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Large-Scale 3D En-Route Conflict Resolution
Cyril Allignol, Nicolas Barnier, Nicolas Durand,Alexandre Gondran and Ruixin Wang
allignol,barnier,durand,gondran,wangrx
@recherche.enac.fr
ATM 2017 – SeattleJune 28th, 2017
Introduction
Background
The Conflict Resolution ProblemResearch on automatic conflict resolution started in the 1980s
Many different models comply with existing resolution techniques
Research from ANSPs focused on realistic models, but not on resolutionmethodsOther approaches focused both on model (e.g. using uncertainty modelsand BADA) and resolution algorithm, but completely tailored to a giventraffic simulator (e.g. CATS)
→ prevents scientific community from comparing different methods
Many generic resolution algorithms able to deal with complex problems(e.g. simplex, Branch & Bound, metaheuristics...): should be testedand compared scientifically on the same instances
Conflict resolution: large-scale combinatorial problem
→ a common model needed to validate the comparison
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 1 / 19
Introduction
The Conflict Resolution Problem
A New Framework for Solving En-Route Conflicts [ATM 2013]
Trajectory maneuver options + prediction with uncertainties
Conflicts discrete detection → combinatorial optimization problem
Resolution solvers independent from models
Benchmark enables scientific comparison of algorithms (e.g. CP vs GA)
What’s New. . .
Scenarios 3D over several FLs with possible in-between waypoints
Maneuvers more versatile, including FL change
Uncertainties more taken into account
Instances larger (up to 100 aircraft)
Solver Memetic Algorithm: harder, better, faster, stronger!
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 2 / 19
Introduction
The Conflict Resolution Problem
A New Framework for Solving En-Route Conflicts [ATM 2013]
Trajectory maneuver options + prediction with uncertainties
Conflicts discrete detection → combinatorial optimization problem
Resolution solvers independent from models
Benchmark enables scientific comparison of algorithms (e.g. CP vs GA)
What’s New. . .
Scenarios 3D over several FLs with possible in-between waypoints
Maneuvers more versatile, including FL change
Uncertainties more taken into account
Instances larger (up to 100 aircraft)
Solver Memetic Algorithm: harder, better, faster, stronger!
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 2 / 19
Introduction
Contents
1 BenchmarkTrajectory PredictionConflict DetectionConflict Resolution Problem
2 ResolutionDataAlgorithmsResults
3 Conclusion
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 3 / 19
Benchmark Trajectory Prediction
Traffic
Initial TrajectoriesLevelled (in our scenarios, but could be climbing or descending)
Following a sequence of waypoints
Associated to a nominal aircraft speed
Sampled into time steps of duration τ (small enough, e.g. 3 s)
→ ready to be embedded in a traffic simulator
FL 310
FL 300
FL 290
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 4 / 19
Benchmark Trajectory Prediction
Maneuver Model
ManeuversStarts at t0 and returns on initial trajectory after t1
Either change heading by α or change FL by δFL
For simplicity, heading and FL changes cannot be combined
parameter size typical valuesstart t0 n0 (= 4) 0,1,2,3 (min)
return t1 n1 (= 4) 5,6,7,8 (min)
horizontal α nα (= 6) -30,-20,-10,+10,+20,+30 (°)vertical δFL nFL (= 4) -20,-10,+10,+20 (FL)
