Petri网与优化算法结合求解FMS调度研究综述

Petri网是基于图形的强有力的建模工具,被用于柔性制造系统调度问题的研究,然而,搜索整个可达树寻找最优调度方案是一个指数倍复杂的问题,由此人们想到利用人工智能算法搜索可达树的一部分获得近优解。该方法被认为是求解调度问题的极具前途的解决方案。从上世纪90年代初期以来,人们对此作了一些卓有成效的研究,对这些研究进行归纳总结,为采用该方法求解调度优化问题的研究提供参考。     

Flexible manufacturing system (FMS) scheduling using filtered beam search

This paper reports our effort to develop a knowledge based system for scheduling jobs in a flexible manufacturing system (FMS). We view FMS scheduling as a two-stage process: static scheduling, followed by real-time rescheduling if unanticipated events were to occur. This paper deals with the static scheduling stage. The system uses a frame-based knowledge representation scheme and a problem-solving strategy based on filtered beam search. Filtered beam search views a scheduling problem as a state space search and generates a good schedule quickly by controlling the amount of search required. Evaluation functions are used to decide which branches are the most promising. An important feature of this system, in our view, is the explicit manner in which environmental, procedural and structural knowledge, (stored in the knowledge base using a frame-based scheme) can be used to improve the quality of the generated schedule. The system has been implemented and tested using Common Lisp on a Macintosh system with a 3MB main memory and a 40MB hard disk. Computational experience with our system is reported.     

Deadlock-free scheduling for flexible manufacturing systems using Petri nets and heuristic search

Deadlock-free control and scheduling are two different problems for flexible manufacturing systems (FMSs). They are significant for improving the behaviors of the systems. Based on the Petri net models of FMSs, this paper embeds deadlock control policies into heuristic search algorithm, and proposes a deadlock-free scheduling algorithm to minimize makespan for FMSs. Scheduling is performed as heuristic search in the reachability graph of the Petri net. The searching process is guided by a heuristic function based on firing count vectors of state equation for the Petri net. By using the one-step look-ahead method in the optimal deadlock control policy, the safety of a state is checked. Experimental results are provided to show effectiveness of the proposed heuristic search approach in deadlock-free scheduling for FMSs.     

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.     

Solving distributed FMS scheduling problems subject to maintenance: Genetic algorithms approach

In general, distributed scheduling problem focuses on simultaneously solving two issues: (i) allocation of jobs to suitable factories and (ii) determination of the corresponding production scheduling in each factory. The objective of this approach is to maximize the system efficiency by finding an optimal planning for a better collaboration among various processes. This makes distributed scheduling problems more complicated than classical production scheduling ones. With the addition of alternative production routing, the problems are even more complicated. Conventionally, machines are usually assumed to be available without interruption during the production scheduling. Maintenance is not considered. However, every machine requires maintenance, and the maintenance policy directly affects the machine's availability. Consequently, it influences the production scheduling. In this connection, maintenance should be considered in distributed scheduling. The objective of this paper is to propose a genetic algorithm with dominant genes (GADG) approach to deal with distributed flexible manufacturing system (FMS) scheduling problems subject to machine maintenance constraint. The optimization performance of the proposed GADG will be compared with other existing approaches, such as simple genetic algorithms to demonstrate its reliability. The significance and benefits of considering maintenance in distributed scheduling will also be demonstrated by simulation runs on a sample problem.     

