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4th International Conference on Flood Defence. C. Hübner , D. Muschalla and M. W. Ostrowski. ihwb. Mixed-Integer Optimization Of Flood Control Measures Using Evolutionary Algorithms. Outline. Introduction Mixed-Integer Optimization Processes of ES-Optimization Pareto Optimal Results - PowerPoint PPT Presentation
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4th International Conferenceon Flood Defence
C. Hübner , D. Muschalla and M. W. Ostrowski
ihwb
Mixed-Integer Optimization Of Flood Control Measures Using Evolutionary Algorithms
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 1 / 20
Outline
Introduction
Mixed-Integer Optimization
Processes of ES-Optimization
Pareto Optimal
Results
Conclusions
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 2 / 20
Introduction
Flood control should be considered integrated
Resources should be used efficient and effective
European Commission proposes new flood protection directive
Costs Benefit is considered as key point
Considering integrated flood control rises the modeling complexity
Optimization of a huge bandwidth of flood control strategies is at present limited
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 3 / 20
Introduction
Urban areas
Restoration
Widening /
River bed modification
Widening
Polder
Flood ControlReservoir
Flood ControlReservoirRemove
sealed areas
ns = 5nc = 144
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 4 / 20
A
Introduction
(HUGHES 1971) Optimierung der Abgabestrategien durch Lagrange Multiplikatoren
(MEYER-ZURWELLE 1975) Optimierung der Abgabestrategien von Hochwasserspeichersystemen durch Dynamische Programmierung (DP)
(BOGÁRDI 1979) Optimierung der Ausbaureihenfolge von Hochwasserrückhaltebecken durch Branch-and-Bound Verfahren
(BAUMGARTNER 1980) Optimierung Hochwasser-Steuerungsprozesse durch reduzierte Gradienten Verfahren
(MAYS & BEDIENT 1982), (BENNETT & MAYS 1985) und (TAUR ET AL. 1987) setzen Dynamische Programmierung zur Optimierung von HWS-Maßnahmen ein
(ORMSBEE, HOUCK, & DELLEUR 1987) erweitern die Anwendung der Dynamischen Programmierung auf zwei verschiedene Zielsetzungen.
(OTERO ET AL. 1995) setzen genetische Algorithmen
(LOHR 2001) optimiert Betriebsregeln Wasserwirtschaftlicher Speichersysteme mit evolutionsstrategischen Algorithmen.
(BRASS 2006) optimiert den Betrieb von Talsperrensystemen allerdings mittels Stochastisch Dynamischer Programmierung (SDP)
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 5 / 20
Introduction
Development of an integrated Modeling System, which allows multicriteria optimization of flood control strategies
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 6 / 20
Optimization of flood control measures according the type of the measure, its location and its specific parameters
Enable „a posteriori“ decision making by the use of multicriteria evolutionary optimization and Pareto Optimal Solutions
The use of evolutionary algorithms allows optimization without reducing the complexity of the models
Hydrologic ModelBlueMR
BlueMEVO
for Real Variables
BlueMEVO
for CombinatorialProblems
+ +
Mixed-Integer Optimization
Continuous variablesThese are variables that can change gradually in arbitrarily small steps
Ordinal discrete variablesThese are variables that can be changed gradually but there are minimum step size(e.g. discretized levels, integer quantities)
Nominal discrete variablesThese are discrete parameters with no reasonable ordering(e.g. discrete choices from an unordered list/set of alternatives, binary decisions).
