<p>Airplane refueling problem is a nonlinear unconstrained optimization problem with <i>n</i>! feasible solutions. Given a fleet of <i>n</i> airplanes with mid-air refueling technique, the question is to find the best refueling policy to make the last remaining airplane travel the farthest. At first, we proposed the definition of sequential feasible solution. We proved that if an airplane refueling instance has feasible solutions, it must have sequential feasible solutions; and the optimal feasible solution must be the optimal sequential feasible solution. We proposed the <i>sequential search algorithm</i> which aims to seek out all of the sequential feasible solutions and to search for the maximal sequential feasible solution by bubble sorting all of the sequential feasible solutions. We observed that the number of the sequential feasible solutions will change to grow at a polynomial rate when <i>n</i> is greater than an inflection point <i>N</i>. Moreover, we built an efficient computability scheme, according to which we could forecast within a polynomial time the computational complexity of the sequential search algorithm that runs on any given airplane refueling instance.</p>