2011/09/08 by Richard Chen, Chen, Richard, Amy Cohn +3
Computer Science · Mathematics · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #cs.DS #math.OC
paper · pdf · doi:10.48550/arxiv.1109.1801
arxiv created 2011/09/08 · arxiv updated 2011/09/09
We consider the problem of designing a network of minimum cost while satisfying a prescribed survivability criterion. The survivability criterion requires that a feasible flow must still exists (i.e. all demands can be satisfied without violating arc capacities) even after the disruption of a subset of the network's arcs. Specifically, we consider the case in which a disruption (random or malicious) can destroy a subset of the arcs, with the cost of the disruption not to exceed a disruption budget. This problem takes the form of a tri-level, two-player game, in which the network operator designs (or augments) the network, then the attacker launches a disruption that destroys a subset of arcs, and then the network operator attempts to find a feasible flow over the residual network. We first show how this can be modeled as a two-stage stochastic program from the network operator's perspective, with each of the exponential number of potential attacks considered as a disruption scenario. We then reformulate this problem, via a Benders decomposition, to consider the recourse decisions implicitly, greatly reducing the number of variables but at the expense of an exponential increase in the number of constraints. We next develop a cut-generation based algorithm. Rather than explicitly considering each disruption scenario to identify these Benders cuts, however, we develop a bi-level program and corresponding separation algorithm that enables us to implicitly evaluate the exponential set of disruption scenarios. Our computational results demonstrate the efficacy of this approach.