Minimizing cycle time and group scheduling, using Petri nets a study of heuristic methods

The objective of this paper is a study of minimizing the maximum completion time min F _max, or cycle time of the last job of a given family of jobs using flow shop heuristic scheduling techniques. Three methods are presented: minimize idle time (MIT); Campbell, Dudek and Smith (CDS); and Palmer. An example problem with ten jobs and five machines is used to compare results of these methods. A deterministic t-timed colored Petri net model has been developed for scheduling problem. An execution of the deterministic timed Petri net allows to compute performance measures by applying graph traversing algorithms starting from initial global state and going into a desirable final state(s) of the production system. The objective of the job scheduling policy is minimizing the cycle time of the last job scheduled in the pipeline of a given family of jobs. Three heuristic scheduling methods have been implemented. First, a sub-optimal sequence of jobs to be scheduled is generated. Second, a Petri net-based simulator with graphical user interface to monitor execution of the sequence of tasks on machines is dynamically designed. A deterministic t-timed colored Petri net model has been developed and implemented for flexible manufacturing systems (FMS). An execution of the deterministic timed Petri net into a reachability graph allows to compute performance measures by applying graph traversing algorithms starting from initial global state to a desirable final state(s) of the production system.     

A decentralized model for flow shop production with flexible transportation system

The recent advances in technology sectors often clash with traditional organizational paradigms which can limit or make difficult an efficient implementation in the real world. In this paper we show how it is possible to exploit the advantages of innovative technologies in manufacturing when these are supported by new and efficient methods for production management. More in details, we face a flow shop scheduling problem in a shoe manufacturing system in which overtaking of jobs is allowed thanks to an innovative transportation system. Overtaking means that a job can be put in waiting state and another job can surpass it, allowing the change of the scheduling sequence. Preemption is not allowed. The objective function of the problem is the minimization of the maximum lateness. We propose a decentralized model, based on multi-agent system theory, to represent the production cells of the plant and to include the potentiality offered by overtaking of jobs at decisional level. The adoption of a decentralized approach increases the system flexibility since each machine is able to solve its local scheduling problem. Adding or removing machines to the plant will not imply a change in the scheduling algorithms. The outcomes of this work are reached firstly through a formulation of the problem with three flow shop scheduling models, secondly through a comparison of the models with respect to different performance indicators. The results highlight as the decentralized approach is able to reach comparable performances with the centralized one for a relevant number of instances. Moreover sensitivity analysis shows as in the decentralized model the computational time required to solve bigger instances increases less quickly than in the case of centralized ones. Finally, simulations of the decentralized approach clarify as the correlation of the local solution procedure is effected by the number of machines of the flow shop and the coordination mechanism is effected by the number of the jobs to be scheduled.     

Scheduling Part‐Families Under FMS: To Mix or Not to Mix?

This paper considers the issue of whether to mix part-types in one or several of the families to be produced in a flexible manufacturing system (FMS). For this input control problem in an FMS, we have derived conditions that support the mixing of a part-type, which can share the setup of other part-types, in deterministic environment. The problem is identified as a special economic lot scheduling problem (ELSP), and is formulated as a linear programming problem. Analytical insights are derived by considering the special case with three part-families. The results are illustrated with a numerical example.     

时间Petri网的可调度分析及在FMS中的应用

在实时系统中,检查任务执行的计划是否满足要求的时间约束称为可调度分析.通过把时间特性与其他行为特性分离,提出了一种以时间Petri网建模的实时系统调度分析方法.如果特定任务的执行是可调度的,则可以计算任务执行的时间跨度,否则确定出不可调度的变迁以便于调整时间约束和纠正设计错误.提出了一种通过把复杂的任务序列分解成一些子序列来进行可调度性分析的综合时序分析技术,它不仅提高了效率,也有助于关于调度的可达性问题的讨论.讨论了柔性制造系统FMS中的车间装配子系统的可调度性.     

基于Petri网的启发式生产调度

提出一种新的柔性制造系统调度方法.该方法可以通过引入测试弧增强普通Petri网 的建模能力,可以对系统中的设备维护、设备优先级以及操作优先级进行建模,并进一步利用搜 索算法对模型的状态转换空间进行启发式搜索得到优化调度.文中的实例展示了算法的有 效性.     

