  Flexible Job Shop Scheduling (FJSSP) is a complex optimization problem
crucial for real-world process scheduling in manufacturing. Efficiently solving
such problems is vital for maintaining competitiveness. This paper introduces
Quantum Annealing-based solving algorithm (QASA) to address FJSSP, utilizing
quantum annealing and classical techniques. QASA optimizes multi-criterial
FJSSP considering makespan, total workload, and job priority concurrently. It
employs Hamiltonian formulation with Lagrange parameters to integrate
constraints and objectives, allowing objective prioritization through weight
assignment. To manage computational complexity, large instances are decomposed
into subproblems, and a decision logic based on bottleneck factors is used.
Experiments on benchmark problems show QASA, combining tabu search, simulated
annealing, and Quantum Annealing, outperforms a classical solving algorithm
(CSA) in solution quality (set coverage and hypervolume ratio metrics).
Computational efficiency analysis indicates QASA achieves superior Pareto
solutions with a reasonable increase in computation time compared to CSA.
