AquatorGA:
AquatorGA: Integrated optimisation for
reservoir operation using Multiobjective
Genetic Algorithms
Lydia VamvakeridouVamvakeridou-Lyroudia, Mark Morley,
Morley, Josef Bicik, Dragan Savic
Centre for Water Systems, University of Exeter, UK
Chris Green, Peter Edgley,
Edgley, Will Clark
Oxford Scientific Software Ltd, Oxford, UK
AQUATOR Users’ meeting, Reading, October 2, 2009
1
What is this presentation about?
•AQUATOR
AQUATOR:
AQUATOR: (OXSCISOFT)
Water
Water supply system simulation software
In
In use by several UK water companies
•Genetic
Genetic Algorithms (GA):
(GA): (University of ExeterExeter-CWS)
Genetic
Genetic Algorithms software for optimisation
(generic software )
•Project
Project Objective:
Objective: Linking and integrating GA and
AQUATOR,
AQUATOR, applying them for the optimisation of single and
multiple reservoir systems AquatorGA
3
3 case studies (2 single + 1 multiple
reservoirs)
2
History of the project
•Single
Single reservoir system optimisation project with UU
Presented
Presented at the previous annual meeting
(September Stirling 2008)
December
December 20082008-Completed
Successful
Successful
AquatorGA
AquatorGA installed at UU (2 test case studies)
•Since
Since then
Moving to multiple reservoir systems
Scottish
Scottish Method for Deployable Output added
Fife system (3 reservoirs)
To be presented today…
today…
3
Single reservoir system
Inflow
Daily time
series
Monthly
control
curve
Ci , i=1..12
Outflow
Demand time series
OR
X (cut back yield)
4
Single reservoir system
Source
Input time series
(daily)
Storage
Single (1)
Monthly control
curve
Ci , i=1,12
Demand
Ouput time
series:
Demand OR
X (cut back
yield)
•Single
Single reservoir
•No
No spills /No energy costs taken into account (gravity fed)
•Target:
Target: Maximising yield (water volume) AND No deficits
•Decision
Decision variables (Unknowns): X and Ci, i=1,12
•Initial
Initial optimal solution given by UU
5
Single reservoir system
Source
Input time series
(daily)
Demand
Storage
Single (1)
Monthly control
curve
Ci , i=1,12
Ouput time
series:
Demand OR
X (cut back
yield)
•Control
Control curve (monthly) Ci , i=1,12
• Ci % of max water volume (reservoir capacity)
• If storage > Ci Outflow= Demand
• If storage < Ci Outflow= X (cutback yield)
• If storage < minimum deficit (To be avoided)
6
Genetic Algorithms (GA)
•Optimisation
Optimisation method suitable
•For
For “hard”
hard” problems (non(non-linear/discrete/non convex)
•For
For “difficult”
difficult” decision variables
•For
For “strange”
strange” constraints
•For
For discrete search space/variables
•For
For one (single
(single)
single) or more (multi
(multimulti-) objective problems
•Directed
Directed random search
•Based
Based on Darwinian evolution principles (“
(“Survival of the
fittest”
fittest” )
•Solutions
Solutions can be reproduced (repeatable)
7
Optimising using Genetic Algorithms
•Decision
Decision variables (unknowns): (Multiple
(Multiple control curves
now possible)
X
X (cutback yield)
Ci
Ci,
Ci, i=1,12 (monthly control curve components)
•Total:
Total: 13 unknowns = string of 13 decision variables for 1
control curve
•13*2=26
13*2=26 unknowns = string of 26 decision variables for 2
control curves, …3*13=39 for 3 control curves…
curves….
•All
All in one step!
•AND
constraints…
…
AND being able to include desirable shape constraints
•AQUATOR
AQUATOR (simulator) treated as “black box”
box”
8
Objectives for the shape of the
control curve
•Smooth
Smooth curve
•Magnitude
Magnitude of change in consecutive months DC
•Objective: minimising DC
•OR
OR
•““Steady”
Steady” curve
•Number
Number of changes in a year> significant step NC
•Objective: minimising NC
9
MultiMulti-objective GA for single reservoir
system
Objective
Objective function (1): max V (Yield/total Water Volume
supplied water over the simulation period)
AND
AND
Objective
Objective function (2): min NC (number of changes in
the control curve in a year)
OR
OR
Objective
Objective function (3): min DC (magnitude of changes in
the control curve for consecutive months)
Constraints
Constraints:
Constraints: No supply deficits (SD=0) / failures (NF=0),
limits to the number of changes in a year, control curve
discretisation step…
step… (any other)
No
No single winner: Multiple optimal solutions
•Trade
TradeTrade-off curve of nonnon-inferior solutions (Pareto points) 10
Maximum control curve change in consecutive months %
40
Multiobjective GAGA-TradeTrade-off curve
35
30
25
20
15
10
5
0
43000
44000
45000
46000
47000
48000
Water volume-Yield (Ml)
49000
50000
51000
52000
11
Implementation Structure
GENETIC
ALGORITHM
Time
consuming!!!
