Robust patrol strategies against attacks at dispersed heterogeneous locations

We study a patrol problem where several patrollers move between heterogeneous locations dispersed throughout an area of interest in order to detect potential enemy attacks. To formulate an effective patrol policy, the patrollers must take into account travel time between locations, as well as location-specific attributes, such as time required for a patrol inspection, time required by an adversary to carry out an attack, and cost incurred due to an undetected attack. The patrol team wants to determine a robust patrol strategy that minimises the expected cost when, and if, an attack happens, regardless of where an intelligent enemy chooses to attack. For the case of a single patroller, we can compute the optimal solution via linear programming. For the case of multiple patrollers, we focus on efficient heuristic strategies based on set partitions and shortest paths.