An exact method for binary fortification games

Markus Leitner, Ivana Ljubić, Michele Monaci, Markus Sinnl and Kübra Tanınmış

European Journal of Operational Research, 2023, vol. 307, issue 3, 1026-1039

Abstract: A fortification game (FG) is a three-level, two-player hierarchical game, also known as defender-attacker-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 when needed 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 strengthened 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 with up to 330 386 nodes and 1 202 458 arcs to optimality.

Keywords: Combinatorial optimization; Three-level optimization; Branch-and-cut; Shortest path fortification; Maximum knapsack fortification (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:307:y:2023:i:3:p:1026-1039

DOI: 10.1016/j.ejor.2022.10.038

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