The OPTIM group conducts research on optimization methods, with the aim to develop and apply methods appropriate to the problems of air traffic management.

The optimization is a discipline involved in many domains, both applications than academic, which has a theoretical framework, a rigorous mathematical modeling, and an effective set of practical methods that can be adapted to the problems of air traffic.

Here are the main issues treated by the OPTIM group, on optimization, its applications and similar related topics . The research topics are grouped according to the classification of the National Council of Universities (CNU)

• Applied Mathematics (CNU 26)
  • Optimization: models and methods for mathematical optimization applied to air traffic management, technical reformulation of models, heuristic for modularity maximization criterion in the graphs.
  • Operations Research
• Computer science (CNU 27)
• Optimization and parallelism cooperative parallelism between meta-heuristic methods and intervals, hybridization methods, operators, suitable for partially separable functions. Applications to solving air conflicts, taxiing, etc..
• Learning: many learning techniques (eg neural networks) use optimization methods (eg BFGS, downhill gradient, meta-heuristics). Application to the prediction of workload prediction of aircraft trajectories.
• Constraint programming, including applications to trajectory planning and takeoff slots.

These activities are described in the Research pages

The optimization methods developped by MAIAA to solve problems of air traffic management include:

• meta-heuristics (evolutionary algorithms, differential evolution, particle swarm, taboo search, hybrid methods, etc.)
• Interval methods (Branch and bound interval)
• Constraint Programming (with minimization or maximization of a variable)
• Tree search methods (A *, Branch and bound, etc.)
• Integer, linear, nonlinear, mixed programming
• Optimization in infinite dimensional space

The Air Traffic Management is a domain where the applications of the optimization are numerous.

Here is a list of major ATM applications on which MAIAA lecturers work:

• Complexity of the air traffic
• Forecasting workload of air traffic controllers
• Forecasting openings control sectors
• Air traffic Planning
• Ground aircraft taxiing
• Aircraft trajectory prediction
• Detection and resolution of air conflicts