michael kupfer - atm seminar · 2010-07-08 · • genetic algorithm with greedy shows better...
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Michael KupferSan Jose State University Research Foundation
NASA Ames, Moffett Field, CA
8th USA ‐ Europe ATM Seminar
June 29th – July 2nd Napa, CA
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Motivation:
OM
28L
Non Transgression Zone 28R
SFO
28R
Dependent runways single runway operationsSimultaneous Offset Instrument ApproachesSOIA
FOG
FOG
FOG
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Objective:
• Development of a scheduling model for very closely spaced parallel approaches
• Investigation of the merits of various scheduling methods
• Throughput increase of ~ 5-10% overfirst-come-first-served scheduling with pairing
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Scope:
• First-come-first-served: with/without pairing allowed• Genetic algorithm: with/without greedy algorithm• Mixed integer linear program• Model based on Terminal Area Capacity Enhancement
Concept
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Methodology:
• Input: earliest and latest possible arrival time of aircraft
• Objective: minimize arrival time at coupling point of last aircraft in set (i.e. makespan)
• Constraints: temporal, pairing, sequencing, separation, route and grouping
Temporal constraints:
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ETA [s]28L
Coupling Point
200180160140120100806040
SFO
Nominal ETA
Earliest possible ETA
Latest possible ETA
Shortest routeMax. speed
Longest routeMin. speed
ETAWindow
Delay
Time advance
Pairing constraints:
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SFO
Sequencing constraint:
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SFO
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Separation constraint:
HH
HL
H
L
HH
L
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Separation constraint:
Very Closely Spaced Parallel Runways
Wake Hazardous Region
Unsafe because of wake intrusion
Collision potential
SafePairingTimeWindow
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Precedence constraint:
• From same route + paired:change of sequence is ok
• From same route + not paired:change of sequence is not ok
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Grouping constraint:
A/C Type Group #
A300 AA310 AA320 AA340 AB727 AB73A AB73C AB74A AB757 AB767 AB777 ADC10 ADC8 ADC9 AL101 AMD11 AMD80 A
A/C Type Group #
BE20 BC560 BF28 BB707 CC130 CC550 CCARJ CCL60 CF100 CF900 CFA10 CFA20 CFA50 CH25B CLJ35 CC421 DBA46 E
Very Closely Spaced Parallel Runways
Wake Hazardous Region
Unsafe because of wake intrusion
Collision potential
SafePairingTimeWindow
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Independent Variables:
• Scheduling method:• FCFS with pairing [FCFSwP]• FCFS without pairing [FCFSwoP]• Genetic Algorithm with Greedy [GAwG]• Genetic Algorithm without Greedy [GAwoG]• Mixed Integer Linear Program [Optimal]
• Pairing Time Window:• 5-10 sec• 5-15 sec• 5-20 sec
• ETA window:• -60–600 sec• -60–1200 sec• -60–1800 sec
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Dependent Variables:
• Makespan (throughput)• Average delay• Computation time• Number of pairs in schedule• Actual spacing between paired aircraft
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Approach:
• One randomly generated traffic sample• 20 aircraft / 30 min• 3 wake categories• 3 routes• 3 groups
• One run per scenario: 45 runs• Constant ETA window for all aircraft in a run• Constant pairing time window for all aircraft in a run
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Assumptions:
• All aircraft have capabilities to perform very closely spaced parallel approaches:• Aircraft surveillance and
aircraft-aircraft communicationusing ADS-B
• High precision navigationsystems (D-GPS)
• Enhanced avionics (primaryflight display, navigation display)
• 2 parallel runways• Computation of earliest ETA and
latest ETA: trajectory predictor available
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Makespan
RelativeThroughput
FCFSwoP
FCFSwP
Upper PairingBound [s]
Scheduling method
Max. Delay per aircraft [s]
10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20
600 1200 1800 600 1200 1800 600 1200 1800
Optimal GAwoG GAwG
32:13 min
30:36 min
37:28 min
105%
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RelativeAverage Delay
Relative Average Time Deviation from Earliest Possible ETA
FCFSwoP
FCFSwP
Upper PairingBound [s]
Scheduling method
Max. Delay per aircraft [s]
10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20
600 1200 1800 600 1200 1800 600 1200 1800
Optimal GAwoG GAwG
02:14 min
03:24 min
01:20 min
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AverageComputation
Time [s]
Average Computation Time
Upper PairingBound [s]
Scheduling method
Max. Delay per aircraft [s]
10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20
600 1200 1800 600 1200 1800 600 1200 1800
Optimal GAwoG GAwG
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Computation Time
GA without Greedy:2% improvement
GA with Greedy:82% improvement
Optimalsolution
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Concluding remarks:
• Advanced scheduling methods improve throughput 5-6%• Genetic Algorithm with Greedy shows better makespan
and delay than FCFS with pairing• Optimal solutions: computation times sensitive to
changes of independent variables• For simulations consider genetic algorithm with greedy
improvement heuristic• Future research:
• More runs• Other optimization objectives• Other optimization methods• Robust schedules
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Thank you for your Attention!
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Decision variables:
⎩⎨⎧
otherwise 0paired are j and i if 1
zij
⎩⎨⎧
otherwise 0paired are j and i if 1
yij
1 if i and j are paired, and i is leading j0 otherwise
1 if i and j are not paired, and i is leading j0 otherwise
Constraints:
• Temporal constraint:STA needs to be withinearliest and latest ETA
• Pairing constraint:Two aircraft per pair
• Sequencing constraint:Paired or not paired
],[ ,, ETALiETAEii ttt −−∈ ),...,1( Ni∈∀
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1≤∑N
jijz }1,0{∈ijz ),...,1( Ni∈∀
1≤∑
N
iijz }1,0{∈ijz ).,...,1( Nj ∈∀
1=+++ jiijjiij yyzz }1,0{,,, ∈jiijjiij yyzz
),...,1(, Nji ∈∀ ji ≠
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Constraints:
• Separation constraint:Standard separation between not paired aircraft.Follower in a pair must be between some lower pairing bound (LPB) and upper pairing bound (UPB) behind its lead.
• Route constraint:If not paired and in trail on same route: no overtaking
ijijjijiij sepyMzytt ⋅+⋅+−≥− )(}1,0{,, ∈ijjiji yzy ),...,1(, Nji ∈∀ ji ≠
LPBzyMzytt ijijjijiij ⋅++⋅+−≥− )()( }1,0{, ∈jiji yz
UPBzMzytt ijjiijij ⋅+⋅+≤− )(}1,0{, ∈ijji yz
),...,1(, Nji ∈∀ ji ≠
Mzytt jiijij ⋅+−≥− )(
ji rr =
ETAjETAi tt ,, <
if
and if
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Constraints:
• VCSPA grouping constraint:paired aircraft must have similar performance (same VCSPA group)
0=ijz 0=jiz ji gg ≠
),...,1(, Nji ∈∀ ji ≠if
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J1J12J234
Nom. ETA
E-ETA
FCFS-IMC
FCFS-VMC
GA_wG
CPLEX