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