Options per aircraft: nman = n0 × n1 × (nα + nFL) + 1 (= 161)
t1
t0α
t0
t1
δFL
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 5 / 19
Benchmark Trajectory Prediction
Maneuver Model
ManeuversStarts at t0 and returns on initial trajectory after t1
Either change heading by α or change FL by δFL
For simplicity, heading and FL changes cannot be combined
parameter size typical valuesstart t0 n0 (= 4) 0,1,2,3 (min)
return t1 n1 (= 4) 5,6,7,8 (min)
horizontal α nα (= 6) -30,-20,-10,+10,+20,+30 (°)vertical δFL nFL (= 4) -20,-10,+10,+20 (FL)
Options per aircraft: nman = n0 × n1 × (nα + nFL) + 1 (= 161)
t1
t0α
t0
t1
δFL
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 5 / 19
Benchmark Trajectory Prediction
Handling Uncertainties
Uncertainties on maneuvers and speed
parameter error typical values
start t0 εt0 ∈ [0, Et0 ] 10-30 s
return t1 εt1 ∈ [0, Et1 ] 10-30 s
angle α εα ∈ [−Eα, Eα] 1-3°
horizontal speed vh εvh ∈ [−Evh , Evh ] 2-6%
vertical speed vv εvv ∈ [−Evv , Evv ] 5-15%
beacon fly mode fm fm ∈ {Fb, Fo} {Fb, Fo}
Beacon Fly Mode
Fb: fly by
Fo: fly over
Fo
Fb
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 6 / 19
Benchmark Trajectory Prediction
Handling Uncertainties
Uncertainties on maneuvers and speed
parameter error typical values
start t0 εt0 ∈ [0, Et0 ] 10-30 s
return t1 εt1 ∈ [0, Et1 ] 10-30 s
angle α εα ∈ [−Eα, Eα] 1-3°
horizontal speed vh εvh ∈ [−Evh , Evh ] 2-6%
vertical speed vv εvv ∈ [−Evv , Evv ] 5-15%
beacon fly mode fm fm ∈ {Fb, Fo} {Fb, Fo}
Reaction Time Uncertainty
Et0 : start error
Et1 : return error t0
t1 t1+ Et1
t0+ Et0
Beacon Fly Mode
Fb: fly by
Fo: fly over
Fo
Fb
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 6 / 19
Benchmark Trajectory Prediction
Handling Uncertainties
Uncertainties on maneuvers and speed
parameter error typical values
start t0 εt0 ∈ [0, Et0 ] 10-30 s
return t1 εt1 ∈ [0, Et1 ] 10-30 s
angle α εα ∈ [−Eα, Eα] 1-3°
horizontal speed vh εvh ∈ [−Evh , Evh ] 2-6%
vertical speed vv εvv ∈ [−Evv , Evv ] 5-15%
beacon fly mode fm fm ∈ {Fb, Fo} {Fb, Fo}
Heading Change Uncertainty
Eα: angle errort0
t1
α
α− Eαα+ Eα
Beacon Fly Mode
Fb: fly by
Fo: fly over
Fo
Fb
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 6 / 19
Benchmark Trajectory Prediction
Handling Uncertainties
Uncertainties on maneuvers and speed
parameter error typical values
start t0 εt0 ∈ [0, Et0 ] 10-30 s
return t1 εt1 ∈ [0, Et1 ] 10-30 s
angle α εα ∈ [−Eα, Eα] 1-3°
horizontal speed vh εvh ∈ [−Evh , Evh ] 2-6%
vertical speed vv εvv ∈ [−Evv , Evv ] 5-15%
beacon fly mode fm fm ∈ {Fb, Fo} {Fb, Fo}
Speed Uncertainty
Evh : speed error
(1− Evh)vh t1
t0(1 + Evh)vh
(1 + Evh)vh
(1− Evh)vh
Beacon Fly Mode
Fb: fly by
Fo: fly over
Fo
Fb
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 6 / 19
Benchmark Trajectory Prediction
Handling Uncertainties
Uncertainties on maneuvers and speed
parameter error typical values
start t0 εt0 ∈ [0, Et0 ] 10-30 s
return t1 εt1 ∈ [0, Et1 ] 10-30 s
angle α εα ∈ [−Eα, Eα] 1-3°
horizontal speed vh εvh ∈ [−Evh , Evh ] 2-6%
vertical speed vv εvv ∈ [−Evv , Evv ] 5-15%
beacon fly mode fm fm ∈ {Fb, Fo} {Fb, Fo}
Climb and Descend Uncertainty
Evv : vertical error
t0
t1
(1 + Evv)vv (1− Evv)vv
(1 + Evv)vv (1− Evv)vvNew FL
Beacon Fly Mode
Fb: fly by
Fo: fly over
Fo
Fb
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 6 / 19
Benchmark Trajectory Prediction
Handling Uncertainties
Uncertainties on maneuvers and speed
parameter error typical values
