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The Netherlands
Belgium
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Munster/Hafen
Voerde
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Flensburg
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Holtriem-Dornum
A Simulated-Annealing-Based Approach
ACM e-Energy 2017 · May 19, 2017Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner
for Wind Farm Cabling
INSTITUTE OF THEORETICAL INFORMATICS · ALGORITHMICS GROUP
Czech RepublicBelgiumFrance
KIT – The Research University in the Helmholtz Association www.kit.edu
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Motivation
Stribog II
Stribog I
Osters Bank 4Osters Bank 3
Osters Bank 2
Ruyter West
Cornelia
Uthland
Riffgrond
Horns Rev Reserved Area
WeißeBank
Horns RevB HR7
Horns RevB HR6
Horns RevB HR5
RuyterOost
Clear-camp
OostFriesland
AmelandPotentiele Zoekgebieden
PNEAtlantis III
PNEAtlantis II
Austern-grund
WitteBank
MeerwindWest
Euklas Diamant
Jules Verne
Nautilus IHTOD 5
HTOD 4 HTOD 3
HTOD 2
HTOD 1
Concordia I
Concordia II
Gaia I
Gaia II
Gaia III
Gaia IV
AiolosApollon
Horizont IHorizont II
Horizont III
SeaStorm II
Seewind III
Seewind IV
AreaC IIIAreaC II
AreaC I
Skua
Bight Power I Bight Power II
Global Tech 2
Kaskasi
Kaskasi II
Nordpassage
H2-20
GodeWind III
BorkumRiffgrund West II
EnBWHe dreiht II
Sandbank 24extension
Sandbank 24extension
?
ProWind 3ProWind 2ProWind 1
Neptune I
Neptune II
Neptune III
HTOD 6 Nemo
Enova OffshoreNSWP 8
Enova OffshoreNSWP 10
Enova OffshoreNSWP 12
Enova OffshoreNSWP 14
Enova OffshoreNSWP 15
Enova OffshoreNSWP 13
Enova OffshoreNSWP 11
Gaia V
Norderland
Norderland
DanTysk DK
PetrelSeagullHeronGannet
SeaStorm I
Nord-OstPassat I
Nord-OstPassat II
Nord-OstPassat III
Aquamarin
EnovaOffshoreNSWP 9
Zee-Energie
Buiten-gaats
GodeWind II
GodeWind I
Sandbank 24
BorkumRiffgrund WestOWP
West
Borkum-Riffgrund II
Borkum-Riffgrund II
Merkur(ehem.
MEG Off-shore I)
InnogyNordsee
3Innogy
Nordsee 2
InnogyNordsee 1
DeltaNordsee 1
DeltaNordsee 2 Gode
Wind IV
DeutscheBucht Veja
Mate
EnBWHe dreiht
EnBWHohe See
Albatros
Albatros FiT
SeaWind 1
Kaikas
Horizont IV
NordlicherGrund
Horns Rev III
Riffgat
Borkum-Riffgrund I
TrianelWindpark
TrianelWindpark
alpha ventus
BARDOffshore 1
GlobalTech 1
Nordsee Ost
MeerwindSud/Ost
Amrumbank West
Butendiek
DanTysk
Horns Rev II
Horns Rev
Schif
ffahr
tsrou
te10
Schifffahrtsroute 4
Schifffahrtsroute 4
Schifffahrtsroute 4Schifffahrtsroute 6
Schifffahrtsroute 6
Sch
ifffa
hrts
rout
e5
German Bight Western ApproachEast Friesland
Terschelling - German Bight
