A Comparative Study of MILP and MINLP for UAV Conflict Resolution Under Different Spatial Configurations

The large-scale deployment of unmanned aerial vehicles (UAVs) in low-altitude airspace requires efficient and reliable conflict resolution methods. This paper presents a comparative study of mixed-integer linear programming (MILP) and mixed-integer nonlinear programming (MINLP) formulations for heading-only UAV conflict resolution under three representative spatial configurations: circular, diamond, and random. To ensure a fair comparison, both formulations are implemented using the SCIP optimization framework. Extensive simulations with varying fleet sizes demonstrate that computational performance is governed primarily by spatial configuration rather than optimization class. In the structured diamond configuration, both models achieve comparable solution quality, with MINLP providing a modest reduction in computation time. In the symmetric circular configuration, MINLP consistently outperforms MILP by avoiding discretization-induced inefficiencies. In the unstructured random configuration, MINLP exhibits substantial advantages in both runtime and solution quality, whereas MILP experiences rapidly increasing computational complexity. These findings indicate that nonlinear optimization is not inherently less efficient than linear optimization for UAV conflict resolution. Instead, the underlying spatial conflict structure plays a decisive role in algorithm performance, providing practical guidance for selecting optimization frameworks in future UAV traffic management systems.