start t0 εt0 ∈ [0, Et0 ] 10-30 s
return t1 εt1 ∈ [0, Et1 ] 10-30 s
angle α εα ∈ [−Eα, Eα] 1-3°
horizontal speed vh εvh ∈ [−Evh , Evh ] 2-6%
vertical speed vv εvv ∈ [−Evv , Evv ] 5-15%
beacon fly mode fm fm ∈ {Fb, Fo} {Fb, Fo}
Beacon Fly Mode
Fb: fly by
Fo: fly over
Fo
Fb
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 6 / 19
Benchmark Trajectory Prediction
Trajectory Hull Model
Horizontal PlaneAt each time step, aircraft positionmodelled as the smallest convexhull containing all possible positions
Red: not maneuvered yet (εvh)
Green: being maneuvered (εt0 , εα)
Blue: returning (εt1)
Gray: smallest convex hull
Vertical PlaneFor simplicity, the 3D convex hull isapproximated by the smallest right “cylinder”(prism) containing all possible horizontal convexhulls according to εvv
alt.max
alt.min
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 7 / 19
Benchmark Trajectory Prediction
Trajectory Hull Model
Horizontal PlaneAt each time step, aircraft positionmodelled as the smallest convexhull containing all possible positions
Red: not maneuvered yet (εvh)
Green: being maneuvered (εt0 , εα)
Blue: returning (εt1)
Gray: smallest convex hull
Vertical PlaneFor simplicity, the 3D convex hull isapproximated by the smallest right “cylinder”(prism) containing all possible horizontal convexhulls according to εvv
alt.max
alt.min
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 7 / 19
Benchmark Trajectory Prediction
Trajectory Hull Model
Horizontal PlaneAt each time step, aircraft positionmodelled as the smallest convexhull containing all possible positions
Red: not maneuvered yet (εvh)
Green: being maneuvered (εt0 , εα)
Blue: returning (εt1)
Gray: smallest convex hull
Vertical PlaneFor simplicity, the 3D convex hull isapproximated by the smallest right “cylinder”(prism) containing all possible horizontal convexhulls according to εvv
alt.max
alt.min
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 7 / 19
Benchmark Conflict Detection
Conflict Matrix
Detection
Trajectories l of aircraft i and k of aircraft j are conflicting iff ∃t = k × τ :
distv(ch(l, t), ch(k, t)) < normv ∧ disth(ch(l, t), ch(k, t)) < normh
where ch(l,t) is the 3D convex hull (prism) of trajectory l at time t, andtypically normv = 1000 ft and normh = 5 NM
For all ordered pairs of aircraft and pairs of trajectories
∀(i, j) ∈ [1, n]2, i < j, ∀(k, l) ∈ [1, nman]2
Ci,j,k,l =
{true if trajectories k and l conflicts
false otherwise
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 8 / 19
Benchmark Conflict Detection
Conflict Matrix
Detection
Trajectories l of aircraft i and k of aircraft j are conflicting iff ∃t = k × τ :
distv(ch(l, t), ch(k, t)) < normv ∧ disth(ch(l, t), ch(k, t)) < normh
where ch(l,t) is the 3D convex hull (prism) of trajectory l at time t, andtypically normv = 1000 ft and normh = 5 NM
For all ordered pairs of aircraft and pairs of trajectories
∀(i, j) ∈ [1, n]2, i < j, ∀(k, l) ∈ [1, nman]2
Ci,j,k,l =
{true if trajectories k and l conflicts
false otherwise
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 8 / 19
Benchmark Conflict Resolution Problem
Combinatorial Optimization
Decision variables M = {mi, i ∈ [1, n]} with mi ∈ [1, nman]
All maneuver options associated with allowed tuples 〈t0, t1, α, δFL〉 arenumbered from 1 to nman
mi represents the maneuver of aircraft i
Size of the search space: nnman
Cost cost(M) =∑n
i=1 c(mi)
Increasing absolute values of parameter ? indexed by k? ∈ [1, n?]