JadeApproach
WeißeBank
HelgolanderBucht
Vorranggebiet 3fur Schifffahrt
VorranggebietSchifffahrtsroute 12
Tief-wasser-reede
Doggerbank
Sudlich Amrumbank
Dollard
Jade-busen
S y l t e r A u ß e n r i f
W e i ß e B a n k
SylWin alphaSylWin beta
DolWin deltaDolWin beta
DolWin alphaDolWin gamma
BorWin alphaBorWin beta
BorWin delta
BorWin epsilonBorWingamma
HelWin alpha BorWin beta
Vorbehaltsgebiet
fur
Rohrleitungen
BorW
in3,4
DolW
in3 BorWin 1,2
DolWin 1,2
BorWin 1,2
Bor
Win
3,4
SylWin 1,2
HelWin 1,2
SylWin 1,2
85 km
160 km
60 km
45 km
75 km
83 km
50 km
141 km 130 km125 km 125 km
Emden
WilhelmshavenBremerhaven
Cuxhaven
Leer
Norden
Norden
Aurich
Esens
Jever
Varel
Groningen
Dokkum
Brundbuttel
Heide
Husum
Niebull
Tondern
Ribe
Varde
Esbjerg
Endrup
Karlsgarde
Buttel
DieleDorpen West
Hagermarsch
Emden/Borssum
Dorpen WestEemshaven
Ameland
Schiermonnikoog
Terschelling
Vlieland
Borkum
Memmert
Juist
NorderneyBaltrum
LangeoogSpiekeroog
Wangerooge
Mellum
Neuwerk
Helgoland
Pellworm
Hooge
Amrum
Fohr
Sylt Sylt
Rømø
Mandø
Fanø
Inhausen
Nordergrunde
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
https://upload.wikimedia.org/wikipedia/commons/a/a1/Map of the offshore wind power farms in the German Bight.png
1
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Motivation
Stribog II
Stribog I
Osters Bank 4Osters Bank 3
Osters Bank 2
Ruyter West
Cornelia
Uthland
Riffgrond
Horns Rev Reserved Area
WeißeBank
Horns RevB HR7
Horns RevB HR6
Horns RevB HR5
RuyterOost
Clear-camp
OostFriesland
AmelandPotentiele Zoekgebieden
PNEAtlantis III
PNEAtlantis II
Austern-grund
WitteBank
MeerwindWest
Euklas Diamant
Jules Verne
Nautilus IHTOD 5
HTOD 4 HTOD 3
HTOD 2
HTOD 1
Concordia I
Concordia II
Gaia I
Gaia II
Gaia III
Gaia IV
AiolosApollon
Horizont IHorizont II
Horizont III
SeaStorm II
Seewind III
Seewind IV
AreaC IIIAreaC II
AreaC I
Skua
Bight Power I Bight Power II
Global Tech 2
Kaskasi
Kaskasi II
Nordpassage
H2-20
GodeWind III
BorkumRiffgrund West II
EnBWHe dreiht II
Sandbank 24extension
Sandbank 24extension
?
ProWind 3ProWind 2ProWind 1
Neptune I
Neptune II
Neptune III
HTOD 6 Nemo
Enova OffshoreNSWP 8
Enova OffshoreNSWP 10
Enova OffshoreNSWP 12
Enova OffshoreNSWP 14
Enova OffshoreNSWP 15
Enova OffshoreNSWP 13
Enova OffshoreNSWP 11
Gaia V
Norderland
Norderland
DanTysk DK
PetrelSeagullHeronGannet
SeaStorm I
Nord-OstPassat I
Nord-OstPassat II
Nord-OstPassat III
Aquamarin
EnovaOffshoreNSWP 9
Zee-Energie
Buiten-gaats
GodeWind II
GodeWind I
Sandbank 24
BorkumRiffgrund WestOWP
West
Borkum-Riffgrund II
Borkum-Riffgrund II
Merkur(ehem.
