Exclusion Constraints Research Articles

Static and Dynamic Partitions of Inequalities: A Unified Methodology for Supervisor Simplification

In the context of automated manufacturing systems, supervisor simplification is drawing increasing attention. As a special class of state specifications, generalized mutual exclusion constraints (GMECs) are a typical kind of supervisory control of Petri nets. In this note, we first propose static and dynamic partitions to reduce the size of supervisor by partitioning inequalities, i.e., GMECs, into redundant and necessary ones. The former considers the specifications themselves and exhibits higher efficiency; while the latter takes into account both specifications and reachable markings and achieves more economical supervisors. In an incremental manner, we develop Type I supervisor simplification method which has a compromised efficiency and complexity. In an integrated manner, we propose Type II supervisor simplification method that further improves efficiency and eases computational complexity. All techniques proposed in this note can be realized in an algebraic manner. Examples are presented for the sake of illustration as well as demonstration.

Computation of Admissible Marking Sets in Weighted Synchronization-Free Petri Nets by Dynamic Programming

We study the computation of admissible marking sets in generalized Petri nets. We first show that the admissibility checking in the generalized Petri net is NP-hard. Then, we consider a special subclass of generalized Petri nets called weighted-synchronization-free nets in which each transition has at most one input place. For a net in this subclass, we propose a generating function to compute by dynamic programming the set of admissible markings for a given generalized mutual exclusion constraint .

Fractional exclusion statistics as an occupancy process

We show the possibility of describing fractional exclusion statistics (FES) as an occupancy process with global and local exclusion constraints. More specifically, using combinatorial identities, we show that FES can be viewed as “ball-in-box” models with appropriate weighting on the set of occupancy configurations (merely represented by a partition of the total number of particles). As a consequence, the following exact statement of the generalized Pauli principle is derived: for an [Formula: see text]-particles system exhibiting FES of extended parameter [Formula: see text] ([Formula: see text] and [Formula: see text] are co-prime integers such that [Formula: see text]), (1) the allowed occupation number of a state is less than or equal to [Formula: see text] and not to [Formula: see text] whenever [Formula: see text] and (2) the global occupancy shape is admissible if the number of states occupied by at least two particles is less than or equal to [Formula: see text] ([Formula: see text]). These counting rules allow distinguishing infinitely many families of FES systems depending on the parameter [Formula: see text] and the size [Formula: see text].

A method for parallel scheduling of multi-rate co-simulation on multi-core platforms

The design of cyber-physical systems is a complex process and relies on the simulation of the system behavior before its deployment. Such is the case, for instance, of joint simulation of the different subsystems that constitute a hybrid automotive powertrain. Co-simulation allows system designers to simulate a whole system composed of a number of interconnected subsystem simulators. Traditionally, these subsystems are modeled by experts of different fields using different tools, and then integrated into one tool to perform simulation at the system-level. This results in complex and compute-intensive co-simulations and requires the parallelization of these co-simulations in order to accelerate their execution. The simulators composing a co-simulation are characterized by the rates of data exchange between the simulators, defined by the engineers who set the communication steps. The RCOSIM approach allows the parallelization on multi-core processors of co-simulations using the FMI standard. This approach is based on the exploitation of the co-simulation parallelism where dependent functions perform different computation tasks. In this paper, we extend RCOSIM to handle additional co-simulation requirements. First, we extend the co-simulation to multi-rate, i.e. where simulators are assigned different communication steps. We present graph transformation rules and an algorithm that allow the execution of each simulator at its respective rate while ensuring correct and efficient data exchange between simulators. Second, we present an approach based on acyclic orientation of mixed graphs for handling mutual exclusion constraints between functions that belong to the same simulator due to the non-thread-safe implementation of FMI. We propose an exact algorithm and a heuristic for performing the acyclic orientation. The final stage of the proposed approach consists in scheduling the co-simulation on a multi-core architecture. We propose an algorithm and a heuristic for computing a schedule which minimizes the total execution time of the co-simulation. We evaluate the performance of our proposed approach in terms of the obtained execution speed. By applying our approach on an industrial use case, we obtained a maximum speedup of 2.91 on four cores.

Time-Varying Automated Manufacturing Systems and Their Invariant-Based Control: A Petri Net Approach

As an important branch of production facilities, automated manufacturing systems are a promising perspective of modern factories which become increasingly complex and flexible. From the perspective of development, time variable is a significant concern. In this paper, we propose a class of time-varying systems, Tv-S4R. After involving a global time information loop, it can represent realistic system whose manufacturing process varies with time variables. Event-based control is introduced for serving two important purposes. First, it exerts time-varying specifications on the system, i.e., different processes are executed at different time stages. Second, it prevents the system from reaching any first-met bad marking which will eventually result in deadlocks. We will show that the event-based control can enhance our specifications' expressivity capability compared to their state-based counterparts in terms of generalized mutual exclusion constraints. At last, supervisors are simplified according to the identification of dependence and independence of inequalities. An experimental study illustrates the application of Tv-S4R and the effectiveness of event-based control method.

