Jean-Loup Farges

Optimizing and assigning price levels for air traffic management

Pricing policies could encourage airline companies to modify departure times and routes of their flights in order to reach a route-slot allocation target that minimizes the en-route congestion. The problem of restricting the number of price levels and the assignment of one price level to each sector at each time period is studied using a simulation based on a Logit discrete choice model. In this model, an option is defined as the combination of a departure time and a route. For each flight, a utility is associated to each option and takes into account the flying cost, the cost of ground delay and the prices of crossed sectors. The optimization of the pricing policy considers average flows and minimizes the quadratic difference between desired and expected flows on each option. A heuristic algorithm that involves successive iterations of simulated annealing and gradient methods performs this optimization. The simulated annealing assigns a price level to each sector at each time period, and the gradient algorithm computes new values of price levels. The test of the method on constructed examples indicates that the use of only four price levels does not significantly deteriorate the performance of the system with respect to the use of independent prices.

Planning in Partially Observable Domains with Fuzzy Epistemic States and Probabilistic Dynamics

A new translation from Partially Observable MDP into Fully Observable MDP is described here. Unlike the classical translation, the resulting problem state space is finite, making MDP solvers able to solve this simplified version of the initial partially observable problem: this approach encodes agent beliefs with possibility distributions over states, leading to an MDP whose state space is a finite set of epistemic states. After a short description of the POMDP framework as well as notions of Possibility Theory, the translation is described in a formal manner with semantic arguments. Then actual computations of this transformation are detailed, in order to highly benefit from the factored structure of the initial POMDP in the final MDP size reduction and structure. Finally size reduction and tractability of the resulting MDP is illustrated on a simple POMDP problem.