MEG Off-shore I)
InnogyNordsee
3Innogy
Nordsee 2
InnogyNordsee 1
DeltaNordsee 1
DeltaNordsee 2 Gode
Wind IV
DeutscheBucht Veja
Mate
EnBWHe dreiht
EnBWHohe See
Albatros
Albatros FiT
SeaWind 1
Kaikas
Horizont IV
NordlicherGrund
Horns Rev III
Riffgat
Borkum-Riffgrund I
TrianelWindpark
TrianelWindpark
alpha ventus
BARDOffshore 1
GlobalTech 1
Nordsee Ost
MeerwindSud/Ost
Amrumbank West
Butendiek
DanTysk
Horns Rev II
Horns Rev
Schif
ffahr
tsrou
te10
Schifffahrtsroute 4
Schifffahrtsroute 4
Schifffahrtsroute 4Schifffahrtsroute 6
Schifffahrtsroute 6
Sch
ifffa
hrts
rout
e5
German Bight Western ApproachEast Friesland
Terschelling - German Bight
JadeApproach
WeißeBank
HelgolanderBucht
Vorranggebiet 3fur Schifffahrt
VorranggebietSchifffahrtsroute 12
Tief-wasser-reede
Doggerbank
Sudlich Amrumbank
Dollard
Jade-busen
S y l t e r A u ß e n r i f
W e i ß e B a n k
SylWin alphaSylWin beta
DolWin deltaDolWin beta
DolWin alphaDolWin gamma
BorWin alphaBorWin beta
BorWin delta
BorWin epsilonBorWingamma
HelWin alpha BorWin beta
Vorbehaltsgebiet
fur
Rohrleitungen
BorW
in3,4
DolW
in3 BorWin 1,2
DolWin 1,2
BorWin 1,2
Bor
Win
3,4
SylWin 1,2
HelWin 1,2
SylWin 1,2
85 km
160 km
60 km
45 km
75 km
83 km
50 km
141 km 130 km125 km 125 km
Emden
WilhelmshavenBremerhaven
Cuxhaven
Leer
Norden
Norden
Aurich
Esens
Jever
Varel
Groningen
Dokkum
Brundbuttel
Heide
Husum
Niebull
Tondern
Ribe
Varde
Esbjerg
Endrup
Karlsgarde
Buttel
DieleDorpen West
Hagermarsch
Emden/Borssum
Dorpen WestEemshaven
Ameland
Schiermonnikoog
Terschelling
Vlieland
Borkum
Memmert
Juist
NorderneyBaltrum
LangeoogSpiekeroog
Wangerooge
Mellum
Neuwerk
Helgoland
Pellworm
Hooge
Amrum
Fohr
Sylt Sylt
Rømø
Mandø
Fanø
Inhausen
Nordergrunde
TrianelWindpark
Borkum-Riffgrund II
Borkum-
Merkur(ehem.MEG Off-shore I)
alpha Ventus
Borkum-Riffgrund I
Riffgrund II
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
https://upload.wikimedia.org/wikipedia/commons/a/a1/Map of the offshore wind power farms in the German Bight.png
1
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
PCC (110 kV)
Grid Point
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
PCC (110 kV)
Grid Point
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
PCC (110 kV)
Grid Point
Wind Turbine (33 kV)
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
SubstationPCC (110 kV)
Grid Point
Wind Turbine (33 kV)
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
SubstationPCC (110 kV)
Grid Point
Wind Turbine (33 kV)
Transport Cable
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
SubstationPCC (110 kV)
Grid Point
Wind Turbine (33 kV)
Transmission Cables
Transport Cable
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
Circuit
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
Circuit
Collector System
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
Circuit
Collector System
Full Farm
2
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cabling
Circuit
Collector System
Full Farm
≤ 2 Wind Turbines; $ 100≤ 6 Wind Turbines; $ 140≤ 9 Wind Turbines; $ 162
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cable Layout Problem
Given VS set of substations, VT set of turbines (each with capacity),for each edge: cable types (each with cost and capacity)
Circuit
Collector System
Full Farm
3
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cable Layout Problem
Given VS set of substations, VT set of turbines (each with capacity),for each edge: cable types (each with cost and capacity)
Circuit
Collector System
Full Farm
3
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cable Layout Problem
Given VS set of substations, VT set of turbines (each with capacity),for each edge: cable types (each with cost and capacity)
Circuit
Collector System
Full Farm
≤ 2 Wind Turbines; $ 100≤ 6 Wind Turbines; $ 140≤ 9 Wind Turbines; $ 162
3
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cable Layout Problem
Given
find
VS set of substations, VT set of turbines (each with capacity),for each edge: cable types (each with cost and capacity)
for each edge: the cable type
Circuit
Collector System
Full Farm
≤ 2 Wind Turbines; $ 100≤ 6 Wind Turbines; $ 140≤ 9 Wind Turbines; $ 162
3
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cable Layout Problem
Given
find
VS set of substations, VT set of turbines (each with capacity),for each edge: cable types (each with cost and capacity)
for each edge: the cable type
total cable costminimizing
Circuit
Collector System
Full Farm
≤ 2 Wind Turbines; $ 100≤ 6 Wind Turbines; $ 140≤ 9 Wind Turbines; $ 162
3
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cable Layout Problem
Given
find
subject to
VS set of substations, VT set of turbines (each with capacity),for each edge: cable types (each with cost and capacity)
for each edge: the cable type
total cable costminimizing
substation capacity constraintsflow conservation constraints
cable capacity constraints Circuit
Collector System
Full Farm
≤ 2 Wind Turbines; $ 100≤ 6 Wind Turbines; $ 140≤ 9 Wind Turbines; $ 162
3
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Wind Farm Cable Layout Problem
Given
find
subject to
VS set of substations, VT set of turbines (each with capacity),for each edge: cable types (each with cost and capacity)
for each edge: the cable type
total cable costminimizing
substation capacity constraintsflow conservation constraints
cable capacity constraints Circuit
Collector System
Full Farm
≤ 2 Wind Turbines; $ 100≤ 6 Wind Turbines; $ 140≤ 9 Wind Turbines; $ 162
Wind farm planning problem⇔ Minimum cost flow problem
OPT(NFFP) ≤∑
j∈VSOPT(NSP(j)) ≤
∑j∈VS
∑i∈N OPT(NCP(j , i))
using [Leibfried et al., 2015]
3
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Simulated Annealing
Metropolis Algorithm Cooling Schedule
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
4
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Simulated Annealing
many local optima
Metropolis Algorithm Cooling Schedule
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
4
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Simulated Annealing
many local optima
local search
Metropolis Algorithm Cooling Schedule
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
4
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Simulated Annealing
many local optima
escape local optimum
?
