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The University of Adelaide, AustraliaSchool of Civil, Environmental & Mining Engineering
Water Systems and Infrastructure Modelling &Management Group(WaterSIMM)
Using Genetic Algorithms to OptimiseNetwork Design and System OperationIncluding Consideration of Sustainability
Professor Angus Simpson
Victorian Modelling Group
24 March 2010
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Outline
1. Simulation of water distribution systems2. Various formulations of equations
3. Todini and Pilati solution method4. Genetic algorithm optimisation of water
distribution system networks
5. Genetic algorithms for optimisingoperations of pumping systems
6. Optimising for sustainability
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My research interests
1. Optimisation of the design and operation ofwater distribution systems using geneticalgorithms [including sustainabilityconsiderations (GHGs)]
2. Monitoring health and assessing conditionof pipes non-invasively in water distributionsystems using small controlled waterhammer events
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My research interests
3. Steady state computer simulation analysis
of water distribution systems - improvingsolvers and modelling of PRVs and FCVs
4. Water hammer modelling in pipelines
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The research team
Total of 14
9 academics (local and overseas) 1 Research Post Doc. 4 PhDs
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The research team - academics
Prof. Angus Simpson Prof. Martin Lambert (condition assessment and
genetic algorithms) Prof. Holger Maier (genetic algorithms and
sustainability) Dr. Sylvan Elhay School of Computer Science,
The University of Adelaide (steady state solution ofpipe networks)
Prof. Lang White School of Electrical andElectronic Engineering, The University of Adelaide
(condition assessment)
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International collaboration
Professor Caren Tischendorf Head of Dept. of Mathematicsand Computer Science, University of Cologne, Germany(steady state solution of pipe networks)
Dr. Jochen Deuerlein 3S Consult, Germany (steady statesolution of pipe networks, correct modelling of PRVs, FCVs inwater networks) ex-University of Karlsruhe
Dr. Arris Tijsseling University of Eindhoven, TheNetherlands (condition assessment)
Prof. Wil Schilders University of Eindhoven, TheNetherlands (speeding up solution of nonlinear steady statepipe network equations)
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Components in a Water Distribution
System
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Simulation of water distributionsystems
Solution of a set on non-linear equations for
flow (Q) and pressure (head or hydraulic grade line H)
EPANET uses Todini and Pilati (1987)method very fast
There are many sophisticated commerciallyavailable software packages
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Assumptions
Fixed demands assumed to be notpressure dependent, for example - 100houses aggregated to a node
Various water demand loadings cases Peak hour (hottest day in summer) Peak day (extended period simulation usually
over 24 hours to check tanks do not run empty) Fire demand loading cases Pipe breakage cases
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Decisions to be made
Diameters and locations of pipes Location of pumps
Locations and setting of valves (PRVs, FCVs) Locations and elevations of tanks Operation of pumps off-peak electricity rates Minimising carbon footprint Reliability considerations
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Design objectives
For theeconomic cost component minimisesumof Capital cost of the water distribution system
(say for a 100 year life) Present value of pump replacement/refurbishment
(every 20 years) Present value of pump operating costs (100 years)
)()()(),(11
pumping NPV pc Ld c P DC k NPUMP
k k k k
NPIPE
k k
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Accounting for Time Present value analysis (PVA)
Usually the discount ratei is selected tobe cost of capital 6 to 8%
For social projects, such as WDSs, asocial discount rate should be used, forexample,i = 1.4% (intergenerational
equity)
t t iC
PV 1
C: Payment/cost on a given future date
t = Number of time periods
i = Discount rate
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Design objectives
Satisfy design criteria for example Minimum/maximum allowable pressures Maximum allowable velocities Tanks must not empty
NDEMANDS j NJ it H t H H ji ji ji ,...,1;,...,1,,)(max,,
min,
NDEMANDS j NP it V t V ji ji ,...,1;,...,1,,)(max,,
