Deadlock-free Scheduling Research Articles

Deadlock-Free Scheduling of Flexible Assembly Systems Based on Petri Nets and Local Search

Deadlock-free scheduling and control is critical for optimizing the performance of flexible assembly systems (FASs). Based on the Petri net models of FASs, this paper integrates a deadlock prevention policy with local search and develops a novel deadlock-free scheduling algorithm. A solution of the scheduling problem is coded as a chromosome representation that is a permutation with repetition of parts. By using the deadlock prevention policy, a repairing algorithm (RA) is developed to repair unfeasible chromosomes. A perturbation strategy based on estimation of distribution algorithm is developed to escape from local optima. Moreover, to improve population diversity, an acceptance criterion (AC) based on Pareto dominance is proposed. The chromosome representation, RA, perturbation strategy, and AC together support the cooperative aspect of local search for scheduling problems strongly.

Local Planning Semantics: A Semantics for Distributed Real-Time Systems

Design, implementation and verification of distributed real-time systems are acknowledged to be very hard tasks. Such systems are prone to different kinds of delay, such as execution time of actions or communication delays implied by distributed platforms. The latter increase considerably the complexity of coordinating the parallel activities of running components. Scheduling such systems must cope with those delays by proposing execution strategies ensuring global consistency while satisfying the imposed timing constraints. In this paper, we investigate a formal model for such systems as compositions of timed automata subject to multiparty interactions, and propose a semantics aiming to overcome the communication delays problem through anticipating the execution of interactions. To be effective in a distributed context, scheduling an interaction should rely on (as much as possible) local information only, namely the state of its participating components. However, as shown in this paper these information is not always sufficient and does not guarantee a safe execution of the system as it may introduce deadlocks. Moreover, delays may also affect the satisfaction of timing constraints, which also corresponds to deadlocks in the former model. Thus, we also explore methods for analyzing such deadlock situations and for computing deadlock-free scheduling strategies when possible.

An Efficient Deadlock Prevention Policy for Noncyclic Scheduling of Multicluster Tools

Scheduling of multicluster tools has received much attention due to its complexity of interaction among cluster tools. A cluster tool comprises several modules such as processing modules, a transfer module with a single or dual-armed handling robot, and loadlock modules. A multicluster tool comprises two, three, or more cluster tools that are interconnected with each other. In this paper, we propose a deadlock prevention policy for noncyclic scheduling of dual-armed multicluster tools. The proposed deadlock prevention policy is effective for generating an efficient schedule for two or three-connected multicluster tools with a single or a dual-path flow. This is proven by analyzing the strict minimal siphon of the Petri net model. The performance of the proposed method is compared with that of a maximal permissible deadlock prevention policy. The results demonstrate that the proposed method is computationally efficient for larger state spaces and more suitable than conventional deadlock prevention policies for generating effective schedules for noncyclic scheduling of multicluster tools. Note to Practitioners —Scheduling of multicluster tools has recently attracted attention in the growing semiconductor manufacturing industry. Most conventional studies on multicluster tools focus on cyclic scheduling to minimize cycle time with swap strategy. The challenge addressed by this paper is to derive a deadlock-free schedule for multicluster tools with noncyclic operations. We propose a simple deadlock prevention policy that can be applied to large-scale timed Petri net (PN) model of general multicluster tools without enumeration of siphon computations or solution of mixed integer programming. A timed PN model is developed for noncyclic operations of dual-armed multicluster tools with a dual ath. The computational results show that the approximately 10% of the total throughput of the proposed method is better than those of the conventional methods. It enables more efficient operations for noncyclic scheduling under transient periods including cleaning operations.

Sufficient and necessary conditions to guarantee deadlock-free scheduling for an extended S3PR with correlated resources

ABSTRACTA deadlock prevention method is proposed for a special class of a system of simple sequential processes with resources (S3PR), where two kinds of interrelated resources exist such that the processing ability of each resource kind equals 1. The extended S3PR with correlated resources (ES3PR-CR) Petri net was first characterized and defined, and modeling procedures presented based on the Petri nets. Secondly, the sufficient and necessary conditions were presented to realize deadlock-free scheduling. By defining the maximal setting boundary for deadlock-free scheduling, a net-structure-based algorithm for resolution was proposed, as long as the initial marking of the Petri net was not greater than any one in , the controlled system never entered a deadlock state. This guaranteed that a controlled system had no deadlock while scheduling. Finally, a locomotive dispatching system in an underground coalmine was analyzed as an example to illustrate the validity of the proposed method. Compared with existing literature results, the proposed deadlock prevention method was net-structured and could be realized without any controller places, which provided a smaller size.