Individual: c(mi) =
(n0 − k0)2 + k12 +
{kα
2 if α 6= 0(1 + kδ)
2 if δFL 6= 00 otherwise
where mi is described by the tuple 〈 k0 , k1 , kα , kδ 〉
Constraints ∀(i, j) ∈ [1, n]2 s.t. i 6= j ¬Ci,j,mi,mj
with Ci,j,k,l = maneuvers k of aircraft i and l of aircraft j conflicts
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 9 / 19
Benchmark Conflict Resolution Problem
Combinatorial Optimization
Decision variables M = {mi, i ∈ [1, n]} with mi ∈ [1, nman]
All maneuver options associated with allowed tuples 〈t0, t1, α, δFL〉 arenumbered from 1 to nman
mi represents the maneuver of aircraft i
Size of the search space: nnman
Cost cost(M) =∑n
i=1 c(mi)
Increasing absolute values of parameter ? indexed by k? ∈ [1, n?]
Individual: c(mi) =
(n0 − k0)2 + k12 +
{kα
2 if α 6= 0(1 + kδ)
2 if δFL 6= 00 otherwise
where mi is described by the tuple 〈 k0 , k1 , kα , kδ 〉
Constraints ∀(i, j) ∈ [1, n]2 s.t. i 6= j ¬Ci,j,mi,mj
with Ci,j,k,l = maneuvers k of aircraft i and l of aircraft j conflicts
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 9 / 19
Benchmark Conflict Resolution Problem
Combinatorial Optimization
Decision variables M = {mi, i ∈ [1, n]} with mi ∈ [1, nman]
All maneuver options associated with allowed tuples 〈t0, t1, α, δFL〉 arenumbered from 1 to nman
mi represents the maneuver of aircraft i
Size of the search space: nnman
Cost cost(M) =∑n
i=1 c(mi)
Increasing absolute values of parameter ? indexed by k? ∈ [1, n?]
Individual: c(mi) =
( 4 − 1 )2 + 3 2 +
{2 2 = 22 if α 6= 0(1 + kδ)
2 if δFL 6= 00 otherwise
where mi is described by the tuple 〈0 min, 7 min, 20°, FL0〉
Constraints ∀(i, j) ∈ [1, n]2 s.t. i 6= j ¬Ci,j,mi,mj
with Ci,j,k,l = maneuvers k of aircraft i and l of aircraft j conflicts
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 9 / 19
Benchmark Conflict Resolution Problem
Combinatorial Optimization
Decision variables M = {mi, i ∈ [1, n]} with mi ∈ [1, nman]
All maneuver options associated with allowed tuples 〈t0, t1, α, δFL〉 arenumbered from 1 to nman
mi represents the maneuver of aircraft i
Size of the search space: nnman
Cost cost(M) =∑n
i=1 c(mi)
Increasing absolute values of parameter ? indexed by k? ∈ [1, n?]
Individual: c(mi) =
(n0 − k0)2 + k12 +
{kα
2 if α 6= 0(1 + kδ)
2 if δFL 6= 00 otherwise
where mi is described by the tuple 〈 k0 , k1 , kα , kδ 〉
Constraints ∀(i, j) ∈ [1, n]2 s.t. i 6= j ¬Ci,j,mi,mj
with Ci,j,k,l = maneuvers k of aircraft i and l of aircraft j conflicts
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 9 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Benchmark Conflict Resolution Problem
Benchmark
Available at clusters.recherche.enac.fr
Instance files: specified by matrix C for a given set of parameters
Current results: optimal solutions, lower and upper bounds
Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances
A Small Sample From a Benchmark File
d 5 161 4 5 11c 0 1 0 6 7 8 12 15c 0 1 1 2 3 12 15 28 39...m 0 19 0 1 0m 1 21 0 1 1...
