A Bilevel Programming Model for Proactive Countermeasure Selection in Complex ICT Systems A. Ridha Mahjoub 1 , M. Yassine Naghmouchi 1,2 , Nancy Perrot 2 Abstract We consider the Proactive Countermeasure Selection Problem (PCSP) for complex Information and Communication Technology (ICT) systems. Given 1) the Risk As- sessment Graphs (RAGs), a set of digraphs, in which a node is either an access point which is the start point of an attacker, or an asset-vulnerability node to be secured; 2) a positive security threshold for each access point and each asset-vulnerability node; and 3) a set of countermeasures to deploy on the asset-vulnerability nodes, the PCSP consists in selecting the countermeasures placement with minimal cost, guaranteeing the security of all the most likely paths- from attackers point of view- between each access point and each asset-vulnerability node. We propose a bilevel programming model for the PCSP. We present two single- level reformulations of the bilevel program. The first formulation is a compact one, based on primal-dual optimality conditions. The second formulation is an extended one, employing an exponential number of path constraints. We propose a branch-and-cut algorithm to solve this formulation to optimality. Several series of experiments are conducted on random instances showing the efficiency of the branch-and-cut algorithm to solve the extended formulation. In addition, prelimi- nary computational comparisons between the two formulations are discussed. Keywords: Bilevel programming, Risk Assessment Graphs, Countermeasure selection, Branch-and-cut. 1 Introduction Today ICT Systems are becoming more and more complex. They include a large number of heterogeneous elements connected by non-linear interactions, 1 Universit´ e Paris-Dauphine, PSL Research University, CNRS, LAMSADE, 75016, Paris, France. Email: mahjoub@lamsade.dauphine.fr, 2 Orange Labs, France. Email: firstname.lastname@orange.com Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 64 (2018) 295–304 1571-0653/© 2018 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm https://doi.org/10.1016/j.endm.2018.02.004