Metropolis Algorithm Cooling Schedule
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
4
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Simulated Annealing
many local optima
multiple mutations
Metropolis Algorithm Cooling Schedule
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
4
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Simulated Annealing
many local optima
multiple mutations
Metropolis Algorithm Cooling Schedule
0.004
0.002
0.006
0.008
0.01
0
Tem
pera
ture
0 5 10 15 20 25 30
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
activity µdynamic, τ = 4 · 10−5standard, τ = 4 · 10−7
Time in min
4
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Simulated Annealing
many local optima
multiple mutations
Metropolis Algorithm Cooling Schedule
0.004
0.002
0.006
0.008
0.01
0
Tem
pera
ture
Diversification Intensification
0 5 10 15 20 25 30
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Diversification
activity µdynamic, τ = 4 · 10−5standard, τ = 4 · 10−7
Time in min
4
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Benchmark Sets
21
21
21
2121
5
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Benchmark Sets
21
21
21
2121
5
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Benchmark Sets
21
21
21
2121
5
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Benchmark Sets
SubstationTurbineCable type 1Cable type 2Cable type 3
21
21
21
2121
21
5
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Benchmark Sets
SubstationTurbineCable type 1Cable type 2Cable type 3
21
21
21
2121
21
5
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Benchmark Sets
SubstationTurbineCable type 1Cable type 2Cable type 3
21
21
21
2121
21
5
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Multiple Instances of Simulated Annealing
100 200 300 400 500
0
0.4
−0.4
−0.8
0.8 1 Instance
2 Instances
4 Instances
Number of Turbines
betterthan Gurobi
worsethan Gurobi
6
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Multiple Instances of Simulated Annealing
100 200 300 400 500
0
0.4
−0.4
−0.8
0.8 1 Instance
2 Instances
4 Instances
Number of Turbines
betterthan Gurobi
worsethan Gurobi
Results depend on a random seed.Multiple instances reduce the overall computation time. This causes a
reduced time spend for the intensification phase.
6
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Performance Influence of the
200 300 400 500
0
1
2
3
−1
4
5
6 τ = 1 · 10−5
τ = 2 · 10−5
τ = 4 · 10−5
τ = 8 · 10−5
τ = 16 · 10−5
Number of Turbines
betterthan Gurobi
worsethan Gurobi
Thermal Conductivity and Capacity τ
7
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Performance Influence of the
200 300 400 500
0
1
2
3
−1
4
5
6 τ = 1 · 10−5
τ = 2 · 10−5
τ = 4 · 10−5
τ = 8 · 10−5
τ = 16 · 10−5
Number of Turbines
betterthan Gurobi
worsethan Gurobi
Thermal Conductivity and Capacity τ
Parameter tuning is difficult for the cooling schedule.
7
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Cooling Schedule Performance
0
0.2
0.4
−0.2
−0.4
−0.8
Standard Cooling Schedule
Dynamic Cooling Schedule
100 200 300 400
Number of Turbines
−0.6
worsethan Gurobi
betterthan Gurobi
8
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Cooling Schedule Performance
0
0.2
0.4
−0.2
−0.4
−0.8
Standard Cooling Schedule
Dynamic Cooling Schedule
100 200 300 400
Number of Turbines
−0.6
worsethan Gurobi
betterthan Gurobi
The dynamic outperorms the standard one without parameter tuning.Parameter tuning improve the standard one for larger instances.
