We study a patrol problem where several patrollers move between heterogeneous locations dispersed throughout an area of interest in order to detect enemy attacks. To formulate an e ective patrol policy, the patrollers must take into account travel time between locations, as well as location-speci c parameters, which include patroller inspection times, enemy attack times, and cost incurred due to an undetected attack. We consider both random and strategic attackers. A random attacker chooses a location to attack according to a probability distribution, while a strategic attacker plays a two-person zero-sum game with the patrollers. In some cases, we can compute the optimal solution using linear programming. This method, however, becomes computationally intractable as the problem size grows. Therefore, our research focuses on developing e cient heuristics, based on aggregate index values, ctitious play, and shortest paths. Numerical experiments demonstrate that our heuristics produce excellent results with computation time orders of magnitude less than what is required to compute the optimal solution.

Subjects: Optimal patrol; Multi-agent patrol; Semi-Markov decision process; Sequential decision making under uncertainty