The conflicts detection and resolution between aircraft trajectories are among the main tasks of air traffic controllers. It is now possible to provide software tools to assist them in these tasks.

In the conflicts detection, false alarm rate and detection are not very dependent on the quality of the trajectory forecast and fine modeling uncertainties. There are at least two ways to model the uncertainty of future positions :

- Frame this uncertainty confidence intervals or tolerance. This approach defines a "box" around the future nominal positions, in which the aircraft presence is provided with a certain probability, or a certain level of certainty.
- define a probability of the plane presence at each point along the planned route.

According to the modeling uncertainties, conflict detection is therefore revert to determine when the distance between areas of uncertainty will be substandard vertical and horizontal separation or to determine whether the probability of a loss of separation is greater than one given threshold.

Resolving conflicts is finding alternative paths, in which deviation is minimal from the original trajectory, and that meet the standards of separation.

It can be a constrained optimization problem. The function to minimize is relatively simple. On the other side, for realistic modeling, the analytical form of the separation constraints is not immediately accessible: evaluation of separation constraints usually requires traffic simulation , with an alternative paths calculation and conflicts detection.

Beyond this formulation, the objectives of a conflict resolution can be different:

- find a solution, even poor quality.
- find a local optimum. For example,by choosing an arbitrary order of priority between the aircraft and/or direction of operation for each one, it greatly reduces the problem difficulty, but we explore possible solutions for these choices.
- find a global optimum for all trajectories deviations, which is a more difficult problem than the previous one.
- prove the existence or the lack of solutions.
- prove the optimality of solutions found.

**Centralized approach or distributed approach**

At the operational level, two approaches are possible for conflict resolution: centralized or distributed. In the first approach, a control system determines and coordinates the operations of conflict resolution for all traffic that it supports, having an overall view of it.

In the distributed approach, each aircraft has only partial visibility of the surrounding traffic. A mechanism for coordinating distributed operations is essential with for example a priority "tokens" distribution, or otherwise a logic for an unambiguous choice of maneuvers.

The distributed approach is suboptimal, in general case, and the solutions quality heavily depends on the priority order between planes. In the centralized approach, conflict resolution becomes a highly combinatorial problem, difficult to solve by conventional methods for more than twenty aircraft with realistic assumptions.

**Resolution methods**

The choice of methods depends on the resolution of the treated problem (centralized or distributed, local or global optimum, resolution etc.) and the degree of desired realism . They also differ according to the model chosen for the trajectories, uncertainties, and maneuvers. In particular, the choice of discrete or continuous variables is essential.

Meta-heuristics are effective on larger bodies with a realistic modeling, but the optimum is not proven.

- Hybridization of interval methods and meta-heuristics for conflict resolution. The objective is to seek a proof of existence and solution optimality for instances and realistic modeling.
- Constraint Programming applied to conflict resolution. It also seeks to prove solutions existence and optimality, with discrete variables for the choice of maneuvers and trajectory modeling.
- Conflict resolution with a new trajectory model curve based on B-splines. The objective is to define a path using a limited number of parameters. From this model, we study a new formulation of the conflict resolution problem for a continuous optimization problem. This is based on a formulation so-called semi-infinite constraint separation between two aircraft. The way of how are defined the objective function and constraint functions allows us to calculate the gradients. We can compare different methods with or without gradient: genetic algorithms, interior point method, and without derivatives method.

The origin of evolutionary algorithms used in European projects ERASMUS (for deconfliction by speed adjustments) and more recently in SESAR 4.7.2 (Separation task in en-route trajectory-based environment ) is the result of some MAIAA researchers' work , prior to the laboratory creation. For more information, see page ERCOS, with reference publications.