In this letter, we address the path planning of multi-robot systems (i.e., a team of identical mobile robots) with a global high-level specification that is given as a Boolean formula over some regions of the environment. The task is composed of logical requirements on the trajectories and the final states of the robots for some interest regions. First, a preprocessing algorithm based on Dijkstra algorithm is developed to calculate the shortest path between each interest region according to the global map information and the Boolean specification. Then, a simulated annealing based approach is developed to obtain a path trajectory of each robot such that the Boolean specification is satisfied on the final state, while the total travel distance is minimized. Finally, several numerical studies are investigated to show that the developed approach is superior to the existing methods in terms of both the computational cost and the quality of the obtained solution.

According to the characteristics of flexible job shop scheduling problems, a dual-resource constrained flexible job shop scheduling problem (DRCFJSP) model with machine and worker constraints is constructed such that the makespan and total delay are minimized. An improved African vulture optimization algorithm (IAVOA) is developed to solve the presented problem. A three-segment representation is proposed to code the problem, including the operation sequence, machine allocation, and worker selection. In addition, the African vulture optimization algorithm (AVOA) is improved in three aspects: First, in order to enhance the quality of the initial population, three types of rules are employed in population initialization. Second, a memory bank is constructed to retain the optimal individuals in each iteration to increase the calculation precision. Finally, a neighborhood search operation is designed for individuals with certain conditions such that the makespan and total delay are further optimized. The simulation results indicate that the qualities of the solutions obtained by the developed approach are superior to those of the existing approaches.

This paper deals with the performance optimization of resource allocation systems with the aim of maximizing the system's throughput under a given budget for acquiring resources. Resources are assumed to be renewable, i.e., they are not consumed by the operations and become available again after they have been released. The systems under consideration are modeled by a subclass of timed Petri nets called deterministic timed weighted marked graphs. In addition, we take into account infinite server semantics, i.e., the degree of self-concurrency of each transition is infinite. We propose an approach which provides an optimal solution, but has a high computational cost. For this reason, we also present two different approaches which can find suboptimal solutions with a reduced computational cost. The performances of the proposed approaches are compared by means of numerical simulations.

In this paper, we comment on the algorithm proposed in the paper mentioned in the title to define and construct a graph, called Modified State Class Graph (MSCG), which summarizes all possible evolutions of a Time Petri net. We first show that under the assumptions mentioned in such a paper, the proposed graph could be infinite. Then, we underline the requirement of revising the notation and adding some information on certain edges of the graph. Finally, we remark that the current version of the algorithm does not consider all possible evolutions of the net system. In the final part of the manuscript, we propose a revised algorithm for the definition and construction of the MSCG that overcomes all such limitations.

Timed marked graphs, a special class of Petri nets, are extensively used to model and analyze cyclic manufacturing systems. Weighted marked graphs are convenient to model automated production systems, such as robotic work cells or embedded systems, and reduce the size of the model. The main problem for designers is to find a tradeoff between minimizing the cost of the resources and maximizing the system's throughput (also called cycle time). It is possible to apply analytical techniques for the cycle time optimization problem of such systems. The problem consists in finding an initial marking to minimize the cycle time (i.e., maximize the throughput) while the weighted sum of tokens in places is less than or equal to a given value. We transform a weighted marked graph into several equivalent marked graphs and formulate a mixed integer linear programming model to solve this problem. Moreover, several techniques are proposed to reduce the complexity of the proposed method. We show that the proposed method can always find an optimal solution.

This article aims to enforce codiagnosability in labeled Petri nets, which are monitored by a series of sites. A labeled Petri net is codiagnosable with respect to a certain fault, if the occurrence of such a fault could be detected by at least one of the sites. We assume that codiagnosability is imposed to a noncodiagnosable system by appropriately positioning additional sensors. In particular, the goal is that of minimizing the cost of the new sensors. The enumeration of the whole state space is avoided, thanks to the notions of basis markings and minimal explanations. An automaton, called unfolded verifier, is introduced to verify codiagnosability. Finally, the set of optimal labeling functions is obtained solving an integer nonlinear programming problem.