Using the incidence matrix in an evolutionary algorithm for computing minimal siphons in Petri net models

Petri nets are graph based tools to model and study concurrent systems and their properties; one of them is liveness, which is related to the possibility of every part of the system to be activated eventually. Siphons are sets of places that are related to liveness properties. When we need to deal with realistic problems its computation is hard or even impossible and this is why in this paper we are approaching it using evolutionary computation, a meta-heuristic that has proved it can successfully find solutions when the search space is big. In a previous work a formulation of the siphon property based on linear constraints and a genetic algorithm was proposed for general Petri Nets. Here we propose to adapt an algebraic method based on the selection of rows of the matrix that cancel in an adequate way input and output transitions so the resulting selection is a siphon. We will also present an evaluation for a family of resource allocation systems (RAS). The proposed solution is based on a genetic algorithm (GA); we can see how siphons can be computed using this genetic algorithm, with experiments showing that in some cases they are able to find a few solutions in less time than previous deterministic algorithms.