Abstract

International audience; The resolution of Air Traffic Control (ATC) conflicts is a constrained optimization problem : the goal is to propose, for a certain number, n, of aircraft, which might be in conflict in a near future, trajectories that satisfy the separation constraints between aircraft, and minimizes the delays due to the conflict's resolution. The type of conflict resolution trajectories we use allows to split the problem in two steps: first we choose, and freeze, what we call a configuration of the problem, i.e. for each aircraft, the direction in which the aircraft is diverted, and for each pair of aircraft, which of the two aircraft passes first at the crossing point of the two aircraft trajectories. We can then compute the optimal trajectories corresponding to this configuration, by solving a simple linear optimization problem. Thus we can use an Genetic Algorithm, along with a linear optimization algorithm, such as the simplex algorithm: the elements of the population, on which the GA operates, code configurations of the problem, and are evaluated using a linear optimization program.The advantage of this approach is that we get, as well as the fitness of an element of the population, the local optima corresponding to the configuration coded by this element. The GA actually searches for the global optimum among these local optima. We applied this methods to conflicts in which up to 6 aircraft are involved, and obtained really promising results. Document type: Part of book or chapter of book

Abstract

We consider a stochastic routing model in which the goal is to find the optimal route that incorporates a measure of risk The problem arises in traffic engineering, transportation and even more abstract settings such as task planning (where the time to execute tasks is uncertain), etc The stochasticity is specified in terms of arbitrary edge length distributions with given mean and variance values in a graph The objective function is a positive linear combination of the mean and standard deviation of the route Both the nonconvex objective and exponentially sized feasible set of available routes present a challenging optimization problem for which no efficient algorithms are known In this paper we evaluate the practical performance of algorithms and heuristic approaches which show very promising results in terms of both running time and solution accuracy. Document type: Part of book or chapter of book