QUBO Model Formulation for Flow-shop Scheduling Problems with Changeover based on Timed Colored Petri Nets

Quadratic unconstrained binary optimization (QUBO) and Ising models are standard formats for the problem instance formulation of quantum annealing and quantum approximate optimization algorithm. This paper proposes a formulation method of QUBO models for flexible flow-shop scheduling problems with resource changeover based on timed colored Petri nets. The proposed method generates QUBO models for such practical flow-shop scheduling problems from Petri net firing rules, problem-specific constraints, and optimization criteria. The proposed method requires us to use only the domain knowledge of the target optimization problem and simple rules of Petri nets. Our method provides a low-cost formulation and reduces the hurdle to increasing the usability of quantum annealing and QAOAs.