Air Traffic Management by Stochastic Optimization

The annual number of flights in Western Europe has increased from about 2.6 million in 1982 to about 4.5 million in 1992, an increase of about 73%. Acute congestion of the Air Traffic Control system has been the result. A similar problem exists in United States, where each of thirtythree major airports has experienced about 20,000 hours of annual delays in 1997. Two kinds of congestion can be identified according to the part of airspace involved : Terminal congestion (around airports) and En-route congestion (between airports). In the past, the first way to reduce these congestions was to modify the structure of the airspace in order to increase the capacity (increasing the number of runways, increasing the number of sectors by reducing their size). This method has a limit due to the cost involved by new runways and the way to manage traffic in too small sectors (a controller needs a minimum amount of airspace to be able to solve conflicts). The other way to reduce congestion is to modify the flight plans in order to adapt the demand to the available capacity. To reach this goal, ground delay programs are often applied on aircraft which are expected to undergo congestion. Ground delays are safer (fewer aircraft waiting in the sky) and cheaper (according to the fuel consumption). When Integer Linear Programming (ILP) is applied to the general Ground Holding Problem, it can be shown that large delays are given to some aircraft in order to match the sector capacities. So, to reduce congestion in sectors and avoid large delays, demand has to be spread in spatial dimension too (route-slot allocation). Our research addresses the general time-route assignment problem : “ One considers a sectorized airspace and a fleet of aircraft with their associated route and slot of departure. For each flight a set of alternative routes and a set of possible slots of departure are defined. One must find “optimal” route and slot allocation for each aircraft in order to significantly reduce the peaks of congestion in sectors and airports, during one day of traffic.” A state of the art of the existing methods (including ILP) shows that this general bi-allocation problem is usually partially treated and the whole problem remains unsolved due to the complexity induced by this new spatial dimension of the state domain. Stochastic Optimization is then adapted to the problem. The strong point of this technique is its ability to investigate any kind of objective function without any regularities such as derivability and linearity. A sector congestion measure has been developed which gather the major control workload indicators. This measure is then computed for each proposed planning by refeering to an off-line simulation. New problem-based stochastic operators have been developed and successfully applied on real instances of the problem. Keywords—Air Traffic Management, Stochastic Optimization, Air Traffic Control, Congestion.