As for the optimal scheduling issue of closely coupled the path planning of automated guided vehicles (AGVs) and task allocation in flexible manufacturing systems (FMSs), a heuristic optimization method is proposed based on Petri nets and an artificial potential field (APF). First, a manufacturing system with AGVs is described as a task Petri net and a path one, and then its Petri net model is obtained by composing the two nets together. Second, the topology of the Petri net model is used to design the potential energy parameters for the network junctions, and, consequently, the APF is designed for the Petri net model. Third, a heuristic functions is proposed to estimate the minimal terminate times of the Petri net model by means of its APF. Further, a heuristic beam search algorithm is presented to calculate a near optimal schedule by the Petri net model and its APF. Finally, numerical experiments are carried out, and the results show that optimal or near-optimal schedules can be calculated in the reasonable times by our algorithm.

Numerous mobile robots are employed for mate-rial transporting in today's manufacturing industry. Therefore,it is crucial to consider the time consumption of both processoperations and transportation to minimize the makespan. Thispaper addresses the joint scheduling optimization problem ofautomated guided vehicle (AGV) routing and task allocationfor robotic job shops (RJSs). A novel artificial potential field(APF) design method is developed based on place-timed Petrinets (PNs) for heuristic scheduling in RJSs. First, a real-life scaleRJS is modeled with a place-timed PN, which contains a routesubnet and several task ones. The scheduling problem is thentransformed into a search one for the transition firing sequencewith the minimum makespan, which can be obtained by theA* algorithm. Second, a task-APF design method is proposedfor sorting processes. It defines potential energy parameters forplaces in task subnets by utilizing the topological structure ofPNs. The heuristic functionhMPDis obtained, and it is proved tobe admissible. Experimental results show that thehMPDheuristicenables the A* algorithm to generate an optimal schedule forRJSs, and its search efficiency surpasses that of the mostadvanced admissible heuristic functions available, particularlyin the scenario described in this paper. However, its searchefficiency decreases significantly when the number of jobs andAGVs increases. Third, a route-APF design method is proposedfor AGV routing, and a novel heuristic function, denoted byhTPD,is developed based on the task-APF and route-APF. Experimentalresults demonstrate thathTPDis more adaptable for schedulingRJSs with large-scale jobs and multiple AGVs thanhMPD, whichimproves the search efficiency by an average of one order ofmagnitude. It can find an optimal or near-optimal schedule withina reasonable amount of time, even when dealing with hundredsof jobs and multiple AGVs.

This work focuses on real-time and joint optimizing issues to handle the routing of automated guided vehicles and allocating processing tasks for automated manufacturing systems. A real-time scheduling approach is proposed based on Petri nets and deep reinforcement learning. First, the considered system is modeled with a placed-timed Petri net, which plays the role of the environment for deep reinforcement learning. Second, a novel graph convolutional network (GCN), called Petri-net-GCN, is designed by using the topological structures of a Petri net model such that it can adapt to changes in Petri-net structures caused by abrupt events such as new orders and failures of devices. Third, a deep Q-network method is presented to train Petri-net-GCN to predict the minimal time to lead a Petri net to its goal if an action (transition) is taken at a present state. Consequently, Petri-net-GCN can replace scheduling rules to schedule an automated manufacturing system in real time. Finally, numerical experiments are carried out where there exist failures of devices and new orders. The results show that Petri-net-GCN can adapt to the Petri-net changes caused by abrupt events and performs much better than the first-in-first-out and longest-processing-time-first rules, which are applicable for real-time scheduling issues in practice.

When using timed Petri nets for modeling, Petri net model often tends to be huge, and this makes it difficult to design neural networks of Petri nets. To address this issue, this paper proposes a resource scheduling system automated guided vehicle(AGV) path planning method based on colored Petri nets and graph neural networks. First, the AGV system is described as a path Petri net, and different task types are assigned to the Petri net in different colors based on different process requirements, so that the same place or transition in the Petri net can represent multiple meanings, greatly simplifying the structure of the Petri net. Secondly, using the topological structure of the Petri net, a graph neural network that can be used on colored Petri nets is designed. The topological structure of the Petri net is divided into four categories, and is applied to the graph neural network as a correlation matrix for feature aggregation, achieving higher accuracy with fewer parameters. Thirdly, deep reinforcement learning is used to train the graph neural network, and the trained model is used as a heuristic to construct the A* algorithm to solve the scheduling problem of the system. Finally, several numerical experiments are conducted, and the results show that the scheduling method based on colored Petri nets and graph neural networks can simplify the structure of the Petri net while solving the joint problem of AGV task allocation and path planning in a limited time.

In this paper, to solve the scheduling problem of discrete event systems modeled by Place-timed Petri nets, a timed state graph with time information is designed to abstract the state space of Place-timed Petri nets. The feasible firing transitions sequence with the minimal duration is kept in the timed state graph. Furthermore, a modified timed state space is further designed with smaller size than the timed state graph, and it also keeps the feasible firing transitions sequence with the minimal duration. By searching these timed state graphs, we can find the optimal solution, i.e., the feasible firing transitions sequence with minimal duration directly.

As for the scheduling issue of flexible manufacturing systems (FMS), a heuristic method is proposed based on Petri nets and deep learning. First, an algorithm is presented to generate a heuristic data set by means of the operation rules of P-timed Petri nets. Second, a deep neural network (DNN) is designed to learn the heuristics of Petri net behavior from the data set. Third, the DNN is used as a heuristic function in a dynamic window search (DWS) algorithm to obtain an optimal or near-optimal schedule strategy for an FMS. Finally, a mechanical arm handling system is taken as an example, and numerical experiments are carried out. The results show that the DNN can represent a heuristic function with high precision, and its average estimation error is less than 0.05%, and that the proposed DWS algorithm is very efficient to resolve a given FMS schedul issue.

Parallel Petri nets are a class of Petri nets which can take into account scheduling and control issues of manufacturing systems [1]. However, Its designed relies on the manual effort, which is very difficult and boring for real manufacturing systems. Therefore, this work defines an improved planning domain definition language (PDDL) to automatically translate it to a parallel Petri net. In details, the PDDL syntax is extended to make it more accurate and convenient to describe actions, tasks and conditions. Elements of an extended PDDL are automatically represented by places and transitions of a parallel Petri net. Finally, an experiment is taken to illustrate and verify our method.