Ant Colony Optimization for Air Traffic Conflict Resolution · 2010. 7. 8. · Introduction Ant Colony Optimization Application to Conﬂict Resolution Conclusion Conﬂict Resolution

Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion

Ant Colony Optimizationfor Air Traffic Conflict Resolution

Nicolas Durand, Jean-Marc Alliot

DSNA/R&D/POM1

http://pom.tls.cena.fr/pom

July 1, 2009

1DSNA/DTI R&D/Planing Optimization Modeling Team


Introduction

Ant Colony Optimization

Application to Conflict Resolution

Conclusion


Conflict Resolution

• Current Situation : no effective tool for separating aircraft

• New means : GPS capabilities (FMS enhancement), Data-Linkcommunications ⇒ Enhance Trajectory Prediction

• Pairwise conflicts ⇒ Clusters• ⇒ High complexity of the underlying problem• Example : solving a n aircraft conflict in the horizontal plane⇒ n(n−1)2 aircraft pairs ⇒ 2

n(n−1)2 connected components to

explore

• ⇒ Local optimization uneffective


Conflict Resolution

• Current Situation : no effective tool for separating aircraft• New means : GPS capabilities (FMS enhancement), Data-Link

communications ⇒ Enhance Trajectory Prediction

• Pairwise conflicts ⇒ Clusters• ⇒ High complexity of the underlying problem• Example : solving a n aircraft conflict in the horizontal plane⇒ n(n−1)2 aircraft pairs ⇒ 2


explore



Conflict Resolution


communications ⇒ Enhance Trajectory Prediction• Pairwise conflicts ⇒ Clusters

• ⇒ High complexity of the underlying problem• Example : solving a n aircraft conflict in the horizontal plane⇒ n(n−1)2 aircraft pairs ⇒ 2


explore



Conflict Resolution


communications ⇒ Enhance Trajectory Prediction• Pairwise conflicts ⇒ Clusters• ⇒ High complexity of the underlying problem

• Example : solving a n aircraft conflict in the horizontal plane⇒ n(n−1)2 aircraft pairs ⇒ 2


explore



Conflict Resolution


communications ⇒ Enhance Trajectory Prediction• Pairwise conflicts ⇒ Clusters• ⇒ High complexity of the underlying problem• Example : solving a n aircraft conflict in the horizontal plane⇒ n(n−1)2 aircraft pairs ⇒ 2


explore



Examples of existing algorithms

• Central & Global approaches• Integer Linear programming

• Semi-definite programming• Branch and Bound Intervals• Genetic Algorithms

• Autonomous approaches

• Neural network• Repulsive forces

• Iterative approaches : give priorities to aircraft and use localoptimization (for example : A∗ algorithm).



• Central & Global approaches• Integer Linear programming• Semi-definite programming

• Branch and Bound Intervals• Genetic Algorithms






• Central & Global approaches• Integer Linear programming• Semi-definite programming• Branch and Bound Intervals

• Genetic Algorithms• Autonomous approaches





• Central & Global approaches• Integer Linear programming• Semi-definite programming• Branch and Bound Intervals• Genetic Algorithms







• Autonomous approaches• Neural network

• Repulsive forces





• Autonomous approaches• Neural network• Repulsive forces



ACO principles

• Use the environment as a medium of communication

• Mimic the ants trying to find the shortest path from theircolony to food

HomeFood


ACO principles

• Use the environment as a medium of communication• Mimic the ants trying to find the shortest path from their

colony to food

HomeFood


ACO algorithm principle

• Ants deposite pheromones according to the quality of the paththey find

• Ants more likely to follow paths with the most pheromones

• Add evaporation process to prevent algorithm from localconvergence

• Stop when no more improvement


ACO for the Traveling Salesman Problem

• Ants sent on graph. Each ant buildscomplete path. Choice of next cityinfluenced by pheromone quantity on paths.

• Ants deposite pheromones on the path

chosen : ∆τij(t) ∝1∑Lij

• At each iteration, evaporate trails :τij ← ρ · τij

• Stop when no more improvement

��

��

��

��

��

��

C

D

BG

F

O

E

A

Vidéo


n aircraft conflict example

Conflict zone

n aircraft


Maneuver modeling

W

U

V

T1

T0

Discretize time into timesteps3 possible angles : 10, 20 or 30 degrees


Possible transitions

END

U V W

Ui+1 = Ui

Vi+1 = Vi + 6

Wi+1 = Vi

U1 = 1, V1 = 6 and W1 = 0Number of possible states at timestep i= Ui + Vi + Wi = 12 i − 5


One ant per cluster or one ant per aircraft

• one ant → one cluster

• for n aircraft and t timesteps : (12 t − 5)ntrails.

