A NEW MODELLING FOR THE AIRCRAFT LANDING PROBLEM AND MATHEURISTIC APPROACH TO SOLVE THE PROBLEM WITH A LARGE NUMBER OF AIRCRAFT

ABSTRACT

Air traffic management has become increasingly complex due to the increasing use of air transport. One of the main management bottlenecks is planning the efficient use of runways for takeoff and landing. This paper aims to investigate the Aircraft Landing Problem, which seeks to minimize earliness and tardiness in aircraft landing time, assigning them to a runway to land and sequencing them. A new mathematical formulation based on Job Shop was proposed for the problem, comparing it with four mathematical formulations in the literature; three directly comparable and another containing a particularity that does not allow a direct comparison with the other formulations. Computational tests were performed on 49 instances of the literature using the Gurobi Optimizer optimization package. These mathematical formulations commonly used for the ALP present difficulties in finding the optimal solution when the number of aircraft to land is large, i.e., more than 50 aircraft. Therefore, we proposed a matheuristic to solve instances with a greater number of aircraft than the Gurobi Optimizer cannot solve optimally. This matheuristic first finds an initial solution using relax-and-fix (RF) and then fix-and-optimize (FO) improves the found solution. Comparisons were also made using the first feasible solution obtained by Gurobi and then was improved with FO. Among the matheuristic variations, the one that obtained the best result was the combination of RF with FO and this also showed efficiency in relation to the work in the literature that uses FO.

Keywords:
aircraft landing problem; mixed integer programming; matheuristic; relax-and-fix; fix-and-optmizer