AQUATOR (Simulator)
Called to run for each
string (potential
solution) at every
generation
12
Problem:
Problem:
•
AquatorGA
Runtime needed (thousands of generations/AQUATOR
simulations) distribution to computers in parallel
AND Reducing the time by
•
•
Critical period concept
•
Optimising for a short critical period
•
Validating for full period
Improving the GA …
•
Improving the algorithm
•
Larger population (100(100-250)
•
‘Near optimal’
optimal’ results in 150150-300 generations (instead
of 3000) in under 1 hour for a single reservoir system
13
Distributed computing for AquatorGA
M
an
ag
es
Master controlling
AQUATOR runs
and the optimisation
Instances of
AQUATOR running
simulations in parallel
14
AquatorGA - Integration
•
GA Optimisation developed as addadd-in to AQUATOR
•
Activated through AQUATOR (AquatorGA
(AquatorGA)
AquatorGA)
•
Optimisation set up by the user (menus in AQUATOR)
15
Multiobjective GAGA-TradeTrade-off curve
16
1st case study: Barnacre system
•1
1st test case study (2006(2006-2008)
•Inflows
Inflows daily time series 192719272002
•Optimisation
Optimisation carried out for the
critical period (1992(1992-1998) to
reduce the computational time
for AQUATOR
Barnacre storage (Ml)
Barnacre storage (Ml)
2500
•Checking
Checking (automatically) for the
whole period after optimisation
2500
2000
2000
•Several
Several Combinations of
objectives tried
1500
1500
1000
1000
500
Storage
500 Storage
Control curve
Control curve
Emergency Storage
Emergency Storage
0
0
1995
1995
1996
1997
01
Jan 1995 - 31 Dec 1998 1997
1996
01 Jan 1995 - 31 Dec 1998
1998
1998
•Initial
Initial “Best solution” provided
by UU for comparison
17
Selected Solutions for Barnacre
Original
UU
Smooth
curve
Smooth
curve
Smooth
curve
Min
changes
1 change
Min
changes
2changes
Max yield
Rate A
Rate B=X
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Failures
Deficit
Volume
6.90
(1)
40.00
1.00
(2)
40.00
2.00
(3)
40.00
3.00
(4)
40.00
13.45
(5)
40.00
42.28
(6)
40.00
38.00
(7)
40.00
19.1800
92.60
99.50
100.00
100.00
100.00
100.00
100.00
100.00
96.30
91.50
88.80
89.80
0
0
48203
19.12898
97.00
98.00
99.00
100.00
100.00
100.00
100.00
100.00
100.00
99.00
98.00
98.00
0
0
49580
19.03226
94.00
96.00
96.00
98.00
100.00
100.00
100.00
100.00
100.00
98.00
96.00
96.00
0
0
50288
19.00012
93.00
92.00
95.00
98.00
100.00
100.00
100.00
100.00
99.00
97.00
94.00
91.00
0
0
50330
19.18536
86.55
86.55
100.00
100.00
100.00
86.55
86.55
86.55
86.55
86.55
86.55
86.55
0
0
49297
19.18536
57.72
57.72
100.00
100.00
100.00
86.55
86.55
86.55
86.55
86.55
86.55
86.55
0
0
50796
19.12691
60.00
60.00
98.00
100.00
100.00
100.00
100.00
100.00
100.00
89.00
74.00
94.00
0
0
50807
Volume increase %
0.00
2.86
4.32
4.41
2.27
5.38
5.40
1992-1998
max dC%
18
Different control curves (Barnacre
(Barnacre)
Barnacre)
52000
51000
Yield
increased by
+4.41%
Yield
increased by
+5.38%
Yield
increased by
+5.40%
Smooth curve
Curve with 2
changes per year.
