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Intruder alert! Optimization models for solving the mobile robot graph-clear problem

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Abstract

We develop optimization approaches to the graph-clear problem, a pursuit-evasion problem where mobile robots must clear a facility of intruders. The objective is to minimize the number of robots required. We contribute new formal results on progressive and contiguous assumptions and their impact on algorithm completeness. We present mixed-integer linear programming and constraint programming models, as well as new heuristic variants for the problem, comparing them to previously proposed heuristics. Our empirical work indicates that our heuristic variants improve on those from the literature, that constraint programming finds better solutions than the heuristics in run-times reasonable for the application, and that mixed-integer linear programming is superior for proving optimality. Given their performance and the appeal of the model-and-solve framework, we conclude that the proposed optimization methods are currently the most suitable for the graph-clear problem.

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Notes

  1. The definition of path used in the graph-clear literature is a generalization of the classical definition in that it is permitted to start or end on an edge.

  2. The distinction between single vs. multiple targets makes no difference in our context.

  3. In this paper we consider only the GCP that minimizes the number of robots used.

  4. Although implemented in Python (which is in practice slower than C++), the implemented polynomial-time heuristics run in less than a second.

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Acknowledgements

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). M.P. Castro is funded by the Comisión Nacional de Investigación Científica y Tecnológica (CONICYT, Becas Chile). M. Morin is funded by the Fonds de Recherche du Québec – Nature et Technologies (FRQNT).

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    Authors and Affiliations

    1. Department of Operations and Decision Support Systems, Université Laval, Québec, QC, Canada

      Michael Morin

    2. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada

      Michael Morin, Margarita P. Castro, Kyle E. C. Booth, Tony T. Tran, Chang Liu & J. Christopher Beck

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    1. Michael Morin
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    2. Margarita P. Castro
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    3. Kyle E. C. Booth
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    Correspondence to Michael Morin.

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    This article belongs to the Topical Collection: Integration of Constraint Programming, Artificial Intelligence, and Operations Research

    Guest Editor: Willem-Jan van Hoeve

    ‡ Margarita P. Castro and Kyle E.C. Booth equally contributing authors.

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    Morin, M., Castro, M.P., Booth, K.E.C. et al. Intruder alert! Optimization models for solving the mobile robot graph-clear problem. Constraints 23, 335–354 (2018). https://doi.org/10.1007/s10601-018-9288-3

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