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Trial and error approach
User has to choose - diameters of pipes,locations of tanks, pumps, and PRVs
Engineering judgment and experience Run simulation model for demand load cases Check design criteria and compute cost Adjust sizes of elements in response topressures Rerun simulation model
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New York Tunnels problem
New York City Water Supply Tunnels
Brooklyn
Hillview Reservoir
EL 340 ft
16
9 21
8
20
19
11
7
6
5
4
17 18
13
14
3
2City Tunnel No. 1
City Tunnel No. 2
Bronx
Queens
Richmond
Manhattan
10
12
15
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A very very large search space size
Any one of the 21 existing pipes could beduplicated
Choose from 16 allowable pipe sizes tomeet demands
Search space size = 1.43 x 1021 Eliminate 99.99% of possible solutions by
engineering experience (leaves 1.43 x 1017)
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A very very large search space size
At 10,000 evaluations per second cancompute 3.15 x 1011 per year
It will take 454,630 years to fully enumerate0.01% of the total search space (only for 21
decision variables)
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A typical simple water distribution system
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Simulation Solving for The Unknowns
q Q1 Q2 Q NP T=
Only consider systems with pipes and reservoirs The unknown flow vector (10 pipes in examples)
The unknown head vector (7 nodes in example)(gives pressures)
h H1 H2 H NJ T=
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A total of 17 unknowns Qs and Hs
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Continuity Equation of Flow at a Junction
Flow In = Flow Out + Demand (or Withdrawal Discharge) where
Q j = flow in pipe j (m3/s or ft3/s)
NPJi = number of pipes attached to node i
DMi = demand at the node i (m3/s or ft3/s)NJ = total number of nodes in the water distribution system(excluding fixed grade nodes such as reservoirs)
Q j1=
NPJi
DM i+ =
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Pipe Head Loss Equations in Terms of NodalHeads
H i Hk r Q Q n 1 =
where = nodal head at node i in the water distribution system (m or ft) r j = resistance coefficient for the pipe j depending on the head loss
relationship (for example, Darcy Weisbach or Hazen Williams) Q j = flow in pipe j (m3/s or ft3/s) n = exponent of the flow in the head loss equation (Darcy Weisbach n = 2 or
Hazen Williams n = 1.852)
H
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Four different non-linear formulations
#1 Q-Equations #2 H-Equations #3 LF- Equations (Loop Flow Equations) #4 Todini and Pilati H-Q Equations
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#1 - The Q-equations formulation(10 unknowns)
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The Q-equations (10 unknowns)
q Q1 Q2 Q NP T=
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The Q-equations (Newton iterativesolution technique)
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#4 -Todini and Pilati Q-H formulation
Define topology matrices Develop block form of equations Use an analytic inverse of block matrices to
reduce matrix size from 17 unknowns to 7unknowns (same as unknown heads H)
Fast algorithm
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Todini and Pilati Q-H formulation
Unknownsh H1 H2 H NJ
T=
q Q1 Q2 Q NP T=
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Todini and Pilati Q-Hformulation - Define
topology matrices
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Todini and Pilati Q-Hformulation - Define
topology matrices
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Todini and Pilati Q-Hformulation- continuity at nodes
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Todini and Pilati Q-Hformulation head lossequations for pipes
Note that later on theinverse of this matrixwill give problems forzero flows
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Todini and Pilati Q-H formulation head lossequations for pipes
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Todini and Pilati Q-H formulation two sets of equations
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The Todini and Pilati equations
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Research Issues
Improving solution speed Making solution algorithms more robust zero
flows cause Todini and Pilati method to fail aregularization method has been developed tocontrol the condition number
An improved convergence criterion for stoppinghas been developed
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Research Issues