• For n = 5 and t = 10 : more than 1010 trails• one ant → one aircraft• for n aircraft and t timesteps : n (12 t − 5)

trails.

• For n = 30 and t = 20 : more than 7050trails instead of 1071

one ant for n aircraft

one ant per aircraft



• one ant → one cluster• for n aircraft and t timesteps : (12 t − 5)n

trails.


trails.







trails.

• For n = 5 and t = 10 : more than 1010 trails

• one ant → one aircraft• for n aircraft and t timesteps : n (12 t − 5)

trails.







trails.

• For n = 5 and t = 10 : more than 1010 trails• one ant → one aircraft

• for n aircraft and t timesteps : n (12 t − 5)trails.







trails.


trails.





Initial amount of pheromones on the graph

END

1

1

1

11

1

1

1

1

1

1

2

2

1

1

126

1

11

1

2

2

3

3

12

1


Algorithm description (1)

• Each path is given a score (the smaller, the better)

• U = +0, V = +2 and W = +1• Conflict → no pheromones• No conflict →

∆τ =n − nout

n· τ0spath

where nout is the number of ”lost”ants, τ0 the originalquantity of pheromones, and spath the score of the pathfollowed by the ant.

• At each node, the next edge is chosen with a probabilitydepending on its quantity of pheromones.



• Each path is given a score (the smaller, the better)• U = +0, V = +2 and W = +1

• Conflict → no pheromones• No conflict →

∆τ =n − nout

n· τ0spath





• Each path is given a score (the smaller, the better)• U = +0, V = +2 and W = +1• Conflict → no pheromones

• No conflict →∆τ =

n − noutn

· τ0spath





• Each path is given a score (the smaller, the better)• U = +0, V = +2 and W = +1• Conflict → no pheromones• No conflict →

∆τ =n − nout

n· τ0spath





• An evaporation principle : the amount of pheromones isdecreased by x% (in the examples x = 10%) at the end ofeach iteration.

• Ending criteria : the score obtained by each bunch of ants nolonger decreases.


Example of 5 aircraft conflict resolution

18 iterations - score=89


Algorithm improvement : constraint relaxation

• High density areas → no ants are able to solve every conflict

• ⇒ Relax the conflict resolution constraint : accept ants with rremaining conflicts

• When solutions are found for a certain number of ants, theconstraint is reinforced

• Example : define r as the minimum number of conflicts of theleast conflicting ant

• r is the number of allowed conflicts per ant at the firstgeneration.

• Reduce r when the number of ants having less than r conflictsis higher than nr


Algorithm improvement : constraint relaxation

• High density areas → no ants are able to solve every conflict• ⇒ Relax the conflict resolution constraint : accept ants with r

remaining conflicts

• When solutions are found for a certain number of ants, theconstraint is reinforced

• Example : define r as the minimum number of conflicts of theleast conflicting ant

• r is the number of allowed conflicts per ant at the firstgeneration.

• Reduce r when the number of ants having less than r conflictsis higher than nr



generation: 0 - 4 conflicts max - 9 aircraft



generation: 45 - 1 conflict max - 20 aircraft




Vidéo


Conclusion

• The modeling can be extended to any trajectory

• Complexity depends on the number of alternate pathsavailable

• Results will be compared to the existing ERCOS (using GAs)• Stochastic optimization : no guarantee of solution or optimum• No effective tool offered to controllers without significant

enhancement of ground TP


Conclusion

• The modeling can be extended to any trajectory• Complexity depends on the number of alternate paths

available




Conclusion


available

• Results will be compared to the existing ERCOS (using GAs)

• Stochastic optimization : no guarantee of solution or optimum• No effective tool offered to controllers without significant



Conclusion


available

• Results will be compared to the existing ERCOS (using GAs)• Stochastic optimization : no guarantee of solution or optimum

• No effective tool offered to controllers without significantenhancement of ground TP


Conclusion


available



IntroductionAnt Colony OptimizationApplication to Conflict ResolutionConclusion

Documents

Ant Colony Optimization for Air Traffic Conflict Resolution · 2010. 7. 8. · Introduction Ant Colony Optimization Application to Conﬂict Resolution Conclusion Conﬂict Resolution