Adaptive Petri net based on irregular cellular learning automata with an application to vertex coloring problem

Abstract

An adaptive Petri net, called APN-LA, that has been recently introduced, uses a set of learning automata for controlling possible conflicts among the transitions in a Petri net (PN). Each learning automaton (LA) in APN-LA acts independently from the others, but there could be situations, where the operation of a LA affects the operation of another LA by possibly enabling or disabling some of the transitions within the control of that LA. In such situations, it is more appropriate to let the learning automata within the APN-LA, cooperate with each other, instead of operating independently. In this paper, an adaptive Petri net system based on Irregular Cellular Learning Automata (ICLA), in which a number of learning automata cooperate with each other, is proposed. The proposed adaptive system, called APN-ICLA, consists of two layers: PN-layer and an ICLA-layer. The PN-layer is a Petri net, in which conflicting transitions are partitioned into several clusters. There should be a controller in each cluster to control the possible conflicts among the transitions in that cluster. The ICLA-layer in APN-ICLA provides the required controllers for the PN-layer. The ICLA-layer is indeed an ICLA, in which each cell corresponds to a cluster in the PN-layer. The LA resides in a particular cell in the ICLA-layer and acts as the controller of the corresponding cluster in the PN-layer. To evaluate the efficiency of the proposed system, several algorithms, based on the APN-ICLA for vertex coloring problem, are designed. Simulation results justify the effectiveness of the proposed APN-ICLA.