A branch-and-cut algorithm for the Edge Interdiction Clique Problem

Furini, Fabio; Ljubić, Ivana; Segundo, Pablo San; Zhao, Yanlu

doi:10.1016/j.ejor.2021.01.030

Cited by 17 publications

(4 citation statements)

References 33 publications

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“…Since the instances of our benchmark are quite dense (see Section 4 ), the maximum independent set problems solved during the SORT procedure are expected to be easy. From a computational perspective, maximum independent sets are typically easy on dense graphs, as observed in several papers, see e.g., Li et al (2017) ;San Segundo et al (2016) , also in the context of interdiction problems, see, e.g., Furini, Ljubi ć, Martin, & San Segundo (2019) ; Furini, Ljubi ć, San Segundo, & Zhao (2021) . This is due to several factors, the two main ones are: i ) dense graphs contain small independent sets and, for this reason, it is easy to find goodquality heuristics solutions; ii ) in dense graphs, the upper bounds used to reduce the branching tree are expected to be tight.…”

Section: The Re-partition Procedures Of Bfilt+mentioning

confidence: 92%

A new branch-and-filter exact algorithm for binary constraint satisfaction problems

Segundo

Furini

Leon³

2022

European Journal of Operational Research

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Section: The Re-partition Procedures Of Bfilt+mentioning

confidence: 92%

A new branch-and-filter exact algorithm for binary constraint satisfaction problems

Segundo

Furini

Leon³

2022

European Journal of Operational Research

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“…At the lower level, the defender solves the recourse problem over the set of surviving or partially damaged assets. IGs arise in military applications (Brown et al, 2006), in controlling the spread of infectious diseases (Assimakopoulos, 1987;Shen et al, 2012;Furini et al, 2021aFurini et al, , 2020Tanınmış et al, 2021), in counter-terrorism (Wang et al, 2016), or in monitoring of communication networks (Furini et al, 2021b(Furini et al, , 2019. Very often, IGs are defined over networks, in which the attacker reduces the capacities of nodes or edges, or even completely removes some of them from the network (Cochran et al, 2011).…”

Section: Previous and Related Workmentioning

confidence: 99%

“…Some of the most famous examples of so-called network-interdiction games include interdiction of shortest paths (Israeli and Wood, 2002) or network flows (Lim and Smith, 2007;Smith and Lim, 2008;Akgün et al, 2011). However, IGs turn out to be much more difficult if the recourse problem is NP-hard, like maximum knapsack (Caprara et al, 2016;Fischetti et al, 2019;Della Croce and Scatamacchia, 2020) or maximum clique (Furini et al, 2021b(Furini et al, , 2019, making the associated IG a Σ P 2 -hard problem (Lodi et al, 2014). In FGs, the defender tries to "interdict" the attacker, by anticipating the attacker's malicious activities, i.e., the defender tries to protect the most vulnerable assets before the attack is taking place.…”

Section: Previous and Related Workmentioning

confidence: 99%

An Exact Method for Fortification Games

Leitner¹,

Ljubić²,

Monaci³

et al. 2021

Preprint

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A fortification game (FG) is a three-level, two-player Stackelberg game, also known as defenderattacker-defender game, in which at the uppermost level, the defender selects some assets to be protected from potential malicious attacks. At the middle level, the attacker solves an interdiction game by depreciating unprotected assets, i.e., reducing the values of such assets for the defender, while at the innermost level the defender solves a recourse problem over the surviving or partially damaged assets. Fortification games have applications in various important areas, such as military operations, design of survivable networks, protection of facilities or power grid protection. In this work, we present an exact solution algorithm for FGs, in which the recourse problems correspond to (possibly NP-hard) combinatorial optimization problems. The algorithm is based on a new generic mixed-integer linear programming reformulation in the natural space of fortification variables. Our new model makes use of fortification cuts that measure the contribution of a given fortification strategy to the objective function value. These cuts are generated on-the-fly by solving separation problems, which correspond to (modified) middle-level interdiction games. We design a branch-and-cut-based solution algorithm based on fortification cuts, their lifted versions and other speed-up techniques. We present a computational study using the knapsack fortification game and the shortest path fortification game. For the latter one, we include a comparison with a state-of-the-art solution method from the literature. Our algorithm outperforms this method and allows us to solve previously unsolved instances to optimality.

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“…Another interdiction problem which recently got more attention in literature is the clique interdiction problem. The problem involves minimizing the size of the maximum clique in a network, by interdicting, i.e., removing, a subset of its edges (Tang et al, 2016;Furini et al, 2021) or vertices (Furini et al, 2019).…”

Section: Previous and Related Workmentioning

confidence: 99%

A branch-and-cut algorithm for submodular interdiction games

Tanınmış¹,

Sinnl²

2021

Preprint

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Many relevant applications from diverse areas such as marketing, wildlife conservation or defending critical infrastructure can be modeled as interdiction games. In this work, we introduce interdiction games whose objective is a monotone and submodular set function. Given a ground set of items, the leader interdicts the usage of some of the items of the follower in order to minimize the objective value achievable by the follower, who seeks to maximize a submodular set function over the uninterdicted items subject to knapsack constraints.We propose an exact branch-and-cut algorithm for these kind of interdiction games. The algorithm is based on interdiction cuts which allow to capture the followers objective function value for a given interdiction decision of the leader and exploit the submodularity of the objective function. We also present extensions and liftings of these cuts and discuss additional preprocessing procedures.We test our solution framework on the weighted maximal covering interdiction game and the bipartite inference interdiction game. For both applications, the improved variants of our interdiction cut perform significantly better than its basic version. For the weighted maximal covering interdiction game for which a mixed-integer bilevel linear programming (MIBLP) formulation is available, we compare the results with those of a state-of-the-art MIBLP solver. While the MIBLP solver yields a minimum of 54% optimality gap within one hour, our best branch-and-cut setting solves all but 4 of 108 instances to optimality with a maximum of 3% gap among unsolved ones.

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A branch-and-cut algorithm for the Edge Interdiction Clique Problem

Cited by 17 publications

References 33 publications

A new branch-and-filter exact algorithm for binary constraint satisfaction problems

A new branch-and-filter exact algorithm for binary constraint satisfaction problems

An Exact Method for Fortification Games

A branch-and-cut algorithm for submodular interdiction games

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