Topology Optimization of Structures Made of Discrete Geometric Components With Different Materials

We present a new method for the simultaneous topology optimization and material selection of structures made by the union of discrete geometric components, where each component is made of one of multiple available materials. Our approach is based on the geometry projection method, whereby an analytical description of the geometric components is smoothly mapped onto a density field on a fixed analysis grid. In addition to the parameters that dictate the dimensions, position, and orientation of the component, a size variable per available material is ascribed to each component. A size variable value of unity indicates that the component is made of the corresponding material. Moreover, all size variables can be zero, signifying the component is entirely removed from the design. We penalize intermediate values of the size variables via an aggregate constraint in the optimization. We also introduce a mutual material exclusion constraint that ensures that at most one material has a unity size variable in each geometric component. In addition to these constraints, we propose a novel aggregation scheme to perform the union of geometric components with dissimilar materials. These ingredients facilitate treatment of the multi-material case. Our formulation can be readily extended to any number of materials. We demonstrate our method with several numerical examples.

Categorizing relational facts from the web with fuzzy rough sets

Significant advances have been made in automatically constructing knowledge bases of relational facts derived from web corpora. These relational facts are linguistic in nature and are represented as ordered pairs of nouns (Winnipeg, Canada) belonging to a category (City_Country). One major problem is that these facts are abundant but mostly unlabeled. Hence, semi-supervised learning approaches have been successful in building knowledge bases where a small number of labeled examples are used as seed (training) instances and a large number of unlabeled instances are learnt in an iterative fashion. In this paper, we propose a novel fuzzy rough set-based semi-supervised learning algorithm (FRL) for categorizing relational facts derived from a given corpus. The proposed FRL algorithm is compared with a tolerance rough set-based learner (TPL) and the coupled pattern learner (CPL). The same ontology derived from a subset of corpus from never ending language learner system was used in all of the experiments. This paper has demonstrated that the proposed FRL outperforms both TPL and CPL in terms of precision. The paper also addresses the concept drift problem by using mutual exclusion constraints. The contributions of this paper are: (i) introduction of a formal fuzzy rough model for relations, (ii) a semi-supervised learning algorithm, (iii) experimental comparison with other machine learning algorithms: TPL and CPL, and (iv) a novel application of fuzzy rough sets.

Structural Decomposition and Decentralized Control of Petri Nets

Control of a large-scale automated manufacturing system is an important and challenging issue. Its discrete event system model represented by Petri nets tends to become highly complicated in structure, especially when there exist uncontrollable or unobservable events. The existing approaches are nontrivial to design both efficient and maximally permissive supervisors to impose constraints on an overall system. In this paper, instead of considering the control problem from an overall system perspective, we intend to transform an overall control problem into the one designing multiple controllers in parallel, each of which is much simpler in structure. A Petri net structure is decomposed via integer linear programming or a polynomial decomposition method to obtain multiple state-machine subnets that constitute a decentralized system. A necessary and sufficient condition for preserving the equivalence in terms of states and behaviors between the overall system and its decentralized version is reported. Constraints representing control requirements are further converted and enforced in the respective subnets. Then, supervisors are generated via a generalized mutual exclusion constraint method. By considering the deviations between the subnet control and overall control, this paper formulates a communication mechanism to guarantee that the decentralized system runs in an appropriate manner. Finally, two examples are presented to demonstrate the proposed approach.

Liveness-Enforcing Supervision in AMS-Oriented HAMGs: An Approach Based on New Characterization of Siphons Using Petri Nets

In the context of automated manufacturing systems, flexibility and synchronization are two main representative formations. Supervisory control techniques for flexibility have gained increasing attention, but those for synchronization operations have received little notice. Based on their comparison, our work makes threefold contributions. First, we propose a novel characterization of siphons, i.e., type I and type II, based on a special kind of Petri nets, namely, hierarchical augmented marked graphs (HAMGs), which integrate multilevel synchronization into a system. This characterization of siphons is further proved to be a crucial and essential description for both synchronization and flexibility. Second, event circular-wait is proposed to describe the occurrence of deadlocks in HAMGs. Its counterpart is resource circular-wait in flexibility. Ours is a more general and accurate characterization of deadlocks. The liveness of HAMGs can be attributed to the absence of undermarked siphons. Third, a unified liveness-enforcing supervisory control is established based on new characterization of siphons with the aid of generalized mutual exclusion constraints. Supervisor simplification based on inequality analysis is provided for structure simplicity. An experimental study illustrates the correctness of such characterization and the effectiveness of our proposed control method.

