The application of
Genetic Algorithms (GAs)
Planning Design and Management of Water
Supply Systems
S J van Vuuren
GA’s - not a solution to all problems !
Layout
• What is a GAs?
• An Example of a GA
• Programming of network problems
• GAs in the Planning Design and
Management of Water Supply Systems
• The road ahead
What is a GA?
GA =
Search procedure based on the
mechanics of natural
selection and natural genetics
– survival of the fittests.
Human Evolution
Natural Evolution
A different view
Processes of a GA
• Production
• Select randomly
• Crossover
• Pairs change (Random process)
• Mutation
• Protects against loss of useful genetic material (secondary
mechanisms to prevent local optimum)
• Reproduction
• Select according to objective function (Best remain)
How do GAs differ from traditional
methods (Goldberg)
• Coding of the parameter set, not the parameters
themselves.
• Search for a population of points, not a single point.
• Use objective functions (payoff) information, not
derivatives or other auxiliary knowledge, to determine
the fitness of the solution.
• GAs use probabilistic transition rules not
deterministic rules
3 Main types of search methods
• Calculus - Enumerative
• Random
• Genetic algorithm
Comparison of
Optimization Methods
Example
Example of a chromosome
string
Basics of a GA
An Example of a GA
MAXIMIZE f(x) = x2
(0 < x < = 31)
CODE x as a finite-length string
Length = 5 in the binary basis
(1x24 + 1x23 + 1x22 + 1x21 + 1x20 = 31)
Select population size - say 4
strings
Crossover and mating
STRING
x
f(x)
01101
11000
01000
10011
13
24
8
19
169
576
64
361
f (x)
 f (x)
0,14
0,49
0,06
0,31
 f ( x )  1170
1,0
Average = 0,25
f (x)
 f ( x ).Ave
0,58
1,97
0,22
1,23
Copies
inmating
pool
1
2
0
1
Crossover
Mating string 1 with 2, and 3 with 4 and crossover at positions 4
and 3 results in:
Mutation
PROBABILITY OF MUTATION
BITS TO MUTATE IN A GENERATION
=
0,001
= 20 X 0,001
= 0,02
No mutation !
Summary after one generation
Start
Sample
Average fitness
293
Maximum fitness
576
Next *
generation
439
729
Note: *Values after one generation and one crossover
Programming procedure of
Genetic Algorithms (GAs)
An Example
1. Problem for the application of Genetic
Algorithms in water supply systems
2. Computer Program
Example Problem - Genetic
Algorithms in water supply
systems: Layout
902
14
12
15
10
11
13
Legend
901
Demand
Reservoir
Pump
Solution objective
For a given demand it is
required that we have to:
Determine the pipe diameters
that will result in the
minimum life cycle cost.
Calculations procedures
Optimum solution through the
use of the GA, while the
pressure/energy requirements
be determined through the use
of hydraulic relationships.
Flow diagram
Start
Possible
solution
Hydraulic
solution
New
Results Report
Crossover
mutation
Cost Calculation
Reproduction
Fitness test
Computer program
• Two problems can be analyzed :
• Gravity line
• Pump line
• Determine the optimal diameter and
pumping time
• Overview of input screens
• Results
Gravitation and Pumping
Systems – Selection Screen
Pumping System – Screen P1
Pump line details – Screen P2
Pump line energy cost – Screen P3
Pump line economic analysis
Capital data - Screen P4
Pump line design parameters
Screen P5
Results from the GA analysis
Pumping Pipeline – Results 1
Results from the GA analysis
Pumping Pipeline – Results 2
Results from the GA analysis
Pumping Pipeline – Results 3
Results from the GA analysis
Pumping Pipeline – Results 4
Network Optimization
Use EPANET to set-up system
•Define pipes that can be changed
•Define a penalty structure/cost on routes
which are difficult to change
•Conceptually develop procedure
EPANET to set-up system
The application of Genetic Algorithms in
the Planning Design and Management of
Water Supply Systems
•WRSM 2000
•Water Resources
The application of Genetic Algorithms
WRSM 2000
Automate calibration of WRSM 2000 parameters
WRSM 2000 – Current process
The application of Genetic Algorithms
WRSM 2000
• Optimise calibration on selected monthly flood size
•
Procedure will select monthly flood size based on
exceedance probability
• Obtain from this, a parameter set that will represent
the calibrated flow record
•
Develop criteria applicable for this optimisation
The application of Genetic Algorithms
WRYM
Optimize water Resources Analyses Procedures
How the GA can be implemented
Genetic Algorithm
(Subroutines)
Simulation Results
• Yield
• Pumping Volumes
Operating Rule
Yield Search
Subroutine
Target Draft
Simulation Results & Files
*SUM.OUT
*PLT.OUT
Supply Results
Network Simulation
Subroutines
Water Resources
Yield Model (WRYM)
Genetic Algorithm
Results
• Step-by-step output
• Fitness function results
• Optimum solution
WRC has funded the conceptual
assessment of the application of GAs
The application of Genetic Algorithms in
the Planning Design and Management of
Water Supply Systems – December 2004
Gas = Where from here ?
Development of routines to be included in
existing modeling procedures
Thank You