Decomposing networks into trees, blocks andbridges to speed up analysis
Growing typical networks that have correct mixof loops, links and junctions
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GENETIC ALGORITHMS FOR OPTIMISATIONOF WATER DISTRIBUTION SYSTEMS
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Types of Evolutionary Algorithms
Genetic algorithms(Holland 1976; Goldberg 1989)
Ant Colony Optimisation (ACO) Tabu search Simulated annealing Particle swarm optimisation (PSO) Evolutionary strategy (Germany)
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History of genetic algorithms applied towater distribution systems
Pioneered at the University of Adelaide by LaurieMurphy under my supervision in an honours project in1990 and a PhD starting in 1991
Initial focus was on the optimisation of the design ofwater distribution systems
A spinoff company of Optimatics Pty Ltd formed byUniversity of Adelaide in 1996 operates in Australia,NZ, USA and UK (employs 20 people)
Research focus is now on optimising operations andaccounting for multiple objectives (sustainability,reliability)
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Genetic algorithm optimisation
Population orientated technique (select apopulation size of say 500)
Based on mechanisms of natural selection
and genetics Selection, crossover and mutation operators
produce new generations of designs
Fitness of strings drives process Uses EPANET type simulation model to
assess performance of all trial waterdistribution networks in each generation
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Creating a string from sub-strings -an example
BINARY CODING
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Chromosome of decision variables
Choice tables are required for eachdecision variable
Chromosome
Existing pipe [3] (binary)00 = no change, e = 2.5 mm01 = clean/line, e = 0.3 mm10 = duplicate 306 mm11 = close the pipe
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Model Operation
Optimisation-Simulation Model Link
GA OPTIMISATION MODEL
HYDRAULIC SIMULATION MODEL
Configuration of water distribution andperformance passes back and forth
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Simulate hydraulics of waterdistribution system
Decode each string using the choice tables Run a computer simulation model Simulate demand loading cases
consecutively peak hour, fire, extended period simulation
Record any violation of constraints(e.g. pressures too low, velocities too high)
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Choices for the decision variables
A decoding lookup table NominalDiameter
(mm)
Actual orInternal
Diameter(mm)
BinaryCoding
IntegerCoding
Roughness height(mm) for Darcy-Weisbach friction
factor
Unit Cost($/m)
150 151 000 1 0.25 49200 199 001 2 0.25 63250 252 010 3 0.25 95300 305 011 4 0.25 133
375 384 100 5 0.25 171450 464 101 6 0.25 220500 516 110 7 0.25 270600 615 111 8 0.25 330
l d d f
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Total cost and corresponding fitnessof the string
Total cost is the: example1. Real cost of the water distribution system
design
PLUS 2. A penalty pseudo-cost (or costs) if the
constraint(s) are not met For example
=K*Maximum pressure deficitwhere K=$50,000 per metre
Fitness is often taken as the inverse of the totalcost
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Steps in a genetic algorithm
optimisation
Select a population size (e.g. N=100 or N=500) Select a reproduction or selection operator Select a probability of crossover (Pc) Select a probability of mutation (P
m)
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A Simple Genetic Algorithm
ThisGeneration
N=500
Selection Crossover&
Mutation
The NextGeneration
MatingPool
N=500
l
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Tournament selection
Randomly selectpairs of
chromosomes
versus
Evaluationof the fittest
Forming theMating Pool
1 1 1 1 1
1 11 11 11
1 11 1
1 1
1
1111
1 1 1
11 1
1 11
1
1
11 1 1
1 11 11
1 1
11 1 1 1 1 1
11 1 1
1
1
11
1
00 0 0
0
0
0 0
00
00 0 0 0
00
0 00
0000 0
00000
00000
00000
0
00
0
0 0
0
0 0
0
1 11 1 11 1 000
65
112
94
8398
143
87
130
Fittest strings win
Two sets of tournament selection are required
versus
versus
versus
FITNESS
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Crossover (one-point)
Chromosome A
Chromosome B Parents
Chromosome A`
Chromosome BOffspring
1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1
1 1 11 1 1
1 1 1 1
0 0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0 0
Randomly select acrossover point
Interchange the tails
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The mutation operator
