Immune System Derived Approach for Finding Firing Sequences of a Sub-class of Petri Nets

Abstract

This paper proposes a novel approach for solving a sub-class of combinatorial problem, which allows decomposition into subproblems that are interconnected by sub-problems objective functions. The optimization problem is solved by an interactive search process based on the Immune System response regulatory mechanism. The original problem constraints and objective function are satisfied by solving the sub-problems independently and by modifying dynamically the objective function of each sub-problem. This approach is applied for finding firing sequences of a sub-class of Petri net defined as P1-net, whose firing sequence problem is decomposable into sub-problems. Considering discrete event systems that can be modeled by P1-net, the objective is to find a sequence of events that leads the system from a known initial state to a desired final state. Simulations were conducted and our approach successfully found 100% of feasible and near-optimal solutions for simulated P1 models. The characteristics of our approach indicate that it may be applied in relatively large systems with distributed characteristics.