Comparative of heuristics on search of supervisors by approximated distinguishers

The Supervisory Control Theory with Distinguishers (SCT-D) was developed in order to simplify the task of modelling complex specifications, while guaranteeing the synthesis of maximally permissive supervisors. Besides, by approximating the language of a distinguisher, a supervisor can be obtained with computational savings in the synthesis, although there is no guarantee that this is the maximally permissive solution or a solution at all. The search for an approximated distinguisher that leads to a maximally permissive solution is a combinatorial problem and heuristics may improve the efficiency of the task. The purpose of this work is to compare the performance of Genetic Algorithm and Tabu Search as embedded heuristic in a procedure to obtain the maximally permissive achievable supervisor in the context of SCT-D with approximations. A language measure is used as function cost in the search procedure. A case study of a manufacturing workcell with feedback is presented for the comparison of the two heuristics. The study suggest that Tabu Search achieves better results than the Genetic Algorithm for systems where some modules are needed for nonblocking while different ones are needed for maximally permissiveness.