Network-based hybrid genetic algorithm for scheduling in FMS environments

Scheduling in flexible manufacturing systems (FMS) must take account of the shorter lead-time, the multiprocessing environment, the flexibility of alternative workstations with different processing times, and the dynamically changing states. The best scheduling approach, as described here, is to minimize makespan t _M, total flow time t _F, and total tardiness penalty p _T. However, in the case of manufacturing system problems, it is difficult for those with traditional optimization techniques to cope with this. This article presents a new flow network-based hybrid genetic algorithm (hGA) approach for generating static schedules in a FMS environment. The proposed method is combined with the neighborhood search technique in a mutation operation to improve the solution of the FMS problem, and to enhance the performance of the genetic search process. We update the change in swap mutation and the local search-based mutation ration. Numerical experiments show that the proposed flow network-based hGA is both effective and efficient for FMS problems.This work was presented in part at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24–26, 2003     

Scheduling in a manufacturing shop with sequence-dependent setups

In this paper, the problem of scheduling multiple jobs in a flexible manufacturing cell with multiple machine stations is addressed. Due to the large capital investments that usually characterize flexible manufacturing systems (FMS), an area of control of great interest to system users is that of maximizing the system performance through the minimization of machine idle and setup times. The magnitude of total time spent on machine setups and idle times is influenced by the availability of jobs, job mix, similarities of jobs and job scheduling procedure used. Similar jobs on the same machine require less setup times. Similarly, the use of an adequate scheduling method also reduces total idle and setup times. Such reduction improves the flow times of jobs. In this paper, a heuristic algoritm for scheduling jobs with sequence dependent setup times in a FMS is presented. The measure of performance for evaluating schedule adequacy is the production makespan.     

LEARNING-BASED SCHEDULING OF FLEXIBLE MANUFACTURING SYSTEMS USING SUPPORT VECTOR MACHINES

Dispatching rules are usually applied to dynamically schedule jobs in flexible manufacturing systems (FMSs). Despite their frequent use a significant drawback is that the performance level of the rule is dictated by the current state of the manufacturing system. Because no rule is better than any other for every system state, it would be highly desirable to know which rule is the most appropriate for each given condition. To achieve this goal we propose a scheduling approach using support vector machines (SVMs). By using this technique and by analyzing the earlier performance of the system, “scheduling knowledge” is obtained whereby the right dispatching rule at each particular moment can be determined. Simulation results show that the proposed approach leads to significant performance improvements over existing dispatching rules. In the same way it is also confirmed that SVMs perform better than other traditional machine learning algorithms as the inductive learning when applied to FMS scheduling problem, due to their better generalization capability.     

Fuzzy rule generation for adaptive scheduling in a dynamic manufacturing environment

This paper proposes a fuzzy rule-based system for an adaptive scheduling, which dynamically selects and applies the most suitable strategy according to the current state of the scheduling environment. The adaptive scheduling problem is generally considered as a classification task since the performance of the adaptive scheduling system depends on the effectiveness of the mapping knowledge between system states and the best rules for the states. A rule base for this mapping is built and evolved by the proposed fuzzy dynamic learning classifier based on the training data cumulated by a simulation method. Distributed fuzzy sets approach, which uses multiple fuzzy numbers simultaneously, is adopted to recognize the system states. The developed fuzzy rules may readily be interpreted, adopted and, when necessary, modified by human experts. An application of the proposed method to a job-dispatching problem in a hypothetical flexible manufacturing system (FMS) shows that the method can develop more effective and robust rules than the traditional job-dispatching rules and a neural network approach.     

GA-based discrete dynamic programming approach for scheduling inFMS environments

The paper presents a new genetic algorithm (GA)-based discrete dynamic programming (DDP) approach for generating static schedules in a flexible manufacturing system (FMS) environment. This GA-DDP approach adopts a sequence-dependent schedule generation strategy, where a GA is employed to generate feasible job sequences and a series of discrete dynamic programs are constructed to generate legal schedules for a given sequence of jobs. In formulating the GA, different performance criteria could be easily included. The developed DDF algorithm is capable of identifying locally optimized partial schedules and shares the computation efficiency of dynamic programming. The algorithm is designed In such a way that it does not suffer from the state explosion problem inherent in pure dynamic programming approaches in FMS scheduling. Numerical examples are reported to illustrate the approach.     

