TY - JOUR
T1 - A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games
AU - Contardo, Claudio
AU - Sefair, Jorge A.
N1 - Funding Information:
History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms — Discrete. Funding: This work was supported by the United States National Science Foundation (NSF) [Grants 1740042 and 2039917] and the Natural Sciences and Engineering Research Council of Canada (NSERC) [Grant DG-2020-06311]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2021.1085.
Publisher Copyright:
© 2021 INFORMS.
PY - 2022/3
Y1 - 2022/3
N2 - We present a progressive approximation algorithmfor the exact solution of several classes of interdiction games in which two noncooperative players (namely an attacker and a follower) interact sequentially. The follower must solve an optimization problem that has been previously perturbed by means of a series of attacking actions led by the attacker. These attacking actions aim at augmenting the cost of the decision variables of the follower's optimization problem. The objective, from the attacker's viewpoint, is that of choosing an attacking strategy that reduces as much as possible the quality of the optimal solution attainable by the follower. The progressive approximationmechanismconsists of the iterative solution of an interdiction probleminwhich the attacker actions are restricted to a subset of thewhole solution space and a pricing subprobleminvokedwith the objective of proving the optimality of the attacking strategy. This scheme is especially useful when the optimal solutions to the follower's subproblem intersect with the decision space of the attacker only in a small number of decision variables. In such cases, the progressive approximation method can solve interdiction games otherwise intractable for classicalmethods.We illustrate the efficiency of our approach on the shortest path, 0-1 knapsack and facility location interdiction games. Summary of Contribution: In this article, we present a progressive approximation algorithm for the exact solution of several classes of interdiction games in which two noncooperative players (namely an attacker and a follower) interact sequentially. We exploit the discrete nature of this interdiction game to design an effective algorithmic framework that improves the performance of general-purpose solvers. Our algorithm combines elements from mathematical programming and computer science, including a metaheuristic algorithm, a binary search procedure, a cutting-planes algorithm, and supervalid inequalities. Although we illustrate our results on three specific problems (shortest path, 0-1 knapsack, and facility location), our algorithmic framework can be extended to a broader class of interdiction problems.
AB - We present a progressive approximation algorithmfor the exact solution of several classes of interdiction games in which two noncooperative players (namely an attacker and a follower) interact sequentially. The follower must solve an optimization problem that has been previously perturbed by means of a series of attacking actions led by the attacker. These attacking actions aim at augmenting the cost of the decision variables of the follower's optimization problem. The objective, from the attacker's viewpoint, is that of choosing an attacking strategy that reduces as much as possible the quality of the optimal solution attainable by the follower. The progressive approximationmechanismconsists of the iterative solution of an interdiction probleminwhich the attacker actions are restricted to a subset of thewhole solution space and a pricing subprobleminvokedwith the objective of proving the optimality of the attacking strategy. This scheme is especially useful when the optimal solutions to the follower's subproblem intersect with the decision space of the attacker only in a small number of decision variables. In such cases, the progressive approximation method can solve interdiction games otherwise intractable for classicalmethods.We illustrate the efficiency of our approach on the shortest path, 0-1 knapsack and facility location interdiction games. Summary of Contribution: In this article, we present a progressive approximation algorithm for the exact solution of several classes of interdiction games in which two noncooperative players (namely an attacker and a follower) interact sequentially. We exploit the discrete nature of this interdiction game to design an effective algorithmic framework that improves the performance of general-purpose solvers. Our algorithm combines elements from mathematical programming and computer science, including a metaheuristic algorithm, a binary search procedure, a cutting-planes algorithm, and supervalid inequalities. Although we illustrate our results on three specific problems (shortest path, 0-1 knapsack, and facility location), our algorithmic framework can be extended to a broader class of interdiction problems.
KW - bilevel optimization
KW - integer programming
KW - Interdiction
KW - Stackelberg games
UR - http://www.scopus.com/inward/record.url?scp=85134468191&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85134468191&partnerID=8YFLogxK
U2 - 10.1287/ijoc.2021.1085
DO - 10.1287/ijoc.2021.1085
M3 - Article
AN - SCOPUS:85134468191
SN - 1091-9856
VL - 34
SP - 890
EP - 908
JO - INFORMS Journal on Computing
JF - INFORMS Journal on Computing
IS - 2
ER -