Metaheuristics for Air Traffic Management

The Context of Air Traffic Management

Introduction

The purpose of this chapter is to present the current air traffic management (ATM) system in a clear and concise manner so that readers unfamiliar with it will understand the issues addressed in this book. ATM covers a wide range of activities, including air traffic control (ATC) in which ground-based controllers monitor aircraft and give instructions to pilots to avoid collisions.

Vocabulary and units

Disregarding instrument errors, CAS is the airspeed used by pilots when conducting flight, along with Mach number, which is the ratio of TAS to the speed of sound in air. Airplanes fly in the air, and air moves over the earth's surface.

Missions and actors of the air traffic management system

CAS) is the TAS that would be required at mean sea level to obtain the same dynamic pressure as that measured in the airplane. In the United States, this regulation takes the form of ground delay (GDP) programs relating to each or several airports in the same area.

Visual flight rules and instrumental flight rules

To avoid airspace or airport congestion, it is necessary to organize and regulate traffic flows. Similar organizations exist in other parts of the world where traffic is dense enough to require such flow rules.

Airspace classes

This continental-scale network management is performed in Europe by the Eurocontrol Network Management Operations Center (NMOC), which enforces air traffic management (ATFM) regulations when required by ATC units anticipating congestion.

Airspace organization and management

Flight information regions and functional airspace blocks
Lower and upper airspace
Controlled airspace: en route, approach or airport control
Air route network and airspace sectoring

In the United States, there is no UIR but the upper airspace sectors start at FL 240. The control tower is in charge of aircraft separation in the neighborhood of the runway.

Figure 1.3. Functional airspace blocks in Europe. For a color version of the figure, see www.iste.co.uk/durand/atm.zip

Traffic separation

Separation standard, loss of separation
Conflict detection and resolution
The distribution of tasks among controllers
The controller tools

Such extended conflicts can be formalized as closures of the relationship "in conflict with". With the emergence of new technologies and new computer-aided control aids being developed, a new division of tasks in the European and American modernization programs of the ATM/ATC systems is discussed.

Figure 1.6. Routes and airspace sectors in Europe (2009), in the upper airspace. For a color version of the figure, see

Traffic regulation

Capacity and demand
Workload and air traffic control complexity

This reported capacity can be seen as an acceptable compromise between the delays experienced by airlines and the workload of air traffic controllers. Capacity is related to a workload threshold that air traffic controllers must not exceed.

Figure 1.9. Intuitive approach of ATC complexity

Airspace management in en route air traffic control centers

Operating air traffic control sectors in real time
Anticipating sector openings (France and Europe)

The candidate sector configurations were then compared and the sector opening scheme deemed most suitable for the traffic demand was then forwarded to the organization in charge of traffic flow management. It questions the quality of the forecast made in relation to the sector opening scheme based on incoming traffic flows and sector capacity.

Figure 1.11. Example of an HMI displaying sector opening schemes.

Air traffic flow management

These differences may explain why researchers in Europe and in the United States sometimes focus on different topics. Since the 1990s, however, these differences between Europe and the United States have tended to disappear as airports have become overcrowded in Europe as well.

Research in air traffic management

The international context
Research topics

A triangular array is used to store some values that are used in the fitness calculation. The center of the new cluster is the barycenter of all points in the cluster;.

Air Route Optimization

Introduction

Optimal positioning of nodes and edges
Node positioning, with fixed topology, using a simulated
Defining 2D-corridors with a clustering

Starting from an initial point, the simulated annealing algorithm explores the search space by randomly selecting a next point near the current point. In the dual representation of the largest flows, the points in the cells with the highest density are replaced by a single corridor (a point in the dual space).

Figure 2.1. Crossing points of the direct routes of traffic flows above 10 flights per day

A network of separate 3D-tubes for the main traffic flows

A simplified 3D-trajectory model
Problem formulations and possible strategies
An A algorithm for the “1 versus n” problem
A hybrid evolutionary algorithm for the global problem
Results on a toy problem, with the
Application to real data, using a more realistic 3D-tube model

For the remaining lanes, there is no clear trend in the variations in the deviation costs and calculation time. The geometric boundaries of the 3D pipes are not used in cost and heuristic functions.

