Scheduling FMSs based on a hybrid Petri net framework

For solving flexible manufacturing system (FMS) scheduling problems based on Petri net execution, search algorithms need fewer redundant states in the reachability graph and a more efficient heuristic function to guide its expansion. In this paper, we illustrate that place-timed Petri nets (PTPNs) own advantages in restraining redundant states while transition-timed Petri nets (TTPNs) are beneficial for developing more efficient heuristic functions. We then propose a hybrid framework of the PTPN and TTPN. In this framework, a PTPN is used to construct the search algorithm and TTPN markings are transformed into PTPN markings. The lower bound of makespan can be calculated through a TTPN heuristic function to guide the search algorithm. As a result, overall search effort can be greatly reduced. The results demonstrate that the proposed method performs much better than existing methods.