  The airplane refueling problem is a nonlinear combinatorial optimization
problem, and its equivalent problem the $n$-vehicle exploration problem is
proved to be NP-complete (arXiv:2304.03965v1, The $n$-vehicle exploration
problem is NP-complete). In Article (arXiv:2210.11634v2, A polynomial-time
algorithm to solve the aircraft refueling problem: the sequential search
algorithm), we designed the sequential search algorithm for solving large scale
of airplane refueling instances, and we proved that the computational
complexity increases to polynomial time with increasing number of airplanes.
Thus the airplane refueling problem, as an NP-complete problem, is solvable in
polynomial time when its input scale is sufficiently large.
