Deadlock analysis and control using Petri net decomposition techniques

Improved random selection strategy, self-adaptive crossover and mutation operators, population co-evolution algorithm are adopted in this paper to set up a new genetic algorithm(GA), guaranteeing the universality of population, the thoroughness of solution and the execution efficiency of algorithm in solving multi-process, process crossover, work-piece flow and other condition based scheduling problem of flexible manufacturing system(FMS). The problem of GA in solving FMS scheduling is summarized in this paper, reasons and countermeasures for GA's pre-maturing are studied, longitudinal and transverse comprehensive state-based correlative self-adaptive crossover and mutation operators are raised according to the analysis on GA to avoid local optimization and pre-maturity, the co-evolutionary GA is designed to solve the scheduling model for FMS, and the algorithm is validated for the scheduling of box-type parts for precise machine tools.

In this study, a new and simple alternate routing heuristics, which would be superior to the conventional routing strategies in terms of various system performance measures and easier to apply practically, was presented. Because of the high investment costs of FMSs, it is also definitely worth choosing the best operating policy and system configuration by analyzing the system model, and adapting to changes over time. In future research, the heuristic rule base will be extended to include other supplementary constraints such as dynamic tool allocation and sequence dependent setup times. For practical implementation of the proposed decision support system, additional research in the area of human interfaces could be useful to develop more user friendly system which automatically constructs simulation model of the system from the knowledge base of a production system.

In flexible manufacturing systems, deadlocks usually occur due to the limited resources. To cope with deadlock problems, Petri nets are widely used to model these systems. This chapter focuses on deadlock prevention for flexible manufacturing systems that are modeled with S4R nets, a subclass of generalized Petri nets. The analysis of S4R leads us to derive an iterative deadlock prevention approach. At each iteration step, a non-max-controlled siphon is derived by solving a mixed integer linear programming. A monitor is constructed for the siphon such that it is max-controlled. Finally, a liveness-enforcing Petri net supervisor can be derived without enumerating all the strict minimal siphons.

Statement of the On-line Control Problem in Flexible Manufacturing Systems

Machine loading problem in flexible manufacturing system is considered as a vital pre-release decision. Loading problem is concerned with assignment of necessary operations of the selected jobs to various machines in an optimal manner to minimize system unbalance under technological constraints of limited tool slots and operation time. Such a problem is combinatorial in nature and found to be NP-hard; thus, finding the exact solutions is computationally intractable and becomes impractical as the problem size increases. To alleviate above limitations, a meta-heuristic approach based on particle swarm optimization (PSO) has been proposed in this paper to solve the machine loading problem. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast toward global optimum and hence reduce computational effort further. Twenty benchmark problems available in open literature have been solved using the proposed heuristic. Comparison between the results obtained by the proposed heuristic and the existing methods show that the results obtained are encouraging at significantly less computational effort.

Optimizing flexible routing in flexible manufacturing systems is one of the aspects that increase the efficiency of flexible manufacturing systems especially in dynamic environment systems. This article presents a multistage approach to solve flexible routing problem in flexible manufacturing systems. Multistage approach includes three stages; the first stage is a production simulation system to find the fitness of the flexible manufacturing systems corresponding to different products’ routes’ groups. The second stage proposes an artificial neural network approach to predict the products’ routes’ group in flexible manufacturing systems. The last stage combines genetic algorithms and artificial neural network to optimize proper routes for all product types in flexible manufacturing systems. Multistage approach proposed in this study aims to reduce the computational time required to obtain and optimize the flexible routes in flexible manufacturing systems. The results of this study show that the artificial neural network can be used efficiently to predict the flexible routes in flexible manufacturing systems and it reduces the computational time for routes’ optimization required with production simulation system. This characteristic improves the flexibility of flexible manufacturing systems since it can be adapted frequently against any change in production ratios.

