Parsimonious Monitor Control of Petri Net models of FMS

Most approaches for deadlock prevention and liveness enforcement in Petri nets rely on siphon control methods or the theory of regions to derive monitor-based supervisors. These techniques raise methodological and computational issues, from the existence of feasible solutions to the hardness of guaranteeing maximal permissivity and optimality in the size and cost of the control subnet. Recently, the supervisor design problem has also been reformulated as a direct monitor optimization task based on integer linear programming, which can more effectively deal with the mentioned issues and objectives. This paper introduces an efficient branch-and-bound scheme for the exploration of the solution space of the direct monitor optimization problem. An extensive computational analysis on a set of benchmark instances demonstrates the efficiency of the approach.