the matlab genetic algorithm toolbox

8/13/2019 The MATLAB Genetic Algorithm Toolbox

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The MATLABGenetic Algorithm Toolbox

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J. Chipperfield and P. J. Fleming 1

1. Introduction

Genetic algorithms (GAs) are stochastic global search and optimization methods that mimic the metaphor of naturalbiological evolution 1!. GAs operate on a population of potential solutions appl"ing the principle of survival of the

.ttest to produce successivel" better appro#imations to a solution. At each generation of a GA$ a ne% set of

appro#imations is created b" the process of selecting individuals according to their level of .tness in the problem

domain and reproducing them using operators borro%ed from natural genetics. &his process leads to the evolution of

populations of individuals that are better suited to their environment than the individuals from %hich the" %ere

created$ 'ust as in natural adaptation.

GAs have been sho%n to be an effective strateg" in the offline design of control s"stems b" a number of

practitioners. For e#ample$ rishna*umar and Goldberg +! and ,ramlette and Cusin -! have demonstrated ho%

genetic optimization methods can be used to derive superior controller structures in aerospace applications in less

time (in terms of function evaluations) than traditional methods such as /0 and Po%ells gain set design. Porter and

2ohamed 3! have presented schemes for the genetic design of multivariable .ight control s"stems using

eigenstructure assignment$ %hilst others have demonstrated ho% GAs can be used in the selection of controllerstructures 4!.

2. The MATLABGA Toolbox

5hilst there e#ist man" good publicdomain genetic algorithm pac*ages$ such as G676898:! and G67;&


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ranking


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Selection #unctions! reins$ rws$ select$ sus

&hese functions select a given number of individuals from the current population$ according to

their fitness$ and return a column vector to their indices. Currentl" available routines are roulette

%heel selection !$ rws$ and stochastic universal sampling 11!$ sus. A highlevel entr"

function$ select$ is also provided as a convenient interface to the selection routines$ particularl"%here multiple populations are used. ;n cases %here a generation gap is reDuired$ i.e. %here the

entire population is not reproduced in each generation$ reins can be used to effect uniformrandom or fitnessbased reinsertion !.$rosso%er oerators! recdis$ recint$ reclin$ recmut$ recombin$ xovdp$ xovdprs$xovmp$ xovsh$ xovshrs$ xovsp$ xovsprs

&he crossover routines recombine pairs of individuals %ith given probabilit" to produce offspring.

8inglepoint$ doublepoint 1+! and shuffle crossover 1-! are implemented in the routines

xovsp$ xovdp and xovsh respectivel". 0educed surrogate 1-! crossover is supported %ithboth single$ xovsprs$ and doublepoint$ xovdprs$ crossover and %ith shuffle$ xovshrs. Ageneral multipoint crossover routine$ xovmp$ that supports uniform crossover 13! is also

provided. &o support realvalued chromosome representations$ discrete$ intermediate and line

recombination are supplied in the routines$ recdis$ recint and reclin respectivel" 14!. &heroutine recmut performs line recombination %ith mutation features 14!. A highlevel entr"function to all the crossover operators supporting multiple subpopulations is provided b" the

function recombin.

Mutation oerators! mut$ mutate$mutbga,inar" and integer mutation are performed b" the routine mut. 0ealvalue mutation is availableusing the breeder GA mutation function 14!$ mutbga. Again$ a highlevel entr" function$mutate$ to the mutation operators is provided.Multile suboulation suort! migrate

&he GA &oolbo# provides support for multiple subpopulations through the use of highlevel

genetic operator functions and a function for e#changing individuals amongst subpopulations$

migrate. A single population is divided into a number of subpopulations b" modif"ing the datastructures used b" the &oolbo# routines such that subpopulations are stored in contiguous bloc*s

%ithin each data element. &he highlevel routines$ such as select and reins$ operateindependentl" on each subpopulation contained in a data structure allo%ing each subpopulation toevolve in isolation from the others. ,ased on theIslandorMigrationmodel 1:!$ migrateallo%sindividuals to be transferred bet%een subpopulations. Bni and bidirectional ring topologies as

%ell as a full" interconnected net%or* are selectable via option settings as %ell as fitnessbased

and uniform selection and reinsertion strategies.

2.& A Simle GA in MATLAB

Fig.1 sho%s the 2A&A, code for a 8imple GA. &he first fe% lines of the code set the

parameters that the GA uses$ such as the number and length of the chromosomes$ the crossover

and mutation rates$ the number of generations and$ in this case$ the binar" representation scheme.

