Roberto Cordone

Selective Siphon Control for Deadlock Prevention in Petri Nets

Deadlock prevention is a crucial step in the modeling of flexible manufacturing systems. In the Petri net framework, deadlock prevention policies based on siphon control are often employed, since it is easy to specify generalized mutual exclusion constraints that avoid the emptying of siphons. However, such policies may require an excessive computational load and result in impractical oversized control subnets. This is often a consequence of the redundancy in the control conditions derived from siphons. In this paper, a novel method is proposed that provides small size controllers, based on a set covering approach that conveniently relates siphons and markings. Some examples are provided to demonstrate the feasibility of the approach and to compare it with other methods proposed in the literature.

Combined Siphon and Marking Generation for Deadlock Prevention in Petri Nets

In Petri-net (PN) modeling of flexible manufacturing systems, deadlock prevention is often addressed by means of siphon-control methods. Constraints that avoid the emptying of siphons can be easily implemented using additional places suitably connected to the PN transitions. Efficient siphon-based techniques achieve highly permissive solutions using as few control places as possible. One such technique employs a set-covering approach to optimally match emptiable siphons to critical markings. In this paper, a modified version of the method is proposed that achieves the same results in terms of permissivity and size of the control subnet but avoids full siphon enumeration. This greatly reduces the overall computational time and memory requirements and allows the applicability of the method to large-size models.

Enumeration algorithms for minimal siphons in Petri nets based on place constraints

The paper addresses the problem of enumerating minimal siphons in an ordinary Petri net. The algorithms developed in this work recursively use a problem partitioning procedure to reduce the original search problem to multiple simpler search subproblems. Each subproblem has specific additional place constraints with respect to the original problem. Some results on algorithm correctness, convergence, and computational complexity are provided, as well as an experimental evaluation of performance. The algorithms can be applied to enumerate minimal, place-minimal siphons, or even siphons that are minimal with respect to given subsets of places.

Partitioning and Scheduling of Task Graphs on Partially Dynamically Reconfigurable FPGAs

This paper proposes a new model for the partitioning and scheduling of a specification on partially dynamically reconfigurable hardware. Although this problem can be solved optimally only by tackling its subproblems jointly, the exceeding complexity of such a task leads to a decomposition into two phases. The partitioning phase is based on a new graph-theoretic approach, which aims to obtain near optimality even if performed independently from the subsequent phase. For the scheduling phase, a new integer linear programming formulation and a heuristic approach are developed. Both take into account configuration prefetching and module reuse. The experimental results show that the proposed method compares favorably with existing solutions.

Tabu Search versus GRASP for the maximum diversity problem

Description: The Maximum Diversity Problem (MDP) consists in determining a subset M of given cardinality from a set of elements N, in such a way that the sum of the pairwise differences between the elements of M is maximum. This problem, introduced by Glover, Hersh and McMillian has been deeply studied using the GRASP methodology. GRASPs are often characterized by a strong design effort dedicated to the randomized generation of high quality starting solutions, while the subsequent improvement phase is usually performed by a standard local search technique. The purpose of this paper is to explore a somewhat opposite approach, that is to refine the local search phase, by adopting a Tabu Search methodology, while keeping a very simple initialization procedure. Extensive computational results show that Tabu Search achieves both better results and much shorter computational times with respect to those reported for GRASP.

Integrated design of optimal supervisors for the enforcement of static and behavioral specifications in Petri net models

Petri net (PN) supervisory control is often performed through a sequential procedure that introduces additional constraint layers over an initial unconstrained PN model, using generalized mutual exclusion constraints (GMECs) implemented as monitor places. This is typical, e.g., in the context of flexible manufacturing systems, where the initial model represents the production sequences and the constraints are used to express static specifications, such as job limitations or the usage of resources, and behavioral ones, as liveness, controllability, etc. This sequential procedure may yield a redundant model, that is not easily reduced a posteriori. Also, it is difficult to ensure maximal permissivity with respect to multiple behavioral specifications. This paper, building on recent results regarding optimal supervisor design with branch & bound methods, proposes an integrated modeling approach that can be used to derive a minimal supervisor guaranteeing the attainment of an arbitrary set of static and behavioral specifications in a maximally permissive way. Among behavioral specifications, deadlock-freeness, liveness, reversibility and behavioral controllability are considered in the paper. The supervisor comes in the form of a simple set of GMECs or of a disjunction of sets of GMECs. Some examples emphasize the potential model size reductions that can be achieved.

Comparing local search metaheuristics for the maximum diversity problem

The Maximum Diversity Problem (MDP) requires to extract a subset M of given cardinality from a set N, maximising the sum of the pair-wise diversities between the extracted elements. The MDP has recently been the subject of much research, and several sophisticated heuristics have been proposed to solve it. The present work compares four local search metaheuristics for the MDP, all based on the same Tabu Search procedure, with the aim to identify what additional elements provide the strongest improvement. The four metaheuristics are an Exploring Tabu Search, a Scatter Search, a Variable Neighbourhood Search and a simple Random Restart algorithm. All of them prove competitive with the best algorithms proposed in the literature. Quite surprisingly, the best ones are the simple Random Restart algorithm and a Variable Neighbourhood Search algorithm with an unusual parameter setting, which makes it quite close to random restart. Although this is probably related to the elementary structure of the MDP, it also suggests that, more often than expected, simpler algorithms might be better.

Parsimonious Monitor Control of Petri Net Models of Flexible Manufacturing Systems

Most approaches for deadlock prevention and liveness enforcement in Petri nets rely on siphon control methods or the theory of regions to derive monitor-based supervisors. These techniques raise methodological and computational issues, from the existence of feasible solutions to the hardness of guaranteeing maximal permissivity and optimality in the size and cost of the control subnet. Recently, the supervisor design problem has also been reformulated as a direct monitor optimization task based on integer linear programming, which can more effectively deal with the mentioned issues and objectives. This paper introduces an efficient branch-and-bound scheme for the exploration of the solution space of the direct monitor optimization problem. An extensive computational analysis on a set of benchmark instances demonstrates the efficiency of the approach.

Solving the Quadratic Minimum Spanning Tree Problem

Abstract Given an undirected graph with costs associated to its edges and pairs of edges, the Quadratic Minimum Spanning Tree Problem (QMSTP) requires to determine a spanning tree of minimum total cost. This is a proper model for network problems in which both routing and interference costs need to be considered. It is NP -hard in the strong sense and not approximable unless P = NP . This paper describes a Tabu Search algorithm, with two independent and adaptively tuned tabu lists, and a Variable Neighbourhood Search algorithm. Both metaheuristics are based on the same neighbourhood, but the Tabu Search proves more effective and robust than the Variable Neighbourhood Search. To assess the quality of these results, we provide a comparison with the heuristic algorithms proposed in the recent literature and we reimplement, with minor improvements, an exact algorithm drawn from the literature, which confirms the optimality of the results obtained on small instances.

The demand-dependent optimization of regular train timetables

Abstract Regular timetables, in which the trains arrive and depart at constant intervals, have been adopted in various European countries, because of the simpler and fairer service they allow. The design of such a timetable has recently received a certain attention in the literature. This paper extends the commonly adopted model to take into account the reciprocal influence between the quality of a timetable and the transport demand captured by the railway with respect to alternative means of transport. The resulting mixed-integer non linear model remains non convex even after relaxing the integrality constraints. We solve it by a branch-and-bound algorithm based on Outer Approximation and a heuristic algorithm exploiting the decomposition and reciprocal update of two submodels. Preliminary computational results concern a regional network in North-western Italy.