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 10 / 19
Resolution
Contents
1 BenchmarkTrajectory PredictionConflict DetectionConflict Resolution Problem
2 ResolutionDataAlgorithmsResults
3 Conclusion
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 11 / 19
Resolution Data
Data
New benchmark
3D instances with aircraft evenly dispatched over 5 FLs
airspace 100 NM radiusaltitude from FL280 to FL320
speed randomly chosen within 20% of 480 knclimb rate 600 ft min−1
From 5 to 100 aircraft
Vertical maneuver options: climb or descend 1000 ft or 2000 ft
→ Aircraft interfere with each other across FLs
Harder than independent layers: search space and forbidden maneuverspairs exponentially increase with the number of layers
But in-between waypoints and beacon fly mode not tested yet. . .
DEMO
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 12 / 19
Resolution Data
Data
New benchmark
3D instances with aircraft evenly dispatched over 5 FLs
airspace 100 NM radiusaltitude from FL280 to FL320
speed randomly chosen within 20% of 480 knclimb rate 600 ft min−1
From 5 to 100 aircraft
Vertical maneuver options: climb or descend 1000 ft or 2000 ft
→ Aircraft interfere with each other across FLs
Harder than independent layers: search space and forbidden maneuverspairs exponentially increase with the number of layers
But in-between waypoints and beacon fly mode not tested yet. . .
DEMOAllignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 12 / 19
Resolution Algorithms
Memetic Algorithm (MA) [J.-K. Hao, 2012]
Hybridization of Evolutionary Algorithm (EA) and Local Search (LS)
Overall evolutionary framework
Recombination: classic crossover with two parents
Local improvement of a candidate: Tabu Search
→ Each element of the population is a local minimum
Tabu Search [F. Glover, 1986]
Local Search with best neighbour selection
Limited memory of forbidden moves to avoid cycling
FitnessF (M) =M ×
∑i<j
Ci,j,mi,mj + cost(M)
M : a big (enough) integer to ensure that F (M1) < F (M2) iff M2 hasmore conflicts than M1
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 13 / 19
Resolution Algorithms
Memetic Algorithm (MA) [J.-K. Hao, 2012]
Hybridization of Evolutionary Algorithm (EA) and Local Search (LS)
Overall evolutionary framework
Recombination: classic crossover with two parents
Local improvement of a candidate: Tabu Search
→ Each element of the population is a local minimum
Tabu Search [F. Glover, 1986]
Local Search with best neighbour selection
Limited memory of forbidden moves to avoid cycling
FitnessF (M) =M ×
∑i<j
Ci,j,mi,mj + cost(M)
M : a big (enough) integer to ensure that F (M1) < F (M2) iff M2 hasmore conflicts than M1
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 13 / 19
Resolution Algorithms
Memetic Algorithm (MA) [J.-K. Hao, 2012]
Hybridization of Evolutionary Algorithm (EA) and Local Search (LS)
Overall evolutionary framework
Recombination: classic crossover with two parents
Local improvement of a candidate: Tabu Search
→ Each element of the population is a local minimum
Tabu Search [F. Glover, 1986]
Local Search with best neighbour selection
Limited memory of forbidden moves to avoid cycling
FitnessF (M) =M ×
∑i<j
Ci,j,mi,mj + cost(M)
M : a big (enough) integer to ensure that F (M1) < F (M2) iff M2 hasmore conflicts than M1
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 13 / 19
Resolution Algorithms
Constraint Programming (CP)
CP ParadigmSeparation between model and search strategies
→ fast incremental prototyping
Focused on combinatorial constraint satisfaction
Complete algorithm: optimality or infeasibility proof
→ but exponential in the worst case...
ResultsImproved solver implementation over [ATM 2013]: optimality proof forall original instances and new 3D ones up to 30 aircraft
With 300 s time limit: optimal solution obtained, most proofs too long
For more than 30 aircraft: challenging or even out of reach to find afirst solution (except for infeasible 100-aircraft instances)
Validates metaheuristics results for reasonable instances
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 14 / 19
Resolution Algorithms
Constraint Programming (CP)
CP ParadigmSeparation between model and search strategies
→ fast incremental prototyping
Focused on combinatorial constraint satisfaction
Complete algorithm: optimality or infeasibility proof
→ but exponential in the worst case...
