A comparative study of crew pairing optimization formulations: Preparing for quantum computing

Quantum computing is widely discussed for its potential to solve challenging optimization problems much faster. However, real-world airline problem sizes currently exceed the capabilities of existing quantum hardware. Preparing for larger quantum hardware requires developing and benchmarking problem formulations most suitable for quantum implementation. In this study, we use the crew pairing problem from aviation as an use case to benchmark different problem formulations: a set partitioning model and two compact formulations, a constrained flow assignment problem and a satisfiability problem (SAT). For classical benchmarking we solve these formulations using mixed integer programming and SAT solvers. For quantum benchmarking we translate the formulations into quadratic unconstrained binary optimization and Ising formulations. Our benchmarking shows that the problem formulations lead to different classical and quantum properties. Among the formulations considered, the SAT formulation emerges as the most promising candidate for future implementation on quantum hardware with the lowest share of non-zero elements and highest spectral gap, despite its larger ratio of linear term coefficients.