Figure 2.6. A simplified model of 3D-trajectory

Conclusion on air route optimization

In [GIA 02a, GIA 02b], Gianazza and Alliot used a genetic algorithm [GOL 89, MIC 92] to construct an optimal airspace partition in ATC sectors. The separation norm is thus tested for each pair of points of the two investigated trajectories (up = 900 points per trajectory for to ton = 9; 500 flights in O(n2p2)), as shown in Figure 4.1 in the horizontal plane.

Airspace Management

Airspace sector design

It is worth asking ourselves whether the division of airspace into sectors is optimal in relation to the evolution of traffic. After his PhD, Delahaye proposed improved models to handle non-convex sectors [DEL 98].

Functional airspace block definition

Simulated annealing algorithm
Ant colony algorithm
A fusion–fission method
Comparison of fusion–fission and classical graph

The minimization criterion chosen by Bichot is the normalized cut ratio measure corresponding to the sum of the flows entering or leaving the functional blocks divided by the sum of the internal flows. During the first phase of the algorithm, the control temperature is still high and the selected sector is connected to a block with a low cut ratio.

Figure 3.2. Graph model for an airspace partition

Prediction of air traffic control sector openings

Problem difficulty and possible approaches
Using a genetic algorithm
Tree-search methods, constraint programming
A neural network for workload prediction
Conclusion on the prediction of sector openings

Second, the number of connected components of the solution set grows exponentially with the number of planes. We denote byjjjjj the cardinality of the constraint, which is the number of forbidden pairs of maneuvers.

Figure 3.6. Existing French functional airspace blocks (left: 16,000 ft; right: 36,000 ft)

Departure Slot Allocation

Introduction

This ground holding scheme is intended to take into account en route capacity constraints provided by each Air Traffic Control Center (ATCC) as the number of aircraft per hour based on their daily schedule. However, one of the limitations of this regulatory model is that the definition of sector capacity (the hourly rate of aircraft entering a sector) is poorly correlated with traffic complexity relative to controller workload, as estimated in [GIA 06b].

Context and related works

Ground holding

Next, we describe Allignol's model of a conflict-free slot allocation, starting with the conflict detection and details on the evolutionary algorithm. One of the key operational ATM concepts of the SESAR program that Episode 3 sought to validate is the design of conflict-free 4D tubes in a crowded airspace (while separation could be delegated to aircraft in less dense areas).

Conflict-free slot allocation

Conflict detection
Sliding forecast time window
Evolutionary algorithm

If it is too large, the problem size will involve very many variables and the solution may be difficult. The advantage of this sharing scheme is its O(plog(p)) complexity (instead of aO(p2) complexity for classical sharing) if the population size is

Figure 4.1. Conflicting points detection

Results

Evolution of the problem size
Numerical results

With our evolutionary algorithm approach, all conflicts could be solved by slowing down less than a fifth of the aircraft. One explanation could be that as the size of the problem increases, the evolutionary algorithm does not converge so easily.

Figure 4.5. Total number of ﬂights (solid) and problem size (i.e. number of delayable aircraft, dotted) at 8 a.m

Concluding remarks

As illustrated in Figure 5.5, the generated delay appears to be 20 s lower (on average per aircraft) than with first-served runway planning (FCFS) and half that measured by a full simulation ( including taxi conflict resolution) of the same traffic. The simulator added random noise to the real plane trajectories so they wouldn't.

Airport Traffic Management

Introduction

Airports’ main challenges
Known difficulties
Optimization problems in airport traffic management

Coordination between different actors is an important issue, which is addressed in the Airport Collaborative Decision Making (ACDM) project in both Europe and the United States [12 EUR]. Arrival management systems (AMAN) predict and organize the arrival flow [10 EUR] from the approach sectors to the airport: these systems help controllers to build optimized arrival schedules with flexible landing fees, ensuring automatic coordination between the approach sectors and the airport.

Gate assignment

Problem description
Resolution methods

Some attempts to solve the gate assignment problem on real airport flight data by exact methods (obtaining and proving the optimal solution) can be found in the literature, using for example linear programming relaxation at Toronto International Airport [MAN 85] or branch and bound techniques at King Khalid International Airport [BOL 00] and at Chiang Kai-Shek Airport in a multi-objective formulation [YAN 01]. For these reasons, the port assignment problem is also often solved using local methods (which do not guarantee that an optimal solution can be found).