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 7 / 20
Mixed-Integer Optimization
1 1 1f ,..., , ,..., , ,..., minr z dn n nr r z z d d
min max, , 1,...,i i i rr r r i n R
min max, , 1,...,i i i zz z z i n Z
,1 ,,..., , 1,...,ii i i di Dd D d d i n
with:
Objective Function:
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 8 / 20
Continuous variables:
Ordinal discrete variables:
Nominal discrete variables:
A
Processes of ES-Optimization
Continuous variables Nominal discrete variables
Selektion (μ + λ)
Reproduktion Selektiv
Multi-Rekombination (x/x) Multi-Rekombination (x/y)
Reproduktion Order Crossover (OX) Cycle Crossover (CX)
Partially-Mapped Crossover (PMX)
Mutation Rechenberg Schwefel
Mutation RND Switch
Dyn RND Switch
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 9 / 20
Evaluation by the use of BlueMRA
1
2
0
2
0
3
1
Nominal discrete Problem &Mixed-Integer Optimization
M B
M A
KM
0
1
2
River
Downstream
Path Representation
AB
C
DE
FG
M B
M A
M C
0
1
2
M B
M A
KM
0
1
2
M B
M A
M C
0
1
2
KM
M A0
1 M B
M A
M C
0
1
2
M B
M A
KM
0
1
2
KM3 M D3
KM4
KM3
0 2 0 23 11
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 10 / 20
A
Mixed-Integer Optimization
Parent Path A: 0 2 0 23 11
Parent Path B: 2 3 1 40 02
Cut Points
Child: 0 2 0 40 02
Partially Mapped Crossover Reproduction
Sub Path Mutation
Child: 0 2 0 40 02
Mutated Child: 1 0 0 42 02
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 11 / 20
Pareto efficiency / Pareto optimality
In case of mono-criteria problems only one exact solution
Reduction of the multi-criteria problems to mono-criteria problems by the use of weighting vectors
Subjective and arbitrary decisions
In the case of flood control optimisation -> multicriteria problem
No single solution
Search for a set of solutions where each solution is optimal
Aim is to find solutions where an improvement of an objective value can only be achieved by degradation of another objective value
This set es called Pareto efficiency or Pareto optimal
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 12 / 20
Pareto Optimal
f1
ψ2 f2
ψ1Pareto Front
Objective SpaceDecision Space
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 13 / 20
Use Case River ErftCombinatorial Optimization
Loc I
River
Downstream
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 14 / 20
Qmax
[m³/s]A
Investment Costs [€]B
Loc II
Loc VII
Loc IXLoc VIII
Loc VI
Loc V
Loc IV
Loc III
maxz Qtat
1
Nz Cnk
n
Objective A:Minimization of the maximum discharge
Objective B:Reducing the Investment costs
Inve
stm
ent
Cos
ts
[€]
BlueMEVO
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 15 / 20
Qmax [m3/s]
Use Case Erft + TestsystemMixed-Integer Optimization
Dike high.Restauration
No Measure
BasinPolder
Basin
No MeasureBypass
Bypass
No Measure
0
1
2
0
1
2
3
0
1
2
MeasureLocation I
MeasureLocation II
MeasureLocation III
River
Downstream
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 16 / 20
Qmax
[m³/s]A
Qmax
[m³/s]B
Investment Costs [€]
0
1
2
0
3
10
1
V, CS, …kst, L, …
L, W, …
A
Use Case Erft + TestsystemMixed-Integer Optimization
maxz Qtat
1
Nz Cnk
n
Objective A:minimization of the maximum discharge
Objective C:Reducing the Investment costs
maxz Qtbt
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 17 / 20
Objective B:minimization of the maximum discharge
Inve
stm
ent C
osts
[€] C
Qmax, A [m3/s]
Qmax, B
[m3/s]
BlueMEVO
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 18 / 20
Inve
stm
ent C
osts
[€]
C
Qmax, A
Qmax, B
[m3/s]
Inve
stm
ent C
osts
[€]
C
Qmax, B
[m3/s]
Qmax, A [m3/s]
BlueMEVO
Hypervolume
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 19 / 20
Conclusions / Outlook
Used model and optimization system BlueMR + BlueMEVO allows Optimization of flood control measures fast and reliable
No restriction concerning the used model, because of the separation of modeling and optimization system
Hydraulic interconnection and influence of the measures is always considered
Defining the optimization variables is complex
Fast and efficient scan of the hole solution space
Algorithm is able to find the global optima
Deliberate use of results
Enhancement of the optimization algorithms for ordinal discrete variables
Parallel optimization
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 20 / 20
Optimierung der HW-Maßnahmen
22.03.2008 | Fachbereich Bauingenieurwesen und Geodäsie | Institut für Wasserbau und Wasserwirtschaft | Prof. Dr.-Ing. M. W. Ostrowski | 21 / xx
Thank you very much
for your attention
www.nofdp.net
www.riverscape.eu
www.ihwb.tu-darmstadt.de Christoph Hübner
Fin
Outline
BA
7 May 2008 | TU Darmstadt | Section of Engineering Hydrology and Water Management | Prof. Dr.-Ing. M. W. Ostrowski | Christoph Hübner | 22 / 20
Schema des Optimierungssystems
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