Selective Simulated Annealing for Large Scale Airspace Congestion Mitigation

This paper presents a methodology to minimize the airspace congestion of aircraft trajectories based on slot allocation techniques. The traffic assignment problem is modeled as a combinatorial optimization problem for which a selective simulated annealing has been developed. Based on the congestion encountered by each aircraft in the airspace, this metaheuristic selects and changes the time of departure of the most critical flights in order to target the most relevant aircraft. The main objective of this approach is to minimize the aircraft speed vector disorder. The proposed algorithm was implemented and tested on simulated trajectories generated with real flight plans on a day of traffic over French airspace with 8800 flights.

Finding Equilibria in the Traffic Assignment Problem with Primal-Dual Gradient Methods for Stable Dynamics Model and Beckmann Model

In this paper, we consider the application of several gradient methods to the traffic assignment problem: we search equilibria in the stable dynamics model (Nesterov and De Palma, 2003) and the Beckmann model. Unlike the celebrated Frank–Wolfe algorithm widely used for the Beckmann model, these gradients methods solve the dual problem and then reconstruct a solution to the primal one. We deal with the universal gradient method, the universal method of similar triangles, and the method of weighted dual averages and estimate their complexity for the problem. Due to the primal-dual nature of these methods, we use a duality gap in a stopping criterion. In particular, we present a novel way to reconstruct admissible flows in the stable dynamics model, which provides us with a computable duality gap.

Congestion Control for Mixed-Mode Traffic with Emission Cost

This paper presents two models to investigate the traffic assignment problem. In the two models, the emission cost for gasoline vehicles (GVs) is considered. The credit schemes are considered in the constraint of the models. The operation costs for battery electric vehicles (BEVs) and GVs are also studied. Particularly, the constraints related to the credit schemes can be utilized to adjust the number of GVs and to promote growth of the number of BEVs, which is a novel idea that was not studied. Preliminary numerical experiments demonstrate that the models are effective and the extended distance limit of BEVs can raise the volume of BEVs under the condition that the unit traffic cost of BEVs is lower than GVs. Therefore, it is feasible to control the quantity of GVs by adjusting the total credit schemes, and it is viable to reduce the emission by enlarging the number of BEVs’ users.