A Petri Net Approach to Generate Integer Linear Programming Problems

This paper proposes a Petri net based mathematical programming approach to combinatorial optimization, in which we generate integer linear programming problems from Petri net models instead of the direct mathematical formulation. We treat two types of combinatorial optimization problems, ordinary problems and time-dependent problems. Firstly, we present autonomous Petri net modeling for ordinary optimization problems, where we obtain fundamental constraints derived from Petri net properties and additional problem-specific ones. Secondly, we propose a colored timed Petri net modeling approach to time-dependent problems, where we generate variables and constraints for time management and for resolving conflicts. Our Petri net approach can drastically reduce the difficulty of the mathematical formulation in a sense that (1) the Petri net modeling does not require deep knowledge of mathematical programming and technique of integer linear model formulations, (2) our automatic formulation allows us to generate large size of integer linear programming problems, and (3) the Petri net modeling approach is flexible for input parameter changes of the original problem