Irvine, CA: University of California, School of Information and Computer Science
Lin FY, Chiu PL (2005) A near-optimal sensor placement algorithm to achieve complete coverage-discrimination in sensor networks. IEEE Commun Lett 9(1):43–45
Ostfeld A, Uber JG, Salomons E, Berry JW, Hart WE, Phillips CA, di Pierro F (2008) The battle of the water sensor networks (BWSN): a design challenge for engineers and algorithms. J Water Resour Plan Manag 134(6):556–568
Paulraj S, Sumathi P (2010) A comparative study of redundant constraints identification methods in linear programming problems. Math Prob Eng. https://doi.org/10.1155/2010/723402
Sela L, Amin S (2018) Robust sensor placement for pipeline monitoring: mixed integer and greedy optimization. Adv Eng Inform 36:55–63
Sela Perelman LS, Abbas W, Koutsoukos X, Amin S (2016) Sensor placement for fault location identification in water networks: a minimum test cover approach. Automatica 72:166–176
Acknowledgements
The first author of this paper was supported by a scholarship from the Shlomo Shmeltzer Institute for Smart Transportation at Tel Aviv University. The authors wish to express their gratitude to Professor Lina Sela Perlman, who provided a valuable dataset for their study.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Douek-Pinkovich, Y., Ben-Gal, I. & Raviv, T. The generalized test collection problem. TOP 29, 372–386 (2021). https://doi.org/10.1007/s11750-020-00554-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-020-00554-1
Keywords
- Test collection problem
- Sensor selection
- Sensor placement
- Water networks
- Integer linear programming
- Constraint reduction