Petri net transformation for decision making: Compound Petri nets to alternatives aggregation petri nets

Resumen

The design and operation of discrete event systems (DES), including their control, require taking decisions in order to guarantee an expected behavior. Usually, this behavior can be characterized by means of performance measurements. To take decisions may require choosing the best solution that optimizes a cost function and complies with certain restrictions, i.e. solving an optimization problem. In the field of DES modeled by Petri nets, it is a classical problem to optimize the initial marking and the sequence of priority assignment to the firing of transitions involved in conflicts (Piera and Music 2011). This problem may be solved by means of simulation and by optimization based on simulation (Piera et al., 2004). The second approach can use a heuristic search to find the best configurations to solve. On the other hand, in the first approach is a human operator who should make this choice and can skip the best solutions to be tested. In the cases, less studied in the literature, of requiring an optimization of the structure of the Petri net, the classical approach is similar to the simulation in the previous problem: several feasible structures are chosen and they are simulated or optimized. If the human operator does not choose the best solutions, the result of the decision taking may be poor. A field of research that has taken the interest of the authors consists of applying a heuristic search to find the best structure for a Petri net (Latorre et al. 2009). This kind of optimization problem requires an adequate formalism as the compound Petri nets or the alternatives aggregation Petri nets to perform an efficient solving process (Latorre et al. 2011). The transformation from the first formalism to the second one is presented in this paper and illustrated with an example. Its utility arises when it is required to compare the performance of both formalisms for a particular case or when it is easier to model a DES as compound Petri net but the optimization process is based on the second formalism.