Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.
-
Upload
giles-mcdaniel -
Category
Documents
-
view
219 -
download
3
Transcript of Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.
![Page 1: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/1.jpg)
Multi-Aircraft Flight Planning Under
Uncertainty
Zehra Akyurt
![Page 2: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/2.jpg)
Problem Description
Multiple aircraft belonging to different airlinesPossibility of facing Temporary Flight Restrictions (TFR)s en routeTFR reduces capacity of airspace which it coversNeed to find optimal routes for aircraft given stochastic travel conditions.
![Page 3: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/3.jpg)
Example
7
0 3214 2 3
4 6
8
11
![Page 4: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/4.jpg)
Multi-Objectives
Minimize Cost: Minimize total expected travel time
of all aircraft.
Maximize Equity: Minimize the expected differences of
total time traveled, between airlines.
![Page 5: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/5.jpg)
Stochastic Program
Will use a multi-stage scenario based stochastic program formulation.
What will a scenario be? A joint realization of all the TFRs.
What will a stage be? Any point at which new decisions
must be made
![Page 6: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/6.jpg)
Assumptions• Aircraft are assumed to have equal
velocity • TFRs are assumed independent.
0 3214 2 34 6
811
7
Stochastic program formulation not totally correct.
![Page 7: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/7.jpg)
Space –Time Network
0 4 6 7 8 9 10 11 12 13 14
0
1
2 2 2
333 333
x2x1
x3
y1
y2
y3
z1
z3
z5
z2z4z6
![Page 8: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/8.jpg)
Program Formulation
. node upto tionsrepresenta identicalh wit
, scenarios and , 0
,, ,
, , 0
,
,
s.t
Min
Min
scenariounder airline from j)(i, arc n arcon flow ofamount
,,
,,
,,
,,
,,
,,
)(,
,
)(,
,
),(
,
),(
,
k
),(
,
k
th,
i
kklxx
klncx
klxx
kFx
kFx
xdxdp
xdp
klx
mnnji
lknji
lk
nji
lknji
lk
n
nhj
lk
n
nji
lk
l
n tAj
nti
lk
l
n sAj
njs
lk
l n Aji
nij
lknij
n Aji
nij
lknij
k
n l Aji
nij
lknij
k
nij
lk
ba
ba
Objective-1
Objective-2
Conservation of Flow Constraints
Arc Capacity Constraints
Non-AnticipativityConstraints
![Page 9: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/9.jpg)
Obstacles in Formulation
Used Xpress-MP to test modelSecond objective contains absolute value
Added additional constraints to overcome this obstacle (see Chvatal)
Example:
dycaxb Min
dcxe
dcye
baxe
baxe
ee
2
2
1
1
21
s.t.
Min
![Page 10: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/10.jpg)
Program is now linear! Had to add integer constraintsProgram is no longer linear, nor convexUsed two general methods to solve the two-objective integer program:
Weighting methodConstraint method
Obstacles in Formulation
![Page 11: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/11.jpg)
Sample ProblemSet• p1=1,p2=0• c1=2,c2=3, all other arcs have capacity=5• 3 airlines with 2,3 and 4 aircraft respectively = 9 aircraft
0 321(4,5) (2,2) (3,5)
(4,5) (6,5)
(8,5)
(11,5)
(7,5)
F=9
![Page 12: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/12.jpg)
0990
0990.1
2.2592921940.2
1.7593931940.3
194942.25920.4
195952.25920.5
195962.25920.6
195972.25920.7
194982.25920.8
099992.25920.9
0991007.75921
DeviationTimeTime Constraint DeviationTimeWeight of Time
Constraint Method Weighting Method
Results
![Page 13: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/13.jpg)
ResultsRecall: Objectives were
Min Total Travel Time
Weighting Method
0
2
4
6
8
10
90 92 94 96 98 100
Travel Time
Dev
iatio
ns
Min Total Deviations
Constraint Method
0
0.5
1
1.5
2
2.5
90 92 94 96 98 100
Travel Time
Dev
iatio
ns
![Page 14: Multi-Aircraft Flight Planning Under Uncertainty Zehra Akyurt.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649efa5503460f94c0c7e2/html5/thumbnails/14.jpg)
Questions?