GAPN-LA: A framework for solving graph problems using Petri nets and learning automata

A fusion of learning automata and Petri nets, referred to as APN-LA, has been recently introduced in the literature for achieving adaptive Petri nets. A number of extensions to this adaptive Petri net have also been introduced; together we name them the APN-LA family. Members of this family can be utilized for solving problems in the domain of graph problems; each member is suitable for a specific category within this domain. In this paper, we aim at generalizing this family into a single framework, called generalized APN-LA (GAPN-LA), which can be considered as a framework for solving graph-based problems. This framework is an adaptive Petri net, organized into a graph structure. Each place or transition in the underlying Petri net is mapped into exactly one vertex of the graph, and each vertex of the graph represents a part of the underlying Petri net. A vertex in GAPN-LA can be considered as a module, which, in cooperation with other modules in the framework, helps in solving the problem at hand. To elaborate the problem-solving capability of the GAPN-LA, several graph-based problems have been solved in this paper using the proposed framework.