Combining solutions of the axial assignment problem

We consider the NP-hard integer three-index axial assignment problem. The task of optimal combination of the pairs of feasible solutions of the problem is posed, and a linear complexity algorithm for its solution is constructed. This algorithm can be used as a supplement to heuristic or approximate algorithms for the three-index assignment problem for post-processing the obtained approximate solutions of the problem. The results of computational experiments, which demonstrate the promising nature of our approach, are presented.