7e#t$ an initial uniforml" distributed random binar" population$ Chrom$ is created using the GA&oolbo# function crtbp. &he ob'ective function$ objfun$ is then evaluated to produce the vectorof ob'ective values$ ObjV. 7ote that as %e do not need the phenot"pic representation inside the

GA$ the binar" strings are converted to real values %ithin the ob'ective function call.&he initialisation complete$ the GA no% enters the generational loop. First$ a fitness vector$ FitnV$is determined using the ran*ing scheme of ,a*er 11!. isualisation and preference articulation

can be incorporated into the generational loop b" the addition of e#tra functions. ;n this e#ample$

the routine plotgraphicsdispla"s the performance of the current best controller allo%ing theuser to asses the state of the search. ;ndividuals are then selected from the population using the

stochastic universal sampling algorithm$ sus$ %ith a generation gap$ GGA !"#$. &he -: (GGA % &'&() selected individuals are then recombined using singlepointcrossover$ xovsp$ applied %ith probabilit" )OV ! "#*. ,inar" mutation$ mut$ is then appliedto the offspring %ith probabilit" +,-. ! "#"/*0$ and the ob'ective function values for the ne%individuals$ ObjV1el$ calculated. Finall"$ the ne% individuals are reinserted in the population$using the &oolbo# function reins$ and the generation counter$ gen$ incremented.&he GA terminates after +A)G& iterations around the generational loop. &he current

population$ its phenot"pic representation and associated cost function values remain in the users

%or*space and ma" be anal"sed directl" using 2A&A, commands.


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3'&( ! /04 5 3ength of individual vars


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#


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&VA. ! 24 5 &o# of decision variable


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s


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&'&( ! 6"4 5 &o# of individual


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s


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GGA ! "#$4 5 Generation ga


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p


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)OV ! "#*4 5 Crossover rat


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e


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+,-. ! "#"/*04 5 +utation rat


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e


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+A)G& ! 7"4 5 &o# of generation


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s


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including

H parametric

optimization

H multiob'ective optimization

H controller structure

selection

H nonlinear s"stem

identi.cationH mi#edmode

modelling

H neural net%or* design

H realtime and

adaptive control

H parallel genetic algorithms

H fault identi.cation H antenna design 5 8inar9 representation scheme Field( !:3'&( 3'&(4 / /4 /""" /"""4 / /4 " "4 " "4 " ";4 5 'nitialisepopulation Chrom ! crtbp&VA.?4 5 Create binar9population ObjV ! objfun


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for ver" different genot"pes to result in nondominated individuals$ a particular problem is the production of


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lethals


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%hen


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t members of the population are mated. &he search then becomes inef


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cient and the GA is li*el" to converge to some suboptimal solution. ;n general$ a combination of mating restriction$

niche formation and redundant coding ma" be appropriate.


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1=!

C. 2. Fonseca and P. J. Fleming$ IGenetic Algorithms for 2ultiple $ 1>.

3! ,. Porter and 8. 8. 2ohamed$ IGenetic ?esign of 2ultivariable FlightControl 8"stems Bsing 6igenstructure

Assignment$Proc. I&&& Conf. Aerospace Control Sste!s$ 1-.

4! A. arse*$ &. Brbacic and ,. Filipic$ IGenetic Algorithms in Controller ?esign and &uning$ I&&& 'rans. Ss.

Man and Cber.$ ol. +-$ 7o. 4$ pp1--1--$ 1-.

:! J. J. Grefenstette$ IA Bsers Guide to G6768;8ersion 4.$ &echnical 0eport$ 7av" Centre for Applied 0esearch

in Artificial ;ntelligence$ 5ashington ?.C.$ B8A$ 1.

=! ?. 5hitle"$ I&he G67;&.

1! J. 6. ,a*er J$ IAdaptive 8election 2ethods for Genetic Algorithms$Proc. ICGA *$ pp. 11111$ 1>4.

11! J. 6. ,a*er$ I0educing bias and inefficienc" in the selection algorithm$Proc. ICGA +$ pp. 13+1$ 1>=.

1+! . ,oo*er$ I;mproving search in genetic algorithms$ ;n Genetic Algorith!s and Si!ulated Annealing$ . ?avis

(6d.)$ pp :1=-$ 2organ aufmann Publishers$ 1>=.

1-! 0. A. Caruana$ . A. 6shelman and J. ?. 8chaffer$ I0epresentation and hidden bias ;; 6liminating defining

length bias in genetic search via shuffle crossover$ ;n &leventh Int. "oint Conf. on AI$ 8ridharan 7. 8. (6d.)$ ol. 1$

pp =4=44$ 2organ aufmann$ 1>.

13! G. 8"s%erda$ IBniform crossover in genetic algorithms$Proc. ICGA %$ pp. +$ 1>.

14! K. 2Lhlenbein and ?. 8chlier*ampoosen$ IPredictive 2odels for the ,reeder Genetic Algorithm$

&volutionar Co!putation$ ol. 1$ 7o. 1$ pp. +43$ 1-.

1:! C. ,. Pett"$ 2. 0. euze. and J. J. Grefenstette$ IA Parallel Genetic Algorithm$ Proc. ICGA +$ pp. 1441:1$

1>=.

the matlab genetic algorithm toolbox

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