Evaluating Land Eligibility Constraints of Renewable Energy Sources in Europe

The amount and distribution of land which is eligible for renewable energy sources (RES) is fundamental to the role these technologies will play in future energy systems. Unfortunately, land eligibility (LE) investigations in the literature are plagued by many inconsistencies between studies, impeding the work of researchers and policy makers interested in energy system development planning. As one factor contributing to this, the criteria used to construct land exclusion constraints have not been the focus of scientific investigation on a large scale, and as such their interactions are not well known.Therefore, an open source LE framework was used to perform evaluations in the European context of 36 commonly used constraints. After direct visualization, three measures by which these constraints are valuable to an LE analysis were computed: independence, exclusivity, and overlap. Results show extensive spatial sensitivity to constrain influence. Furthermore, some constraints, such as proximity to agriculture and woodland areas, rank high in all three measures; others, such as distance from airports and camping sites, consistently rank low; and still others, such as elevation, score highly in one measure but not the others. With these results, LE researchers can better understand the contributions of the constraints used in their analyses.

Online Fault Diagnosis in Discrete Event Systems with Partially Observed Petri Nets

This paper investigates the fault detection problem for Discrete Event Systems (DES) which can be modeled by Partially Observed Petri Nets (POPN). To overcome the problem of low diagnosability in the POPN online fault diagnoser in current use, we propose an improved online fault diagnosis algorithm that integrates Generalized Mutual Exclusion Constraints (GMEC) and Integer Linear Programming (ILP).We assume that the POPN structure and its initial markings are known, and the faults are modeled as unobservable transitions. First, the event sequence is observed and recorded. We use GMEC for elementary diagnosis of the system behavior,then the ILP problem of POPN is solved for further diagnosis. Finally, we modeled and analyzed an example of a real DES to test the new fault diagnoser. The proposed algorithm increased the diagnosability of the DES remarkably, and the effectiveness of the new algorithm integrating GMEC and ILP was verified.

Online fault diagnosis in partially observed Petri nets

This paper investigates the fault detection problem for discrete event systems (DES) which can be modelled by partially observed Petri nets (POPN). To overcome the problem of low diagnosability in the POPN online fault diagnoser in current use, we propose an improved online fault diagnosis algorithm that integrates generalised mutual exclusion constraints (GMEC) and integer linear programming (ILP). We assume that the POPN structure and its initial markings are known, and the faults are modelled as unobservable transitions. First, the event sequence is observed and recorded. Then, the ILP problem of POPN is solved for elementary diagnosis of the system behaviour. While this system diagnoses that some faults may have happened, we also use GMEC for further diagnosis. Finally, we modelled and analysed an example of a real DES to test the new fault diagnoser. The proposed algorithm increased the diagnosability of the DES remarkably, and the effectiveness of the new algorithm integrating GMEC and ILP was verified.

Metastability of hard-core dynamics on bipartite graphs

We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New particles appear subject to a neighbourhood exclusion constraint, while existing particles disappear, all according to independent Poisson clocks. We consider the regime in which the appearance rates are much larger than the disappearance rates, and there is a slight imbalance between the appearance rates on the two parts of the graph. Starting from the configuration in which the weak part is covered with particles, the system takes a long time before it reaches the configuration in which the strong part is covered with particles. We obtain a sharp asymptotic estimate for the expected transition time, show that the transition time is asymptotically exponentially distributed, and identify the size and shape of the critical droplet representing the bottleneck for the crossover. For various types of bipartite graphs the computations are made explicit. Proofs rely on potential theory for reversible Markov chains, and on isoperimetric results.

Improved design of online fault diagnoser for partially observed Petri nets with generalized mutual exclusion constraints

Improved design of online fault diagnoser for partially observed Petri nets with generalized mutual exclusion constraints

Theory of Regions for Control Synthesis without Computing Reachability Graph

This paper addresses the design of Petri net (PN) supervisor using the theory of regions for forbidden state problem with a set of general mutual exclusion constraints. In fact, as any method of supervisory control based on reachability graph, the theory of regions suffers from a technical obstacle in control synthesis, which is the necessity of computing the graph at each iteration step. Moreover, based on the reachability graph, which may contain a large number of states, with respect to the structural size of the system, the computation of PN controllers becomes harder and even impossible. The main contribution of this paper, compared to previous works, is the development of a control synthesis method in order to decrease significantly the computation cost of the PN supervisor. Thus, based on PN properties and mathematical concepts, the proposed methodology provides an optimal PN supervisor for bounded Petri nets following the interpretation of the theory of regions. Finally, case studies are solved by CPLEX software to compare our new control policy with previous works which use the theory of regions for control synthesis.

Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines

Abstract In the paper we consider the problem of scheduling n identical jobs on 4 uniform machines with speeds s1 ≥ s2 ≥ s3 ≥ s4, respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are subject to some kind of mutual exclusion constraints modeled by a bipartite incompatibility graph of degree Δ, where two incompatible jobs cannot be processed on the same machine. We show that the general problem is NP-hard even if s1 = s2 = s3. If, however, Δ ≤ 4 and s1 ≥ 12s2, s2 = s3 = s4, then the problem can be solved to optimality in time O(n1.5). The same algorithm returns a solution of value at most 2 times optimal provided that s1 ≥ 2s2. Finally, we study the case s1 ≥ s2 ≥ s3 = s4 and give a 32/15-approximation algorithm running also in O(n1.5) time.

A suboptimal deadlock control policy for designing non-blocking supervisors in flexible manufacturing systems

This work aims to resolve deadlock problems in flexible manufacturing systems. A novel deadlock control policy in the frame of Petri nets formalism is presented for a class of generalized Petri nets, namely G-systems, which can usually model assembly and disassembly operations of multiple resource acquisition. Based on the concept of elementary siphons, all strict minimal siphons (SMS) in an uncontrolled net system are first divided into elementary siphons and dependent ones. After that, a set of linear inequality constraints expressed by state vectors can be formalized for elementary siphons. After being modified by utilizing the conjunctive/disjunctive resources upstream neighborhood policy, a set of generalized mutual exclusion constraints expressed by marking vectors can be obtained. Then, the additional monitors are only designed for elementary siphons, whose control depth variables can be obtained by solving a linear programming problem. As a result, the controllability of dependent ones can be ensured by properly supervising its elementary siphons. Finally, all strict minimal siphons are max′-controlled and no insufficiently marked siphon is generated, which indicates that the sequential resources are allocated reasonably to guarantee the absence of deadlock states. The proposed method can usually lead to a near-optimal non-blocking supervisor with simple structure. A G-system example prone to deadlocks is used to illustrate the applicability and the effectiveness of the proposed method.

A Minimal Supervisory Structure to Optimally Enforce Liveness on Petri Net Models for Flexible Manufacturing Systems

This paper presents a new method of computing a minimal supervisory structure that optimally enforces liveness on the Petri net models for flexible manufacturing systems (FMSs). The proposed method utilizes the structural properties of a Petri net model to avoid the computation of its reachability graph, which in general leads to the state explosion problem. This paper aims to design a single control place for each concurrent process of a Petri net model or a sub-net model, which thus provides a constant number of control places in a supervisor regardless of the number of resource places in a Petri net or sub-net model. It is shown that the structural size of a supervisor is minimal as the number of control places depends on the number of concurrent processes in the Petri net model. Precisely, two algorithms are developed in this paper. The first aims to compute active uncontrolled transitions and the second is concerned with a method to compute the generalized mutual exclusion constraints (GMECs) for each process of the Petri net model of an FMS. Furthermore, it provides an approach to design control places for each computed GMEC without solving integer linear programming problems, which greatly reduces the computational costs. When the computed control places are coupled with the uncontrolled Petri net model for an FMS, it optimally enforces liveness behavior of the Petri net model, and hence ensures the high utilization of resources in a considered system.

Scheduling of Identical Jobs with Bipartite Incompatibility Graphs on Uniform Machines. Computational Experiments

Abstract. In the paper we consider the problem of scheduling of unit-length jobs on 3 or 4 uniform parallel machines to minimize schedule length or total completion time. We assume that jobs are subject to some kind of mutual exclusion constraints, modeled by a bipartite graph of bounded degree. The edges of the graph correspond to pairs of jobs that cannot be processed on the same machine. Although the problem is generally NP-hard, we show that under some conditions imposed on machine speeds and the structure of incompatibility graph our problem can be solved to optimality in polynomial time. Theoretical considerations are accompanied by computer experiments with some particular model of scheduling.

Online Fault Diagnoser for Partially Observed Petri Nets

This paper investigates the fault detection problem for Discrete Event Systems which can be modeled by Partially Observed Petri Nets (POPN). To overcome the shortage of the low diagnosability of the currently POPN online fault diagnoser, we propose an improved on-line fault diagnosis algorithm that integrates Generalized Mutual Exclusion Constraints(GMEC) and Integer Linear Programming (ILP). We assume that the POPN structure and its initial markings are known, the faults are modeled as unobservable transitions. First, the event sequence is observed and recorded. The ILP problem of POPN is solved for elementary diagnosis for the system behavior. While the system is diagnosed that some faults may have happened, we use the GMEC for the further diagnosis. Finally, a real discrete event system is taken as an example, we model and analyse the discrete event system, the proposed algorithm increases the diagnosablity remarkably.