Shortest Legal Firing Sequence of Net Condition/Event Systems Using Integer Linear Programming

Abstract

Net condition/event systems (NCESs) are modular extensions of the well-known Petri nets. Due to their modular property and non-interleaving semantics, NCESs are applied in modeling, analysis, and control of dynamic reconfigurable discrete event systems in recent years. A system reconfiguration should be finished before the maximum permissible reconfiguration delay. Therefore, to compute a shortest legal firing sequence (SLFS) from the state where a reconfiguration requirement arises to a target state which is proper for implementing the required reconfiguration is necessary. This paper combines the optimality principle and integer linear programming (ILP) techniques to find an SLFS in NCESs under the firing rule `arbitrary maximal steps', where both event processing modes `AND' and `OR' of transitions are considered. An SLFS can be computed in a single ILP step. The amount of variables and constraints is polynomial with the size of the underlying NCES and the maximum permissible reconfiguration delay. A manufacturing system is adopted as an illustrative example.