Keyi Xing

Optimal Petri-Net-Based Polynomial-Complexity Deadlock-Avoidance Policies for Automated Manufacturing Systems

Even for a simple automated manufacturing system (AMS), such as a general single-unit resource allocation system, the computation of an optimal or maximally permissive deadlock-avoidance policy (DAP) is NP-hard. Based on its Petri-net model, this paper addresses the deadlock-avoidance problem in AMSs, which can be modeled by systems of simple sequential processes with resources. First, deadlock is characterized as a perfect resource-transition circuit that is saturated at a reachable state. Second, for AMSs that do not have one-unit resources shared by two or more perfect resource-transition circuits that do not contain each other, it is proved that there are only two kinds of reachable states: safe states and deadlock. An algorithm for determining the safety of a new state resulting from a safe one is then presented, which has polynomial complexity. Hence, the optimal DAP with polynomial complexity can be obtained by a one-step look-ahead method, and the deadlock-avoidance problem is polynomially solved with Petri nets for the first time. Finally, by reducing a Petri-net model and applying the design of optimal DAP to the reduced one, a suboptimal DAP for a general AMS is synthesized, and its computation is of polynomial complexity.

Resource-Transition Circuits and Siphons for Deadlock Control of Automated Manufacturing Systems

The resource-transition circuit ( RTC) and siphon are two different structural objects of Petri nets and used to develop deadlock control policies for automated manufacturing systems. They are related to the liveness property of Petri net models and thus used to characterize and avoid deadlocks. Based on them, there are two kinds of methods for developing deadlock controllers. Such methods rely on the computation of all maximal perfect RTCs and strict minimal siphons (SMSs), respectively. This paper concentrates on a class of Petri nets called a system of simple sequential processes with resources, establishes the relation between two kinds of control methods, and identifies maximal perfect RTCs and SMSs. A graph-based technique is used to find all elementary RTC structures. They are then used to derive all RTCs. Next, an iterative method is developed to recursively construct all maximal perfect RTCs from elementary ones. Finally, a one-to-one correspondence between SMSs and maximal perfect RTCs and, hence, an equivalence between two deadlock control methods are established.

Deadlock-Free Genetic Scheduling Algorithm for Automated Manufacturing Systems Based on Deadlock Control Policy

Deadlock-free control and scheduling are vital for optimizing the performance of automated manufacturing systems (AMSs) with shared resources and route flexibility. Based on the Petri net models of AMSs, this paper embeds the optimal deadlock avoidance policy into the genetic algorithm and develops a novel deadlock-free genetic scheduling algorithm for AMSs. A possible solution of the scheduling problem is coded as a chromosome representation that is a permutation with repetition of parts. By using the one-step look-ahead method in the optimal deadlock control policy, the feasibility of a chromosome is checked, and infeasible chromosomes are amended into feasible ones, which can be easily decoded into a feasible deadlock-free schedule. The chromosome representation and polynomial complexity of checking and amending procedures together support the cooperative aspect of genetic search for scheduling problems strongly.

Transition Cover-Based Design of Petri Net Controllers for Automated Manufacturing Systems

In automated manufacturing systems (AMSs), deadlock problems must be well solved. Many deadlock control policies, which are based on siphons or Resource-Transition Circuits (RTCs) of Petri net models of AMSs, have been proposed. To obtain a live Petri net controller of small size, this paper proposes for the first time the concept of transition covers in Petri net models. A transition cover is a set of Maximal Perfect RTCs (MPCs), and the transition set of its MPCs can cover the set of transitions of all MPCs. By adding a control place with the proper control variable to each MPC in an effective transition cover to make sure that it is not saturated, it is proved that deadlocks can be prevented, whereas the control variables can be obtained by linear integer programming. Since the number of MPCs in an effective transition cover is less than twice that of transition vertices, the obtained controller is of small size. The effectiveness of a transition cover is checked, and ineffective transition covers can be transformed into effective ones. Some examples are used to illustrate the proposed methods and show the advantage over the previous ones.

Deadlock prevention for flexible manufacturing systems via controllable siphon basis of Petri nets

Siphons are a kind of special structural objects in a Petri net, and plays a key role in synthesizing a live Petri net controller for flexible manufacturing systems. In order to obtain a small size Petri net controller, this paper introduces the concept of a controllable siphon basis. It then proves that a live Petri net controller can be established by adding a control place and related arcs to each strict minimal siphon (SMS) in a controllable siphon basis. The initial markings of control places are determined by an integer linear program. The number of control places in the obtained controllers is the same as the number of SMSs in the controllable siphon basis, while the latter is no more than that of the activity places in a Petri net model. An algorithm for constructing a controllable siphon basis is proposed, and a new deadlock prevention policy based on it is established. A few examples are provided to demonstrate the proposed concepts and policy and used to compare them with the state-of-the-art methods.