ResultsImproved solver implementation over [ATM 2013]: optimality proof forall original instances and new 3D ones up to 30 aircraft
With 300 s time limit: optimal solution obtained, most proofs too long
For more than 30 aircraft: challenging or even out of reach to find afirst solution (except for infeasible 100-aircraft instances)
Validates metaheuristics results for reasonable instances
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 14 / 19
Resolution Results
Memetic Algorithm vs Constraint Programming
0
10
20
30
40
50
60
70
80
90
16 18 20 22 24 26 28 30
mean e
xecu
tion t
ime (
s)
number of aircraft
CPMA
Mean execution time (in seconds) to find the optimal solution
MA and CP both obtain the optimal solution
MA scales better with larger and harder instances
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 15 / 19
Resolution Results
Global Cost of Best Solutions
0
200
400
600
800
1000
1200
1400
1600
20 30 40 50 60 70 80 90 100
mean c
ost
and e
xtr
em
e v
alu
es
number of aircraft
ε = 1ε = 2ε = 3
Mean cost found by the MA with 300 s time limit
MA always obtains conflict-free solutions within the allocated timeOptimal solution consistently reached whenever provable by CPCost increases w.r.t. number of aircraft and uncertainty level
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 16 / 19
Resolution Results
Mean Cost Per Aircraft
0
2
4
6
8
10
12
14
16
20 30 40 50 60 70 80 90 100
mean c
ost
per
air
craft
number of aircraft
ε = 1ε = 2ε = 3
Mean cost per aircraft found by the MA with 300 s time limit
Constrainedness/tightness: “density of trajectories” increases w.r.t.number of aircraft and uncertainty level in a fixed airspace volumeAs expected, more costly maneuvers needed to satisfy all constraints
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 17 / 19
Resolution Results
Convergence of the Memetic Algorithm
1400
1450
1500
1550
1600
1650
1700
1750
0 200 400 600 800 1000 1200 1400 1600 1800 2000 0
1
2
3
4m
aneuvers
cost
num
ber
of
rem
ain
ing c
onflic
ts
time (s)
maneuvers costnumber of remaining conflicts
Cost and conflicts w.r.t. elapsed time for 100 aircraft and ε = 3
First: number of conflicts decreased until feasibleSecond: maneuvers cost improved while maintaining feasibilityMA efficient enough on instances comparable to real-life scenarios
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 18 / 19
Conclusion
Conclusion and Further Work
Conclusions3D extension of the en-route conflict resolution framework [ATM 2013]
In-between waypoints with more complete uncertainty model
New Memetic Algorithm with outstanding results
Further WorkScenarios based on real data with simulated flight plans
Embedded resolution: integration into fast-time simulator (CATS)
Parallel cooperation of solvers to achieve better performances/proofs
GO CHECK YOUR ALGO AT
clusters.recherche.enac.fr
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 19 / 19
Conclusion
Conclusion and Further Work
Conclusions3D extension of the en-route conflict resolution framework [ATM 2013]
In-between waypoints with more complete uncertainty model
New Memetic Algorithm with outstanding results
Further WorkScenarios based on real data with simulated flight plans
Embedded resolution: integration into fast-time simulator (CATS)
Parallel cooperation of solvers to achieve better performances/proofs
GO CHECK YOUR ALGO AT
clusters.recherche.enac.fr
Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 19 / 19
Conclusion
Conclusion and Further Work
Conclusions3D extension of the en-route conflict resolution framework [ATM 2013]
In-between waypoints with more complete uncertainty model
New Memetic Algorithm with outstanding results
Further WorkScenarios based on real data with simulated flight plans
Embedded resolution: integration into fast-time simulator (CATS)
Parallel cooperation of solvers to achieve better performances/proofs
GO CHECK YOUR ALGO AT
clusters.recherche.enac.frAllignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 19 / 19