A Branch and Price Approach to Solving Security Games with Arbitrary Scheduling Constraints

Algorithms to solve security games have seen successful real-world deployment by LAX police and the Federal Air Marshal Service. These algorithms provide randomized schedules to optimally allocate limited security resources for infrastructure protection. Unfortunately, these algorithms fail to scale-up or to provide a correct solution for massive security games with arbitrary scheduling constraints. This paper provides ASPEN, a branch-and-price algorithm which exploits an innovative compact network flow representation, avoiding a combinatorial explosion of schedule allocations. ASPEN also uses a novel upper-bound generation to speed up the branch and bound. ASPEN is the first method for efficiently solving real-world-sized security games with arbitrary schedules.