Figure 5.2. Neighborhood moves for the gate assignment problem

Runway scheduling

An example of problem formulation
Resolution methods

Hybridization between different metaheuristics is also often used in the literature to improve the efficiency of algorithms. In his PhD thesis [DEA 10], the author provided a formulation for the problem of scheduling aircraft on a runway that can be used in either single or mixed mode, and where some of the departures are constrained by a specific CTOT.

Surface routing

Related work

The objective function to be minimized is a weighted combination of the total taxi time and the total waiting time. This hybridization provides some significant improvements to the solutions found by the genetic algorithm in medium traffic situations (during busy periods, the simplified flow management algorithm does not help the genetic algorithm find better solutions).

Figure 5.6. Trajectory prediction under speed uncertainties

Global airport traffic optimization

Coordination scheme between the different predictive systems
Simulation results

OPT sequential: optimal trajectory planning and the sequential method used to resolve the surface conflicts;. OPT hybrid GA: optimal path planning and the hybrid genetic algorithm used to solve the surface conflicts.

Figure 5.10. Global airport traffic optimization

Conclusion

This calculation is the most time-consuming aspect of creating the problem because the number of pairs tested is large. For each combination, 10 scenarios of aircraft converging to the center of the considered airspace volume were randomly constructed.

Conflict Detection and Resolution

Introduction

Their main tool is a two-dimensional (2D) traffic display with some indication of aircraft altitude, speed and routes taken. The literature on air traffic conflict detection and resolution was very poor before the early 1990s.

Conflict resolution complexity

If there are n aircraft involved in a cluster, the number of aircraft pairs is n(n2 1) and the number of connected components is 2n(n21). For an aircraft cluster, the number of aircraft pairs is (n2 1), but each aircraft sees only (n 1) possible intruders.

Figure 6.2. Different cluster structures for two, three, four and five aircraft.

Free-flight approaches

Reactive techniques
Iterative approach
An example of reactive approach: neural
A limit to autonomous approaches: the speed constraint

In the example of Figure 6.3, with a priority order (A > C > B), aircraft B receives two tokens, while with a priority order (A > B > C), the aircraft receives one token from aircraft A, the aircraft receives one token from plane B; We chose a three-layer network (see Figure 6.5), which returned a heading change of 45 maximum (for a time step of 15 seconds).

Figure 6.3. Three aircraft configurations. Left: priority order = A>C>B.

Iterative approaches

When slon = 0, the longitudinal velocity of the aircraft cannot be modified and the results show that the algorithm cannot always handle low density, while kurslon = 0:3.80%.

Global approaches

PAL 01, PAL 02] developed a mathematical model using mixed integer linear programming that can be solved by CPLEX and ensured the global optimality of the solution. In a transition context in which controllers will still be in control of the traffic, but automated tools can help them in their task, the problem modeling must also take into account the controller uncertainties;.

Figure 6.15. Total number of failures for different densities of aircraft as a function of the speed range s lon 2 [0:; 1:]

A global approach using evolutionary computation

Maneuver modeling
Uncertainty modeling
Real-time management
Evolutionary algorithm implementation
Alternative modeling
One-day traffic statistics
Introducing automation in the existing system

For function [6.1], the probability of increasing fitness with the classical or the adapted operator can be calculated mathematically for all possible parent pairs. An aircraft is chosen from among those whose local suitability is higher than a given threshold (eg the aircraft still in conflict).

A global approach using ant colony optimization

Problem modeling
Algorithm description
Algorithm improvement: constraint relaxation
Results
Conclusion and further work

If the number of aircraft is , a bunch of ants is created to represent each aircraft group at each generation of the optimization process. At the next generation, the number of ants that have less than one conflict is still 20 and increases to 30 at generation 47.

A new framework for comparing approaches

Introduction
Trajectory prediction model
Conflict detection
Benchmark generation
Conflict resolution

After each move, the convex hull of the generated point cloud is calculated for each state. This approach can be easily generalized to the third dimension (the vertical plane), taking into account uncertainties in the aircraft's rate of climb.

Conclusion

ALL 13] ALLIGNOL C., BARNIER N., DURAND N., et al., “A new framework for en-route conflict resolution,” Proceedings of the 10th USA/Europe Air Traffic Management Research and Development Seminar, 2013. Autonomous Conflict Resolution Analysis in a Speed Restricted Environment”, Proceedings of the 11th Air Traffic Management Research and Development Seminar, 2015.