Optimizing Job Coscheduling by Adaptive Deadlock-Free Scheduler

It is ubiquitous that multiple jobs coexist on the same machine, because tens or hundreds of cores are able to reside on the same chip. To run multiple jobs efficiently, the schedulers should provide flexible scheduling logic. Besides, corunning jobs may compete for the shared resources, which may lead to performance degradation. While many scheduling algorithms have been proposed for supporting different scheduling logic schemes and alleviating this contention, job coscheduling without performance degradation on the same machine remains a challenging problem. In this paper, we propose a novel adaptive deadlock-free scheduler, which provides flexible scheduling logic schemes and adopts optimistic lock control mechanism to coordinate resource competition among corunning jobs. This scheduler exposes all underlying resource information to corunning jobs and gives them necessary utensils to make use of that information to compete resource in a free-for-all manner. To further relieve performance degradation of coscheduling, this scheduler enables the automated control over the number of active utensils when frequent conflict becomes the performance bottleneck. We justify our adaptive deadlock-free scheduling and present simulation results for synthetic and real-world workloads, in which we compare our proposed scheduler with two prevalent schedulers. It indicates that our proposed approach outperforms the compared schedulers in scheduling efficiency and scalability. Our results also manifest that the adaptive deadlock-free control facilitates significant improvements on the parallelism of node-level scheduling and the performance for workloads.

Near-Optimal Scheduling for Petri Net Models With Forbidden Markings

This paper is about control design for discrete event systems modeled with Petri nets. It addresses the problems of reachability and of firing sequence design. The untimed and timed cases are successively studied by searching control sequences from an initial marking to a reference one with length or duration that approach the minimal value, avoiding forbidden states and nonpromising branches. The proposed algorithms are applicable to a large class of discrete event systems in particular in the domain of flexible manufacturing, engineering. To accelerate the computation and make robust the control strategy, only a small area of the reachability graph is worked out and an approach inspired from model predictive control is used. The approach is suitable for deadlock-free scheduling and fault-tolerant control problems.

Petri Nets and Deadlock-Free Scheduling of Open Shop Manufacturing Systems

In this paper, we study the open shop scheduling problem with blocking and deadlocks. First, we develop a new Petri net class that extends the well-known $\text{S}^{3}\text{R}$ nets to handle the features of open shop systems. Next, we establish necessary conditions for deadlock-free operation based on the properties of a particular structural siphon. Then, we implement a graph search algorithm that intelligently explores the net reachability graph and uses a search strategy based on a double filtering mechanism and new evaluation functions. We conducted computational tests on a set of classical instances adapted from the literature. The quality of the solutions was established with a lower bound calculated with the aforementioned siphon. The results show the validity of the approach: the proposed algorithm found solutions with values that were very close to the lower bound in most cases.

Algorithms of reduced complexity to design control sequences for untimed Petri nets in varying and uncertain environments

Petri nets have been widely used for the modelling, analysis, control and optimization of discrete event systems with shared resources in the domains of engineering. This article concerns the design of control sequences for such systems modelled with untimed Petri nets. The aim of the controller is to incrementally compute sequences of transition firings with minimal size. Such sequences aim to move the marking from an initial value to a reference value. The resulting trajectory must avoid some forbidden markings and limit as possible the exploration of non-promising branches. For this purpose, the approach explores a small part of the reachability graph in the neighbourhood of the current marking. Then from the explored markings, it estimates a distance to the reference. The main contributions are (a) to reduce the explored part of the reachability graph according to a double limitation in breadth and in depth in order to provide solutions with a low computational effort; (b) to provide conditions to ensure the converge and optimality of the proposed algorithms and derive necessary and sufficient conditions for reachability; and (c) to include the firing sequence design in a global control schema suitable for reactive scheduling problems in uncertain and perturbed environments. The main application concerns deadlock-free scheduling problems in the domain of flexible manufacturing systems, but the approach is also applicable for systems in computer science and transportation.

An estimation of distribution algorithm for scheduling problem of flexible manufacturing systems using Petri nets

• This is the first report on applying estimation of distribution algorithm (EDA) to the studied problem. • A kind of PN-based deadlock controllers for FMSs is imbedded to exclude infeasible individuals. • An effective voting procedure is adopted to construct the probabilistic model of EDA. • The longest common subsequence is also embedded in the model for mining excellent genes. • A new modified variable neighborhood search is developed as an efficiency enhancement of EDA. Based on the place-timed Petri net models of flexible manufacturing systems (FMSs), this paper proposes a novel effective estimation of distribution algorithm (EDA) for solving the scheduling problem of FMSs. A candidate solution is represented as an individual with two sections: the first contains the route information while the second is a permutation with repetition for parts. The feasibility of individuals is checked and guaranteed by a highly permissiveness deadlock controller. A feasible individual is interpreted into a deadlock-free schedule while the infeasible ones are amended. The probabilistic model in EDA is constructed via a voting procedure. An offspring individual is then produced based on the model from a seed individual, and the set of seed individuals is extracted by a roulette method from the current population. The longest common subsequence is also embedded into the probabilistic model for mining good genes. A modified variable neighborhood search is applied on offspring individuals to obtain better solutions in their neighbors and hence to improve EDA’s performance. Computational results show that our proposed algorithm outperforms all the existing ones on benchmark examples for the studied problem. It is of important practice significance for the manufacturing of time-critical and multi-type products.