8
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Performance Influence of the
0.85 0.9 0.95 1−1.5
−1
−0.5
0
0.5
1
1.5
2
Substation Capacity Tightness
betterthan Gurobi
worsethan Gurobi
Substation Capacity Tightness
9
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Performance Influence of the
0.85 0.9 0.95 1−1.5
−1
−0.5
0
0.5
1
1.5
2
Substation Capacity Tightness
betterthan Gurobi
worsethan Gurobi
Substation Capacity Tightness
The tighter the substation capacity or the more substations the harderthe instance is to solve. Thus, the solution quality reduces with same
duration.
9
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
Circuit ProblemSubstation ProblemFull Farm Problem
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
Circuit
Collector System
Full Farm
Circuit ProblemSubstation ProblemFull Farm Problem
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
Circuit
Collector System
Full Farm
P (MST)NP-hard (CMST)
NP-hard (Heuristics)
Circuit ProblemSubstation ProblemFull Farm Problem
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
Circuit
Collector System
Full Farm
Circuit
Collector System
Full Farm
P (MST)NP-hard (CMST)
NP-hard (Heuristics)
Circuit ProblemSubstation ProblemFull Farm Problem
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
Circuit
Collector System
Full Farm
Circuit
Collector System
Full Farm
NP-hardNP-hardNP-hard
P (MST)NP-hard (CMST)
NP-hard (Heuristics)
Circuit ProblemSubstation ProblemFull Farm Problem
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
Circuit
Collector System
Full Farm
Circuit
Collector System
Full Farm
(Clustering)NP-hardNP-hardNP-hard
P (MST)NP-hard (CMST)
NP-hard (Heuristics)
Circuit ProblemSubstation ProblemFull Farm Problem
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
}
Circuit
Collector System
Full Farm
Circuit
Collector System
Full Farm
Sim
ulat
edA
nnea
ling(Clustering)NP-hard
NP-hardNP-hard
P (MST)NP-hard (CMST)
NP-hard (Heuristics)
Circuit ProblemSubstation ProblemFull Farm Problem
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
}
Circuit
Collector System
Full Farm
Circuit
Collector System
Full Farm
Sim
ulat
edA
nnea
ling(Clustering)NP-hard
NP-hardNP-hard
P (MST)NP-hard (CMST)
NP-hard (Heuristics)
Circuit ProblemSubstation ProblemFull Farm Problem
RESULTS
Number of Turbines
-0.2-0.4
-0.8
Number of Turbines
-0.6
00.20.4
Standard Cooling ScheduleDynamic Cooling Schedule
100 200 300 400 100 200 300 400 500
1 Instance2 Instances4 Instances
0
0.4
-0.4
-0.8
0.8
200 300 400 500
0123
-1
45
τ= 1·10-5τ= 1·10-5τ= 2·10-5τ= 4·10-5
τ=16·10-5
Number of Turbines
6
τ= 8·10-5
0.85 0.9 0.95 1
00.511.52
Substation Capacity Tightness
-0.5
-1.5-1
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Conclusion & Future Work
}
Circuit
Collector System
Full Farm
Circuit
Collector System
Full Farm
Sim
ulat
edA
nnea
ling(Clustering)NP-hard
NP-hardNP-hard
P (MST)NP-hard (CMST)
NP-hard (Heuristics)
Circuit ProblemSubstation ProblemFull Farm Problem
Number of Turbines
-0.2-0.4
-0.8
Number of Turbines
-0.6
00.20.4
Standard Cooling ScheduleDynamic Cooling Schedule
100 200 300 400 100 200 300 400 500
1 Instance2 Instances4 Instances
0
0.4
-0.4
-0.8
0.8
200 300 400 500
0123
-1
45
τ= 1·10-5τ= 1·10-5τ= 2·10-5τ= 4·10-5
τ=16·10-5
Number of Turbines
6
τ= 8·10-5
0.85 0.9 0.95 1
00.511.52
Substation Capacity Tightness
-0.5
-1.5-1
RESULTS&FUTURE WORK
10
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling
Institute of Theoretical InformaticsAlgorithmics Group
Are you a metal fan, too?
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