Automatic Design of Deterministic and Non-Halting Membrane Systems by Tuning Syntactical Ingredients

To solve the programmability issue of membrane computing models, the automatic design of membrane systems is a newly initiated and promising research direction. In this paper, we propose an automatic design method, Permutation Penalty Genetic Algorithm (PPGA), for a deterministic and non-halting membrane system by tuning membrane structures, initial objects and evolution rules. The main ideas of PPGA are the introduction of the permutation encoding technique for a membrane system, a penalty function evaluation approach for a candidate membrane system and a genetic algorithm for evolving a population of membrane systems toward a successful one fulfilling a given computational task. Experimental results show that PPGA can successfully accomplish the automatic design of a cell-like membrane system for computing the square of n(n ≥ 1 is a natural number) and can find the minimal membrane systems with respect to their membrane structures, alphabet, initial objects, and evolution rules for fulfilling the given task. We also provide the guidelines on how to set the parameters of PPGA.