Airport ground movement

Worldwide air traffic tends to increase and for many airports it is no longer an op-tion to expand terminals and runways, so airports are trying to maximize their op-erational efficiency. Many airports already operate near their maximal capacity. Peak hours imply operational bottlenecks and cause chained delays across flights impacting passengers, airlines and airports. Therefore there is a need for the opti-mization of the ground movements at the airports. The ground movement prob-lem consists of routing the departing planes from the gate to the runway for take-off, and the arriving planes from the runway to the gate, and to schedule their movements. The main goal is to minimize the time spent by the planes during their ground movements while respecting all the rules established by the Ad-vanced Surface Movement, Guidance and Control Systems of the International Civil Aviation. Each aircraft event (arrival or departing authorization) generates a new environment and therefore a new instance of the Ground Movement Prob-lem. The optimization approach proposed is based on an Iterated Local Search and provides a fast heuristic solution for each real-time event generated instance granting all safety regulations. Preliminary computational results are reported for real data comparing the heuristic solutions with the solutions obtained using a mixed-integer programming approach.

The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.