ant colony optimization for air traffic conflict resolution · 2010. 7. 8. · introduction ant...
TRANSCRIPT
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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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Introduction
Ant Colony Optimization
Application to Conflict Resolution
Conclusion
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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
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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-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
n(n−1)2 connected components to
explore
• ⇒ Local optimization uneffective
-
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-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
n(n−1)2 connected components to
explore
• ⇒ Local optimization uneffective
-
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-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
n(n−1)2 connected components to
explore
• ⇒ Local optimization uneffective
-
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-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
n(n−1)2 connected components to
explore
• ⇒ Local optimization uneffective
-
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-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
n(n−1)2 connected components to
explore
• ⇒ Local optimization uneffective
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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).
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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).
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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).
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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).
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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).
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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).
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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).
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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).
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
ACO principles
• Use the environment as a medium of communication
• Mimic the ants trying to find the shortest path from theircolony to food
HomeFood
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Vidéo
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Vidéo
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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C
D
BG
F
O
E
A
Vidéo
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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D
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F
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Vidéo
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
n aircraft conflict example
Conflict zone
n aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Maneuver modeling
W
U
V
T1
T0
Discretize time into timesteps3 possible angles : 10, 20 or 30 degrees
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
One ant per cluster or one ant per aircraft
• one ant → one cluster• for n aircraft and t timesteps : (12 t − 5)n
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.
• For n = 30 and t = 20 : more than 7050trails instead of 1071
one ant for n aircraft
one ant per aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
One ant per cluster or one ant per aircraft
• one ant → one cluster• for n aircraft and t timesteps : (12 t − 5)n
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.
• For n = 30 and t = 20 : more than 7050trails instead of 1071
one ant for n aircraft
one ant per aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
One ant per cluster or one ant per aircraft
• one ant → one cluster• for n aircraft and t timesteps : (12 t − 5)n
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.
• For n = 30 and t = 20 : more than 7050trails instead of 1071
one ant for n aircraft
one ant per aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
One ant per cluster or one ant per aircraft
• one ant → one cluster• for n aircraft and t timesteps : (12 t − 5)n
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.
• For n = 30 and t = 20 : more than 7050trails instead of 1071
one ant for n aircraft
one ant per aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
One ant per cluster or one ant per aircraft
• one ant → one cluster• for n aircraft and t timesteps : (12 t − 5)n
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.
• For n = 30 and t = 20 : more than 7050trails instead of 1071
one ant for n aircraft
one ant per aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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.
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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.
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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 − noutn
· 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.
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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.
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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.
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Algorithm description (2)
• 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.
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Algorithm description (2)
• 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.
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 5 aircraft conflict resolution
18 iterations - score=89
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 5 aircraft conflict resolution
46 iterations - score=78
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 5 aircraft conflict resolution
105 iterations - score=50
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 30 aircraft conflict resolution
generation: 0 - 4 conflicts max - 9 aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 30 aircraft conflict resolution
generation: 14 - 3 conflicts max - 13 aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 30 aircraft conflict resolution
generation: 15 - 2 conflicts max - 13 aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 30 aircraft conflict resolution
generation: 44 - 2 conflicts max - 20 aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 30 aircraft conflict resolution
generation: 45 - 1 conflict max - 20 aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 30 aircraft conflict resolution
generation: 47 - 1 conflict max - 30 aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 30 aircraft conflict resolution
generation: 48 - 0 conflict max - 30 aircraft
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Example of 30 aircraft conflict resolution
generation: 65 - 0 conflict max - 30 aircraft
Vidéo
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Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
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
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Conclusion
• The modeling can be extended to any trajectory• Complexity depends on the number of alternate paths
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
enhancement of ground TP
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Conclusion
• The modeling can be extended to any trajectory• Complexity depends on the number of alternate paths
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
enhancement of ground TP
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Conclusion
• The modeling can be extended to any trajectory• Complexity depends on the number of alternate paths
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
-
Introduction Ant Colony Optimization Application to Conflict Resolution Conclusion
Conclusion
• The modeling can be extended to any trajectory• Complexity depends on the number of alternate paths
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
enhancement of ground TP
IntroductionAnt Colony OptimizationApplication to Conflict ResolutionConclusion