Dynamical Scheduling and Robust Control in Uncertain Environments with Petri Nets for DESs

This paper is about the incremental computation of control sequences for discrete event systems in uncertain environments where uncontrollable events may occur. Timed Petri nets are used for this purpose. The aim is to drive the marking of the net from an initial value to a reference one, in minimal or near-minimal time, by avoiding forbidden markings, deadlocks, and dead branches. The approach is similar to model predictive control with a finite set of control actions. At each step only a small area of the reachability graph is explored: this leads to a reasonable computational complexity. The robustness of the resulting trajectory is also evaluated according to a risk probability. A sufficient condition is provided to compute robust trajectories. The proposed results are applicable to a large class of discrete event systems, in particular in the domains of flexible manufacturing. However, they are also applicable to other domains as communication, computer science, transportation, and traffic as long as the considered systems admit Petri Nets (PNs) models. They are suitable for dynamical deadlock-free scheduling and reconfiguration problems in uncertain environments.

A new Hybrid Filtered Beam Search algorithm for deadlock-free scheduling of flexible manufacturing systems using Petri Nets

This paper presents a new Hybrid Filtered Beam Search algorithm for deadlock-free scheduling of flexible manufacturing systems. The proposed algorithm uses a diversification/intensification strategy that aims to selectively explore the state space of a Timed Place Petri Net that represents the dynamics of the system. The exploration strategy is based on a double filtering mechanism that limits the number of markings that can be expanded at each level of the search tree. The algorithm, which was tested on several benchmark instances from the literature, not only produces good quality schedules but it is also efficient in terms of memory requirements and computational time. In addition, the algorithm requires little tune-up and produces consistent results. Computational experiments show the effectiveness of the algorithm in comparison with other recent and state of the art methods.

Noncyclic scheduling of dual-armed cluster tools for minimization of wafer residency time and makespan

Cluster tools are used for semiconductor wafer fabrication. A cluster tool consists of several loadlock modules, processing modules, and material handling armed robots to transfer wafers between loadlocks and processing modules. Most conventional scheduling methods consider a cyclic schedule to minimize makespan. We consider noncyclic scheduling of dual-armed cluster tools. In practice, it is important to minimize wafer residency time in processing modules to maintain the surface quality of wafers. In the noncyclic operations, the cluster tool causes deadlock which may lead to excessive loss in the wafer fabrication process. We propose an efficient deadlock-free scheduling method for the noncyclic scheduling problem of a dual-armed cluster tool to minimize the residency time and makespan. The proposed method is applied to a dual-armed cluster tool with a non-revisiting process and a revisiting process. Computational results demonstrate the effectiveness of the proposed method.

Hybrid heuristic search approach for deadlock-free scheduling of flexible manufacturing systems using Petri nets

Based on the Petri net models of flexible manufacturing systems (FMSs), this paper focuses on deadlock-free scheduling problem with the objective of minimizing the makespan. Two hybrid heuristic search algorithms for solving such scheduling problems of FMSs are proposed. To avoid deadlocks, the deadlock control policy is embedded into heuristic search strategies. The proposed algorithms combine the heuristic best-first strategy with the controlled backtracking strategy based on the execution of the Petri nets. The scheduling problem is transformed into a heuristic search problem in the reachability graph of the Petri net, and a schedule is a transition sequence from the initial marking to the final marking in the reachability graph. By using the one-step look-ahead method in the deadlock control policy, the safety of a state in the reachability graph is checked, and hence, deadlock is avoided. Experimental results are provided and indicate the effectiveness of the proposed hybrid heuristic search algorithms in solving deadlock-free scheduling problems of FMSs. Especially, the comparison against previous work shows that both new algorithms are promising in terms of solution quality and computing times.

A hybrid discrete differential evolution algorithm for deadlock-free scheduling with setup times of flexible manufacturing systems

This paper proposes an effective hybrid discrete differential evolution (DDE) algorithm for solving a scheduling problem of flexible manufacturing systems (FMSs), where sequence-dependent setup times are considered. The objective is to find a deadlock-free schedule that minimizes the makespan. Based on the timed Petri net models of FMSs, a possible solution of the scheduling problem is represented as an individual that is a permutation with repetition of jobs. For the existence of deadlocks, most of the individuals cannot be directly decoded into feasible (live) schedules. Therefore, a deadlock controller is applied in the decoding scheme, and infeasible individuals are amended into feasible ones. Moreover, in order to overcome the premature convergence of DDE algorithm and improve solution quality, a variable neighbourhood search algorithm, which performs a systematic change of neighbourhood in solution searching, is adopted. Then a hybrid scheduling algorithm that combines a DDE with a variable neighbourhood search is presented. Computational results and comparison based on a variety of instances show the feasibility and superiority of the proposed algorithm.