Mutation occurs with a very small probability One bit switches to a new value
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Produce many generations
Continue to create a series of newgenerations (say 100,000 differentnetworks)
Repeat selection, crossover andmutation
Increasingly fit solutions are
generated The 10 or so lowest cost solutions
must be remembered along the way
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Optimisation of pumping plant operations
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Murray Bridge operations
optimisation United Utilities Riverland water treatment
plant project at Murray Bridge, South Australia
GA optimisation minimises operationselectricity costs by
maximizing off-peak pumping and minimizing static pump head
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Background
Pumps
ElevatedStorage
Water TreatmentPlant
Clear WaterStorage
Case study Murray Bridge system
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Case study Murray Bridge systemlayout
White HillStorage Tank (WHS)
OffTakes
MurrayBridge
OnkaparingaPipeline
Murray Bridge WaterTreatment Plant
Clear WaterStorage Tank (CWS)
3 Parallel FixedSpeed Pumps
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Traditional approach to control
Trigger levels in storage tanksOR Pump scheduling
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Controls based on trigger levels
Lower Trigger Level (Minimum Allowable Level)
Upper Trigger Level (Maximum Allowable Level) More Peak
Pumping thanNecessary
Time
T a n
k L e v e
l
Peak Tariff Period
Tank not Fullfor Next
Peak TariffPeriod
Tank not Full atStart of PeakTariff Period
Off-Peak Tariff Period
7am 7am 9pm
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Optimisation-Simulation Model Link
GA OPTIMISATION MODEL
HYDRAULIC SIMULATION MODEL
Operating policies for pumpingsystem - trigger levels, schedules for
pumps turning on and turning off
Model operation
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Decision variables - operationsoptimisation at Murray Bridge
Used a combination of real-value and integer valuerepresentation of the decision variables
Four decision variable for final formulation: Pump start time to fill tank Pump stop time to drain tank to minimum level Reduced upper trigger level for tank Initial level in CWS tank
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A system controlled with original trigger
levels and schedules
Lower Trigger Level(Minimum Allowable Level)
Upper Trigger Level (Maximum Allowable Level)
Time
Peak Tariff Period
Tank Full atStart of Peak
Tariff Period
Off-Peak Tariff Period
7am 7am9pm
Start PrimaryPump
Stop PrimaryPump
Tank at Minimum Level atEnd of Peak Tariff Period
T a n
k L e v e
l
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A system controlled with both schedulesand a reduced upper trigger level (1)
Time
Lower Trigger Level(Minimum Allowable Level)
Upper Trigger Level (Maximum Allowable Level)
Peak Tariff Period
Tank Full at Start of PeakTariff Period
Off-Peak Tariff Period
7am 7am9pm
Start PumpReduced Upper Trigger Level
Tank at Minimum Level at
End of Peak Tariff Period
T a n
k L e v e
l
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T a n
k L e v e
l
Lower Trigger Level(Minimum Allowable Level)
Upper Trigger Level (Maximum Allowable Level)
Time
Peak Tariff Period
Tank Full at Start ofPeak Tariff Period
Off-Peak Tariff Period
7am 7am9pm
Start Pump
Reduced Upper Trigger LevelExtended into Off-Peak Tariff Period
Tank at Minimum Levelat End of Peak Tariff Period
Switch Time
A system controlled with both schedulesand a reduced upper trigger level (2)
Modelled System - Original Trigger
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Modelled System Original TriggerLevels
L e v e
l ( m )
4
5
6
7
Daily electricity cost (averaged over 28 days) = $313.65
Time (hrs)
Daily peak pumping(averaged over 28 days): $286.05
Initial Level in CWS = 3.4m
Lower trigger level = 5.49m
Upper trigger level = 6.98m
0
1
2
3
8
11 am 9 am 7 am 7 am 5 am 3 am 1 am 11 pm 9 pm 7 pm 5 pm 3 pm 1 pm
Daily off-peak pumping(averaged over 28 days): $27.60
WHS (m)
CWS (m)
WHS and CWS tank levels for first 24hours of a 28-day simulation under fixedtrigger level control for a 7.17 ML/D flow
Optimised system new approach
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Optimised system - new approach
Initial Level in CWS = 3.675 m
Lower trigger level = 5.49 m
Reduced trigger level = 5.76 m
Upper trigger level = 6.98m
WHS and CWS tank levels after optimisationfor a 7.17 ML/D flow
0
1
2
3
4
5
6
7
8
Time (hrs)
L e v e
l ( m )
WHS
CWS
Pump on at 1:54:13 am
