Coordinated defender strategies for border patrols

Víctor Bucarey 1 Carlos Casorrán 2 Martine Labbé 2 Fernando Ordóñez 1 Oscar Figueroa 3
2 INOCS - Integrated Optimization with Complex Structure
ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : An effective patrol of a large area can require the coordinated action of diverse security resources. In this work we formulate a Stackelberg Security game that coordinates such resources in a border patrol problem. In this security domain, resources from different precincts have to be paired to conduct patrols in the border due to logistic constraints. Given this structure the set of pure defender strategies is of exponential size. We describe the set of mixed strategies using a polynomial number of variables but exponentially many constraints that come from the matching polytope. We then include this description in a mixed integer formulation to compute the Strong Stackelberg Equilibrium efficiently with a branch and cut scheme. Since the optimal patrol solution is a probability distribution over the set of exponential size, we also introduce an efficient sampling method that can be used to deploy the security resources every shift. Our computational results evaluate the efficiency of the branch and cut scheme developed and the accuracy of the sampling method. We show the applicability of the methodology by solving a real world border patrol problem.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-01917782
Contributor : Martine Labbé <>
Submitted on : Friday, November 9, 2018 - 4:46:26 PM
Last modification on : Friday, April 19, 2019 - 4:55:04 PM
Long-term archiving on : Sunday, February 10, 2019 - 3:00:32 PM

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Víctor Bucarey, Carlos Casorrán, Martine Labbé, Fernando Ordóñez, Oscar Figueroa. Coordinated defender strategies for border patrols. 2018. ⟨hal-01917782⟩

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