Deadlock-free Production Scheduling with Dynamic Buffers in MES

In order to enable enterprises to change the production management mode and improve efficiency, MES provides overall solutions to information integration of manufacturing enterprises. Production scheduling is an important functional module in MES, and research of shop scheduling in MES has important significance. The concept deadlock is first put forward by computer science researchers who are engaged in resource allocation in the operation system. Modern manufacturing enterprises need to process complex workpieces with different processing step, so it is easy to produce a deadlock in the production process. A deadlock will bring many serious consequences for the system. Equipping with enough buffers can solve the problem of deadlock. However, it is costly and there is even no way to allocate buffers in some manufacturing industries. Considering the buffer cost and scheduling index, this paper puts forward the dynamic buffers deadlock-free scheduling to reduce cost and lower risk of the enterprise to a minimum.

Deadlock-free scheduling for flexible manufacturing systems using untimed Petri nets and model predictive control

This paper proposes algorithms that incrementally compute control sequences that drive the marking of untimed Petri nets from an initial value to a reference one, avoiding forbidden states with a length or duration that approaches the minimal value. The proposed algorithms are applicable to a large class of discrete event systems with or without temporal specifications in particular in the domain of flexible manufacturing, communication and computer science or transportation and traffic. To overcome the most burdensome part of the computations, the sequences encoded in a small area of the reachability graph are worked out. The main contribution is to propose an estimation of the minimal length or duration of the remaining sequences to the reference based on the computation of the firing count vectors. The approach is suitable for deadlock-free scheduling problems encountered with flexible manufacturing systems.

A Petri net-based particle swarm optimization approach for scheduling deadlock-prone flexible manufacturing systems

This paper proposes an effective hybrid particle swarm optimization (HPSO) algorithm to solve the deadlock-free scheduling problem of flexible manufacturing systems (FMSs) that are characterized with lot sizes, resource capacities, and routing flexibility. Based on the timed Petri net model of FMS, a random-key based solution representation is designed to encode the routing and sequencing information of a schedule into one particle. For the existence of deadlocks, most of the particles cannot be directly decoded to a feasible schedule. Therefore, a deadlock controller is applied in the decoding scheme to amend deadlock-prone schedules into feasible ones. Moreover, two improvement strategies, the particle normalization and the simulated annealing based local search, are designed and incorporated into particle swarm optimization algorithm to enhance the searching ability. The proposed HPSO is tested on a set of FMS examples, showing its superiority over existing algorithms in terms of both solution quality and robustness.

An impending deadlock-free scheduling method in the case of unified automated material handling systems in 300 mm wafer fabrications

Impending deadlock is difficult to detect on the track of the unified automated material handling systems in 300 mm wafer fabrications, and has been less examined. This paper proposes an impending deadlock detection model using a graphic formulation with new concepts of critical chains and shared nodes. A novel controlling method is presented to ensure critical chains have at least one empty node and sequence the OHTs’ entry of the shared nodes. This method is easy to apply and features real-time operation and large-scale systems. The effectiveness and efficiency of the proposed method is confirmed by simulation experiments.

Deadlock-Free Scheduling Method for Flexible Manufacturing Systems Based on Timed Colored Petri Nets and Anytime Heuristic Search

This paper addresses the deadlock (DL)-free scheduling problem of flexible manufacturing systems (FMS) characterized by resource sharing, limited buffer capacity, routing flexibility, and the availability of material handling systems. The FMS scheduling problem is formulated using timed colored Petri net (TCPN) modeling where each operation has a certain number of preconditions, an estimated duration, and a set of postconditions. Based on the reachability analysis of TCPN modeling, we propose a new anytime heuristic search algorithm which finds optimal or near-optimal DL-free schedules with respect to makespan as the performance criterion. The methodology tackles the time-constrained problem of very demanding systems (high diversity production and make-to-order) in which computational time is a critical factor to produce optimal schedules that are DL-free. In such a rapidly changing environment and under tight customer due-dates, producing optimal schedules becomes intractable given the time limitations and the NP-hard nature of scheduling problems. The proposed anytime search algorithm combines breadth-first iterative deepening A* with suboptimal breadth-first heuristic search and backtracking. It guarantees that the search produces the best solution obtained so far within the allotted computation time and provides better solutions when given more time. The effectiveness of the approach is evaluated on a comprehensive benchmark set of DL-prone FMS examples and the computational results show the superiority of the proposed approach over the previous works.

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.