Peak Pumping: $189.51 Off-peak Pumping: $67.63
Total electricity cost = $257.14. Hence a $56.51 or 18.0%
11 am 9 am 7 am 7 am 5 am 3 am 1 am 11 pm 9 pm 7 pm 5 pm 3 pm 1 pm
Switch time 2:15 am
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Results - savings from new approach
18.284.34378.76463.110
13.646.3293.02339.328
18.056.48257.16313.647.17
22.459.72207.13266.866
22.936.17121.57157.744
54.950.6141.6592.262
(%)($)ImprovedControlsCurrent
Controls
SavingsPumping Cost($/Day)DailyDemand(ML/Day)
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Accounting for Sustainability in theDesign and Operation of WaterDistribution Pumping Systems
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Research Objectives
To construct a sustainability integratedmulti-objective genetic algorithmoptimisation model for the planning,design and evaluation of WDSs
To explore the impacts different
sustainability criteria (Greenhouse Gasemissions) will have on the results ofWDS optimisation
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Aspects of Sustainability-
Social
Environmental
Economic Technical
1: Total cost ofthe system
2: GHGemissions
3:Systemreliability 4: Robustness ofPareto-optimal Front
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Two of the Main Conflicting Objectives
Minimisation of thetotal life cyclesystem costs
Minimisation of thetotal life cycle systemGHG emissions
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Higher CostLower GHG
Lower Cost
Higher GHG
Big pumpSmall pipe
Small pumpBig pipe
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Evaluating multi-objective optimisation
results using a Pareto tradeoff curve
Cost
GHG
TradeoffCurve
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Determining life cycle economic costs
Total Cost
Capital CostsPump
Refurbishment
Costs (PVA)
Operating Costs
(PVA)
Pipes andPump Stations
Pumps Pumping
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Determining life cycle GHG emissions(no discounting i = 0% IPCC)
Total Emissions
Capital Emissions Operating Emissions
Embodied Energyof Pipes
Electricity Consumptionof Pumping
Emission Factor Analysis
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Optimisation Framework
Generate Options
M O GA
Simulation
Evaluation
Comparison& Selection
WDS Optimisation
O b j e c t i v e s
Minimisationof total cost
Minimisation ofGHG emissions
Maximisation ofsystem reliability
Maximisationof robustness
of Pareto-optimal
solutions
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Multi-objective optimisation using genetic
algorithms MOGA: NSGA-II Generate initial population Objectiveevaluation
Simulationmodels
Ranking
Generate globalpopulation
Non-dominatedsorting
Crowding
distance
Comparison &selection
Constrainthandling
Generate child population
Crossover
Mutation
Stoppingcriteria met?
Stop
Yes
No
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Case Study The network consistsof a lower reservoir
(water source), onepump, one rising main
and an upper reservoir
1,500,000
951,500120100
Average peakday flow (L/s)Design life (years)
Design conditions of case 1 Annual demand (m 3)
Static headPipe length
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Pareto optimal tradeoff curve
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Pareto optimal tradeoff curve multi-objective optimisation i = 6%
6% discount rate for costs
A
B
G H
C D E F
87.0
91.0
95.0
99.0
103.0
4.3 4.7 5.1 5.5
System cost (M$)
G H G
( k - t
o n n e )
$21.8/tonneCO 2-e
$134/tonneCO 2-e
$371/tonne CO 2-e
(300)
(450)(375)
6% discount rate for costs
A
B
G H
C D E F
87.0
91.0
95.0
99.0
103.0
4.3 4.7 5.1 5.5
System cost (M$)
G H G
( k - t
o n n e )
$21.8/tonneCO 2-e
$134/tonneCO 2-e
$371/tonne CO 2-e
(300)
(450)(375)
Diameter for lowest cost solution
Tradeoff for i = 1.4%
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1.4% discount rate for costs
B
C DE
H
FG
88.5
89.5
90.5
91.5
92.5
10.1 10.3 10.5 10.7 10.9 11.1
System cost (M$)
G H G
( k - t o n n e
) $72.1/tonneCO2-e
$376/tonne
CO2-e $1,468/tonne CO2-e
(375)
(450)
1.4% discount rate for costs
B
C DE
H
FG
88.5
89.5
90.5
91.5
92.5
10.1 10.3 10.5 10.7 10.9 11.1
System cost (M$)
G H G
( k - t o n n e
) $72.1/tonneCO2-e
$376/tonne
CO2-e $1,468/tonne CO2-e
(375)
(450)
Lowest cost
Lowest GHGs
Conclusions
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Conclusions
Evolutionary algorithm optimisation hasapplication in design and operation of waterdistribution systems
It is relatively easy to tack on an evolutionaryalgorithm optimisation onto existing simulationmodels
Capital costs and operating costs can bereduced significantly Sustainability can be optimised