Petri net-based QUBO Model Formulation for Multi-Resource Flow-Shop Scheduling Problems

This paper introduces a Petri net-based approach to addressing multi-resource flow-shop scheduling problems within multi-objective quantum optimization. The multi-resource flow-shop problem, which holds both theoretical and practical significance, represents a real-world application scenario. The practical nature of the problem necessitates incorporating multiple objective functions, which adds complexity to its formulation, particularly in representing the energy function within the QUBO (Quadratic Unconstrained Binary Optimization) model. Our approach mitigates the complexity of formulating the QUBO model by employing Petri net theory, providing a more efficient solution for these inherently complex problems. The paper further demonstrates the effectiveness of this method through computational examples utilizing a CPU-based QUBO optimization platform.