A Semidefinite Relaxation for Air Traffic Flow Scheduling

TL;DR

This paper introduces a semidefinite relaxation approach to optimize air traffic flow scheduling, transforming a complex mixed integer problem into a convex form and proposing a randomization method for better solutions.

Contribution

It presents a novel semidefinite relaxation technique tailored for air traffic scheduling, improving solution quality over traditional methods.

Findings

Convex relaxation effectively approximates the original problem.

The approach handles large-scale instances with specific structure.

Randomization enhances solution quality.

Abstract

We first formulate the problem of optimally scheduling air traffic low with sector capacity constraints as a mixed integer linear program. We then use semidefinite relaxation techniques to form a convex relaxation of that problem. Finally, we present a randomization algorithm to further improve the quality of the solution. Because of the specific structure of the air traffic flow problem, the relaxation has a single semidefinite constraint of size dn where d is the maximum delay and n the number of flights.