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

Modified immune algorithm for job selection and operation allocation problem in flexible manufacturing systems

In the flexible manufacturing system deadlock prevention domain, researchers’ almost final target is to seek the maximally permissive controllers for solving the deadlock problems of flexible manufacturing systems. However, it seems a challenging work. Whatever you adopt, what kinds of methods, policies, and strategies, it seems complicated to obtain optimal controllers for deadlock prevention even if they claim their algorithms are optimal until the deadlock recovery is developed. Therefore, many experts, including us, have decided to design all kinds of actual maximally permissive recovery policies based on control transitions. It is a pity that these policies usually solve some particular flexible manufacturing systems’ deadlock problems. The controllers failed to recover the deadlock situation of flexible manufacturing systems once the idle or resource places were changed. In other words, these policies could never know or identify the real number of maximally permissive controllers in the same structure with different idle places. The precise combination of the number of idle places is called the saturated line, and it divides the reachability states into two region (saturated region and unsaturated region). Accordingly, this paper proposes a novel concept that achieves the precise maximum permissiveness and fits all kinds of flexible manufacturing systems. The experimental results show how our policy does in practice.

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.

The loading problem in flexible manufacturing systems (FMS) consider several different manufacturing settings and objective functions but some crucial aspects of FMS environments, such as flexible process plans (FPP), have not yet received adequate attention. FPPs are vital in coping with bottlenecks and breakdowns, and decreasing the flow time. Modelling FPPs within a loading model, however, increases the problem complexity. In this study, we work on the integrated version of FMS part type selection and loading problems, and propose two models that consider operation allocation at different levels of detail for an FMS with FPP. Operation allocation is modelled explicitly along with tool loading in our first model, while the second one considers it implicitly to obtain a more compact and efficient formulation. Both models show remarkable reduction in run time compared to an existing loading model proposed for a similar FMS environment. [Received 19 August 2012; Revised 15 November 2013; Accepted 21 November 2013]

This paper extends the deterministic energy optimization problem of flexible manufacturing systems (FMSs) recently presented in [1] with its robust counterpart, where both productive and idle powers are considered as random variables. Based on the weighted p-timed Petri net models of FMSs, the robust energy-optimal schedule is determined by searching the robust shortest path of reachability graph. We select the most suitable model of uncertainties for our robust shortest path problem and propose a novel robustness measure, called Renyi mean-entropy criterion, using Renyi quadratic entropy. Experiment results with energy data logged from an industrial stamping system verify the practicality of considered problem and the effectiveness of Renyi mean-entropy criterion for robustness measure in terms of computational complexity and deviation from optimality.

This paper addresses the deadlock problems in flexible manufacturing systems (FMS) by using a Petri net siphon control method and the theory of regions. The proposed policy consists of two stages. The first one, called siphons control, is to add, for every siphon that we identify, a monitor to the original net model such that it is optimally invariant controlled. In the second stage, the theory of regions is utilized to derive the net supervisors such that deadlocks can be prevented. The first-stage work significantly lowers the computational cost compared with the approach where the theory of regions is used alone. An FMS example is presented to illustrate the technique. By varying the markings of given net structures, this paper shows its computational advantages.

Generally speaking, the flexible manufacturing systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, a recursive formulation is developed for the dynamic analysis of open-loop flexible manufacturing systems. The nonlinear generalized Newton-Euler equations are developed for rigid and deformable bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve equations of motion for open-loop systems consisting of interconnected rigid and deformable bodies is presented in this paper. This method applies recursive method with the Newton-Euler method for deformable bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the modern computer systems. The algorithms presented in this paper are demonstrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The recursive formulation developed in this investigation is illustrated by a practical numerical example.

Production planning in flexible manufacturing systems is concerned with the organization of production in order to satisfy a given master production schedule. The planning problem typically gives rise to several hierarchical subproblems which are then solved sequentially or simultaneously. In this paper, we address one of the subproblems: the part type selection problem. The problem is to determine a subset of part types having production requirements for immediate and simultaneous processing over the upcoming period of the planning horizon, subject to the tool magazine and processing time limitation. Several versions of tabu search (TS) algorithm are proposed for solving the problem. A systematic computational test is conducted to test the performance of the TS algorithms. The best TS algorithm developed is compared to a simulated annealing algorithm.