Search strategy for scheduling flexible manufacturing systems simultaneously using admissible heuristic functions and nonadmissible heuristic functions

To scheduling flexible manufacturing system (FMS) efficiently, we propose and evaluate an improved search strategy and its application to FMS scheduling in the P-timed Petri net framework. On the execution of Petri net, the proposed method can simultaneously use admissible heuristic functions and nonadmissible heuristic functions for A^* algorithm. We also prove that the resulting combinational heuristic function is still admissible and more informed than any of its constituents. The experimental results of an example FMS and several sets of random generated problems show that the proposed search method performs better as we expected.     

Filtered-beam-search-based algorithm for dynamic rescheduling in FMS

In the practical production process of a flexible manufacturing system (FMS), unexpected disturbances such as rush orders arrival and machine breakdown may inevitably render the existing schedule infeasible. This makes dynamic rescheduling necessary to respond to the disturbances and to improve the efficiency of the disturbed FMS. Compared with the static scheduling, the dynamic rescheduling relies on more effective and robust search approaches for its critical requirement of real-time optimal response. In this paper, a filtered-beam-search (FBS) -based heuristic algorithm is proposed to solve the dynamic rescheduling problem in a large and complicated job shop FMS environment with realistic disturbances. To enhance its performance, the proposed algorithm makes improvement in the local/global evaluation functions and the generation procedure of branches. With respect to a due date-based objective (weighted quadratic tardiness), computational experiments are studied to evaluate the performance of the proposed algorithm in comparison with those of other popular methods. The results show that the proposed FBS-based algorithm performs very well for dynamic rescheduling in terms of computational efficiency and solution quality.     

Improved methods for scheduling flexible manufacturing systems based on Petri nets and heuristic search

This paper proposes and evaluates two improved Petri net （PN）-based hybrid search strategies and their applications to flexible manufacturing system （FMS） scheduling. The algorithms proposed in some previous papers, which combine PN simulation capabilities with A＊ heuristic search within the PN reachability graph,may not find an optimum solution even with an admissible heuristic function. To remedy the defects an improved heuristic search strategy is proposed, which adopts a different method for selecting the promising markings and reserves the admissibility of the algorithm. To speed up the search process, another algorithm is also proposed which invokes faster termination conditions and still guarantees that the solution found is optimum. The scheduling results are compared through a simple FMS between our algorithms and the previous methods. They are also applied and evaluated in a set of randomly-generated FMSs with such characteristics as multiple resources and alternative routes.     

Improved methods f or scheduling flexible manufacturing systems based on Pet ri nets and heuristic search

This paper proposes and evaluates two improved Petri net (PN) - based hybrid search strategies and their applications to flexible manufacturing system (FMS) scheduling. The algorithms proposed in some previous papers ,which combine PN simulation capabilities with A 3 heuristic search within the PN reachability graph ,may not find an optimum solution even with an admissible heuristic function. To remedy the defects an improved heuristic search strategy is proposed ,which adopts a different method for selecting the promising markings and reserves the admissibility of the algorithm. To speed up the search process ,another algorithm is also proposed which invokes faster termination conditions and still guarantees that the solution found is optimum. The scheduling results are compared through a simple FMS between our algorithms and the previous methods. They are also applied and evaluated in a set of randomly- generated FMSs with such characteristics as multiple resources and alternative routes.     

整合Petri网和蚁群优化算法用于柔性制造系统调度优化研究

以Petri网与蚁群优化算法相结合，求解柔性制造系统的调度问题，取得了明显的优化效果。以一个典型算例的调度优化为例，证明了算法的有效性。