Max yield
Yield (in Ml)
50000
49000
+/- 0.00%
48000
47000
46000
Original curve by
UU
19
100.00
100.00
90.00
90.00
Control Curve C %
Control Curve C %
Different control curves (Barnacre
(Barnacre)
Barnacre)
80.00
70.00
80.00
70.00
60.00
60.00
50.00
50.00
Jan
Feb
Mar
Apr
May
Jun
Jul
Months
(1) Original curve UU, dC=6.90% Yield=48203
(3) Smooth dC=2%, Yield=50288
(5) 1change, Yield=49297
(7) max Yield=50807
Aug
Sep
Oct
Nov
Dec
(2) Smooth dC=1%, Yield=49580
(4) Smooth dC=3%, Yield=50330
(6) 2changes , Yield=50796
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Months
(1) Original curve UU, dC=6.90% Yield=48203
(2) dC=1%, Yield increase by 2.86%
(3) dC=2%, Yield increase by 3.26%
(4) dC=2%, Yield increase by 4.04%
(5) dC=2%, Yield increase by 4.25%
(6) dC=2%, Yield increase by 4.32%
(7) dC=2%, Yield increase by 4.41%
Dec
100.00
Steady curves
Control Curve C %
90.00
Smooth curves
80.00
70.00
Maximum yield
60.00
50.00
Jan
Feb
Mar
Apr
May
Jun
Jul
Months
(1) Original curve UU, dC=6.90% Yield=48203
(3) Yield increase by 5.20%
(5) Yield increase by 5.26%
(7) Yield increase by 5.40%
Aug
Sep
Oct
(2) Yield increase by 4.84%
(4) Yield increase by 5.24%
(6) Yield increase by 5.38%
Nov
Dec
20
Multiobjective GAGA-tradetrade-off curves
(Barnacre)
Barnacre)
21
2nd case study:
Watergrove & Springmill
Source
Input time series
(daily)
19271927-2005
Storage
Single (1)
Monthly control
curve
Ci , i=1,12
Demand
Ouput time
series:
15.21 Mld OR
X (cut back
yield)
•Single
Single reservoir
•Spills
Spills /No energy costs taken into account (gravity fed)
•Target:
Target: Maximising yield (water volume) AND No deficits
•Decision
Decision variables (Unknowns): X and Ci, i=1,12
•Initial
Initial optimal solution given by UU (X fixed at UU request)
22
Selected Solutions for W&S
1993-1997
Original Smoother Smoother
UU
curve
curve
max dC%
15.67
Rate A
Rate B=X
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Failures
Deficit
Volume
15.21
8.2900
72.24
84.92
92.99
97.16
100.00
98.66
87.76
72.09
60.30
52.53
54.77
61.64
16077
Volume increase %
Volume full period
Volume increase %
full period
371165
Smoother
curve
Smoother
curve
Max yield
Max yield
10.90
(2)
15.21
11.32
(3)
15.21
12.77
(4)
15.21
13.38
(5)
15.21
18.48
(6)
15.21
20.21
(7)
15.21
8.29000
68.47
77.89
84.08
94.80
90.57
87.55
76.96
68.03
58.35
55.70
50.10
57.57
0
0
16748
8.29000
68.47
76.98
84.08
94.90
91.19
87.55
76.24
66.88
58.35
55.70
50.10
57.91
0
0
16783
8.29000
62.60
69.48
82.26
94.96
91.19
87.55
75.48
66.94
58.62
55.98
49.94
57.63
0
0
16824
8.29000
66.73
69.26
82.63
95.33
89.44
86.25
76.37
67.13
57.45
54.24
49.54
53.76
0
0
16852
8.29000
51.17
69.65
87.68
95.34
89.44
86.83
76.28
66.85
57.56
52.85
49.54
50.90
0
0
16866
8.29000
49.37
69.58
82.44
95.33
91.23
84.57
75.95
66.85
57.43
54.18
49.54
58.12
0
0
16880
4.18
4.39
4.65
4.82
4.91
4.99
390659
391171
391662
392901
392597
393226
5.25
5.39
5.52
5.86
5.77
5.94
23
TradeTrade-off curve for W&S/Critical period
Initial
solution
Population 100
Generations 150
Results obtained
under 1hr
Demo !!