Deadlock-Free Scheduling of Automated Manufacturing Systems Using Petri Nets and Hybrid Heuristic Search

This paper focuses on the deadlock-free scheduling problem of automated manufacturing systems with shared resources and route flexibility, and develops novel scheduling methods by combining deadlock control policies and hybrid heuristic search. Place-timed Petri nets are used to model the systems and find a feasible sequence of firing transitions in the built model such that the firing time of its last transition is as small as possible. Based on the reachability graph of the net and a minimum processing time matrix, new heuristic and selection functions are designed to guide search processes. The proposed hybrid heuristic search is based on state space exploration and hence suffers from the state space explosion problem. In order to reduce the explored space, the search is restrained within a limited local search window. By embedding the deadlock-avoidance policies into the search processes, a novel deadlock-free hybrid heuristic search algorithm is developed. Experimental results indicate the effectiveness and superiority of the proposed algorithm over the state-of-the-art method.

Deadlock-free genetic scheduling for flexible manufacturing systems using Petri nets and deadlock controllers

In this paper, a new deadlock-free scheduling method based on genetic algorithm and Petri net models of flexible manufacturing systems is proposed. The optimisation criterion is to minimise the makespan. In the proposed genetic scheduling algorithm, a candidate schedule is represented by a chromosome that consists of two sections: route selection and operation sequence. With the support of a deadlock controller, a repairing algorithm is proposed to check the feasibility of each chromosome and fix infeasible chromosomes to feasible ones. A feasible chromosome can be easily decoded to a deadlock-free schedule, which is a sequence of transitions without deadlocks. Different kinds of crossover and mutation operations are performed on two sections of the chromosome, respectively, to improve the performance of the presented algorithm. Computational results show that the proposed algorithm can get better schedules. Furthermore, the proposed scheduling method provides a new approach to evaluate the performance of different deadlock controllers.

Minimizing the total completion time in a distributed two stage assembly system with setup times

In this paper, a novel distributed two stage assembly flowshop scheduling problem (DTSAFSP) is addressed. The objective is to assign jobs to several factories and schedule the jobs in each factory with the minimum total completion time (TCT). In view of the NP-hardness of the DTSAFSP, we develop heuristics method to deal with the problem and propose three hybrid meta-heuristics (HVNS, HGA-RVNS, and HDDE-RVNS). The parameters of HGA-RVNS and HDDE-RVNS are tuned by using the Taguchi method and that of HVNS is done by using the single factor ANOVA method. Computational experiments have been conducted to compare the performances of the proposed algorithms. The analyses of computational results show that, for the instances with small numbers of jobs, HDDE-RVNS obtains better performances than HGA-RVNS and HVNS; whereas for the instances with large numbers of jobs, HGA-RVNS is the best one in all the proposed algorithms. Computational results indicate that the performances of the HDDE-RVNS and HGA-RVNS are not much affected by the number of machines at the first stage and factories. The experimental results also show that the RVNS-based local search steps in both HGA-RVNS and HDDE-RVNS are efficient and effective.

Robust supervisory control for avoiding deadlocks in automated manufacturing systems with one specified unreliable resource

The design of supervisory controllers to resolve any deadlock issue in automated manufacturing systems (AMSs) has attracted the efforts of many researchers. A great deal of work, which assumes that allocated resources do not fail, has been done, while only a few works pay attention to the existence of unreliable resources in AMSs. In this paper, we focus on the robust supervisory control for avoiding deadlocks in AMSs, each of which has one specified unreliable resource. We develop a robust supervisory control policy under which the system can continue producing without manual intervention in the face of the unreliable resource’s failure and recovery. Our policy consists of a modified Banker’s Algorithm and the available resource constraints. After proving the correctness of our policy, we show that there are more reachable states under our policy than the existing one. Therefore, our policy imposes less restrictive constraints on the system and is more permissive than the original one. Finally, an example is provided to illustrate our control policy’s advantage in permissiveness.

A robust deadlock prevention control for automated manufacturing systems with unreliable resources

For a deadlock problem in automated manufacturing systems (AMSs) with unreliable resources, the existing control methods mostly belong to the class of deadlock avoidance. This paper focuses on deadlock prevention for AMSs with an unreliable resource. We use Petri nets to model such AMSs and develop their robust deadlock prevention controller. The controller is designed in three layers. In the first layer, the optimal controller is used to ensure that the system can process all types of parts in the absence of resource failures. The function of the second layer controller is to ensure that, when a fault of the unreliable resource occurs at any reachable state, all parts not requiring the faulty resource can be processed and all resources, that they need, but are held by parts requiring the faulty resource for further processing, can be released in order to maximize the resource utilization. The so-called second-level deadlocks caused by the controllers are prevented by the third layer controller. These three controllers together are shown to satisfy the desired properties and hence, able to ensure the robust deadlock-free operation of AMSs with an unreliable resource.