S J van Vuuren

The application of Genetic Algorithms (GAs)

Planning Design and Management of Water Supply Systems

GA’s - not a solution to all problems !GA’s - not a solution to all problems !

LayoutLayout

• WhWhat is a at is a GAs?GAs?

• AAn Example of a GAn Example of a GA

• Programming of network problemsProgramming of network problems

• GAs in the Planning Design and Management of Water Supply Systems

• The road ahead

• WhWhat is a at is a GAs?GAs?

• AAn Example of a GAn Example of a GA

• Programming of network problemsProgramming of network problems

• GAs in the Planning Design and Management of Water Supply Systems

• The road ahead

WhWhat is a Gat is a GA?A?

GA =GA =Search procedure based on the mechanics of natural selection

and natural genetics – survival of the fittests.

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 GAProcesses 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)

• 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 How do GAs differ from traditional methods (Goldberg)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 notdeterministic rules

• 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 notdeterministic rules

3 Main types of search methods3 Main types of search methods

• Calculus - Enumerative

• Random

• Genetic algorithm

• Calculus - Enumerative

• Random

• Genetic algorithm

Comparison of Optimization Methods

ExampleExample

Example of a chromosome Example of a chromosome stringstring

Basics of Basics of a GAa GA

An Example of a GAAn 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

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 matingCrossover and matingS T R I N G x f ( x )

)x(f

)x(f

Ave).x(f

)x(f C o p i e si n m a t i n g

p o o l0 1 1 0 1 1 3 1 6 9 0 , 1 4 0 , 5 8 11 1 0 0 0 2 4 5 7 6 0 , 4 9 1 , 9 7 20 1 0 0 0 8 6 4 0 , 0 6 0 , 2 2 01 0 0 1 1 1 9 3 6 1 0 , 3 1 1 , 2 3 1

1170)x(f 1 , 0A v e r a g e = 0 , 2 5

S T R I N G x f ( x ) )x(f

)x(f

Ave).x(f

)x(f C o p i e si n m a t i n g

p o o l0 1 1 0 1 1 3 1 6 9 0 , 1 4 0 , 5 8 11 1 0 0 0 2 4 5 7 6 0 , 4 9 1 , 9 7 20 1 0 0 0 8 6 4 0 , 0 6 0 , 2 2 01 0 0 1 1 1 9 3 6 1 0 , 3 1 1 , 2 3 1

1170)x(f 1 , 0A v e r a g e = 0 , 2 5

Crossover

Mating string 1 with 2, and 3 with 4 and crossover at positions 4

and 3 results in:

Crossover

Mating string 1 with 2, and 3 with 4 and crossover at positions 4

and 3 results in:

MutationMutation

PROBABILITY OF MUTATION = 0,001PROBABILITY OF MUTATION = 0,001

BITS TO MUTATE IN A GENERATION = 20 X 0,001 = 0,02

No mutation !Summary after one generation

StartSample

Next *generation

Average fitness 293 439Maximum fitness 576 729

Note: *Values after one generation and one crossover

Programming procedure ofGenetic Algorithms (GAs)

An Example

Programming procedure ofGenetic Algorithms (GAs)

An Example

1.1. Problem for the application of Genetic Problem for the application of Genetic Algorithms in water supply systems Algorithms in water supply systems

2. 2. Computer ProgramComputer Program

Example Problem - Genetic Example Problem - Genetic Algorithms in water supply Algorithms in water supply

systems: Layoutsystems: Layout

9 0 110

11

12

13

14

15

L eg en d

D em an d

R eservo ir

P u m p

9 0 2

Solution objectiveSolution 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.

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 Calculations proceduresprocedures

Optimum solution through the use of the GA, while the

pressure/energy requirements be determined through the

use of hydraulic relationships.

Optimum solution through the use of the GA, while the

pressure/energy requirements be determined through the

use of hydraulic relationships.

Flow diagramFlow diagramStart

Possible solution

Hydraulic solution

Cost Calculation

Fitness test

Crossover

mutation

NewNewResults Report

Reproduction

Computer programComputer 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 Gravitation and Pumping Systems – Selection ScreenSystems – Selection Screen

Pumping System – Screen P1Pumping System – Screen P1

Pump line details – Screen P2

Pump line energy cost – Screen P3Pump line energy cost – Screen P3

Pump line economic analysis Pump line economic analysis Capital data - Screen P4Capital data - Screen P4

Pump line design parametersPump line design parametersScreen P5Screen P5

Results from the GA analysis Results from the GA analysis Pumping Pipeline – Results 1Pumping Pipeline – Results 1

Results from the GA Results from the GA analysis Pumping Pipeline – analysis Pumping Pipeline –

Results 2Results 2

Results from the GA Results from the GA analysis Pumping Pipeline – analysis Pumping Pipeline –

Results 3Results 3

Results from the GA Results from the GA analysis Pumping Pipeline – analysis Pumping Pipeline –

Results 4Results 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 AlgorithmsWRSM 2000

Automate calibration of WRSM 2000 parameters

WRSM 2000 – Current process

The application of Genetic AlgorithmsWRSM 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 AlgorithmsWRYM

Optimize water Resources Analyses Procedures

How the GA can be implementedHow the GA can be implemented

Genetic Algorithm(Subroutines)

Yield SearchSubroutine

Water Resources Yield Model (WRYM)

Operating RuleSimulation Results• Yield• Pumping Volumes

Simulation Results & Files*SUM.OUT*PLT.OUT

Supply Results

Network Simulation Subroutines

Target Draft

Genetic AlgorithmResults

• 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 application of Genetic Algorithms in the Planning Design and Management of the Planning Design and Management of Water Supply Systems – December 2004Water Supply Systems – December 2004

Gas = Where from here ?

Development of routines to be included Development of routines to be included in existing modeling proceduresin existing modeling procedures

Thank YouThank You