, Volume 23, Issue 3, pp 335–354 | Cite as

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

  • Michael MorinEmail author
  • Margarita P. Castro
  • Kyle E. C. Booth
  • Tony T. Tran
  • Chang Liu
  • J. Christopher Beck
Part of the following topical collections:
  1. Topical Collection on Integration of Constraint Programming, Artificial Intelligence, and Operations Research


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.


Pursuit-evasion Graph-clear problem Constraint programming Mixed-integer linear programming Optimization Mobile robotics 



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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Operations and Decision Support SystemsUniversité LavalQuébecCanada
  2. 2.Department of Mechanical and Industrial EngineeringUniversity of TorontoTorontoCanada

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