Philipp Schworm, Xiangqian Wu, Matthias Klar, Moritz Glatt, Jan Aurich

• Flexible Job Shop Scheduling (FJSSP) is a challenging optimization problem with multiple conflicting objectives used to model and compute real-world process scheduling tasks. In order for a manufacturing system to remain competitive, it is necessary to compute such optimization problems quickly and efficiently. The limitations of conventional optimization methods frequently stem from a delicate balance between solution quality and computation time. Consequently, a pressing need for solution algorithms arises that can effectively transcend these limitations. This paper presents a novel Quantum Annealing-based solving algorithm (QASA) for computing FJSSP, leveraging the power of Quantum Annealing combined with classical techniques. The proposed approach aims to optimize a multi-criterial FJSSP considering makespan, total workload, and job priority simultaneously. QASA employs a Hamiltonian formulation with Lagrange parameters to integrate the problem's constraints and objectives. By assigning appropriate weights to the objectives, the method allows the prioriti-zation of certain objectives over others. To handle the computational complexity of large FJSSP instances, the problem is decomposed into smaller subproblems, and a decision logic based on bottleneck factors is employed to select critical jobs for computation combined with variable pruning techniques. To evaluate the effectiveness of the proposed approach, experiments are conducted on benchmark problems, considering makespan, total workload, and priority objectives. Therefore, QASA combining tabu search, simulated annealing, and Quantum Annealing is used for efficient computation and is compared with a classical solving algorithm (CSA) combining tabu search and simulated annealing. The results demonstrate that QASA outperforms CSA in terms of solution quality, as measured by set coverage and hypervolume ratio metrics. Furthermore, computational efficiency analysis reveals that QASA achieves superior Pareto solutions compared to the classical approach, with a reasonable increase in computation time.