24
3rd case study: Fife system
25
Fife system
•
3rd case study: Fife system.
system. Multiple reservoirs (3)
•
Three control curves (Ci
(Ci,
Ci, i=1,12). In total 3*12=36 decision
variables (unknowns)
•
Optimisation in one step (Ci simultaneously for all reservoirs),
system as a whole
•
Daily input time series (1918(1918-1998) 81 years
•
Scottish method of Deployable Output (DO) as primary
objective (maximise DO) for a return period T=40 years
•
Supply Deficits > 0,
0, because DO for T=40 between 2 and 3
years of failure (NF) for N=81 years
•
Initial solution provided by OSS for comparison: Deployable
Output DO=136.2 Mld -computational step 1 Mld (or 135.9
MldMld- computational step 0.5 Mld)
Mld)
26
Deployable Output in AQUATOR
27
Fife system
•
Deployable Output (DO) as primary objective (maximise DO)
•
Additional time consuming computations. Testing different
demands for the same (Ci
(Ci)
Ci) set of potential solutions, in order
to compute the DO for T=40 years.
•
Optimisation carried out for 9 critical years (non consecutive)
to reduce the computational time needed.
•
With 9 years, 1515-20 min for a single DO simulation to run in
AQUATOR, with a computational step of 1Mld for the DO!
•
Specific methods to overcome the computational problem for
the GA have been adopted, including parallelisation…
parallelisation…
•
Efficiency of different configurations for the GA and the
objective functions have been tried…
tried…
•
Not a trivial problem: Days or weeks to run for a single
optimisation…
optimisation… (10 days in July, down to 36 hours now)
28
Fife system: Objective functions
(1):
(1): max DO (Deployable Output for return period T=40 yearsyearsbetween NF=2 and NF=3 failure years)
(2):
(2): min DC (magnitude of changes in the control curve for
consecutive months taken as a sum of the 3
reservoirs)
(3):
(3): min ((DCmax
DCmax)
DCmax) (the maximum monthly change in the control
curve for consecutive months in all 3 reservoirs)
(4):
(4): min (SD) (supply deficit). SD>0 in all cases, because the
DO for T=40 relates to computations with 2 or 3
failure years (NF)
Other
inefficient
nt
Other objective functions tried (e.g. cost) but proved inefficie
or unsuitable.
Specific
Specific computational method introduced to the GA for
estimating the DO for T=40 quicker.
29
Fife system: TradeTrade-off –Pareto curves
Pareto “surface”
surface” for
three objectives
1.max DO
Deployable Output
(Mld)
Mld)
2.min DC
(total magnitude of
change at all three
control curves)
2.min SD
Supply deficit (Ml)
30
Smoothness
Fife system: TradeTrade-off curves
31
Pareto optimal solutions
With supply deficit
as objective
Without supply
deficit as objective
32
Control curves optimal decision space
33
Control curves for the 3 reservoirs
Lom ond Hills
Glendevon
100.0
90.0
90.0
90.0
80.0
80.0
80.0
70.0
70.0
70.0
60.0
60.0
60.0
50.0
% full
100.0
% full
% full
Glenfarg
100.0
50.0
50.0
40.0
40.0
40.0
30.0
30.0
30.0
20.0
20.0
20.0
10.0
10.0
10.0
0.0
0.0
0.0
1
2
3
4
5
6
7
8
Month
Manual
9
10
11
12
1
2
3
4
5
6
7
8
9
Manual
11
12
1
2
3
4
5
6
7
8
9
10
Month
Month
GA
10
GA
Manual solution
(reference)
Manual
GA
AquatorGA
solution
34
11
12
Thank you for your attention!
Demo available…
available…
Paper:
VamvakeridouVamvakeridou-Lyroudia, L.S., Morley M.S., Bicik J., Green C., Smith M.
and Savic,
Savic, D.A. (2009). AquatorGA:
AquatorGA: Integrated optimisation for reservoir
operation using multiobjective genetic algorithms, in “Integrating
Integrating Water
Systems”,
Systems , Proc. 10th Int. Conf. on Computing and Control for the Water
Industry CCWI 2009, 11-3 Sept 2009 University of Sheffield, UK, pp 493493500
Website:
http://centres.exeter.ac.uk/cws/projects/waterhttp://centres.exeter.ac.uk/cws/projects/water-resourcesresourcesmanagement/165management/165-gaga-aquator
35