Greedy-Heuristic-Aided Mixed-Integer Linear Programming Approach for Arrival Scheduling

Abstract

Scheduling arriving aircraft in terminal airspace can be formulated using mixed-integer linear programming and solved by a branch and bound algorithm. Given that the problem is intrinsically nondeterministic polynomial-time hard, success in solving the problem within a reasonable time is not always guaranteed. This paper proposes an efficient optimization approach that calculates the minimum total delay necessary for a conflict-free arrival sequence. A greedy heuristic is developed to find a feasible solution quickly, which serves as a “hot start” so that the branch and bound algorithm can prune as many search tree nodes as it can. Unnecessary searching is thus saved. The greedy heuristic also provides an estimated upper bound for the maximum delay that guarantees a feasible solution for the mixed-integer linear programming. In addition, it identifies a group of aircraft associated with high delays, which are suspended in the first stage of scheduling and sequenced in the second stage based on available time slots. This tactic decreases the computational difficulty. The proposed approach is validated using arriving traffic in 40 major United States airports. Compared to a standalone mixed-integer linear programming, the greedy-heuristic-aided mixed-integer linear programming yields suboptimal solutions in a more efficient manner, and the compromise of optimality is limited.