Genetic Algorithms (GA) Presentation

8/8/2019 Genetic Algorithms (GA) Presentation

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Genetic Algorithms (GA)Genetic Algorithms (GA)

Genetic Algorithms are good at taking large, potentially huge search spaces and navigating them, looking for optimal combinations of

things, solutions you might not otherwise find in a lifetime.


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Introduction

Computing pioneers (especially in AI) lookedto natural systems as guiding metaphorsEvolutionary computation

Any biologically-motivated computing activitysimulating natural evolution

Genetic Algorithms are one form of thisactivity

Directed search algorithms based on the mechanicsof biological evolution

Original goalsFormal study of the phenomenon of adaptation

John HollandAn optimization tool for engineering problems


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Provide efficient, effectivetechniques for optimization and

machine learning applicationsWidely-used today in business,scientific and engineering circles

Introduction (cont..)


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Classes of Search Techniques

Finonacci Newton

Direct etho

s In

irect etho

s

Calculus-base t

echniques

Evolutionary strate

ies

Centralized Distributed

Parallel

Steady-state Generational

Sequential

Genetic algorithms

Evolutionary algorithms Si

ulate annealin

Guidedrandomsearchtechniques

Dyna

ic pro

ra

in

Enu

erativetechniques

Searchtechniques


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Wh e olution as a meta hor

o Ability to efficiently guide a search througha large solution spaceAbility to adapt solutions to changingenvironments

Emergent behavior is the goal The hoped-for emergent behavior isthe design of high-quality solutions todifficult problems and the ability toadapt these solutions in the face of achanging environment

Melanie Mitchell, An Introduction to GeneticAlgorithms


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Ev olutionar terminolog

Abstractions imported from biologyChromosomes, Genes, AllelesFitness, SelectionCrossover, Mutation


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Com onents of a GA

Encoding technique ( gene, chromosome )Initialization procedure ( creation)Evaluation function ( environment)Selection of parents ( reproduction)Genetic operators ( mutation, recombination)Parameter settings ( practice and art)( Parameters that affect GA are initial population, size of the

population, selection process and fitness function)


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GA terminolog

GA chromosomes are strings of genesEach gene has a number of alleles; i.e.,settings

Each chromosome is an encoding of asolution to a problem

A population of such chromosomes isoperated on by a GA


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Encoding

A data structure for representing candidatesolutions

Often takes the form of a bit string

Usually has internal structure; i.e., differentparts of the string represent differentaspects of the solution)


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Crosso ver

Mimics biological recombinationSome portion of genetic material is swappedbetween chromosomes

Typically the swapping produces an offspring

Mechanism for the dissemination of building blocks (schemas)


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Mutation

Selects a random locus gene location with some probability and alters the alleleat that locus

The intuitive mechanism for thepreservation of variety in the population


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A Sim le GA

Generate initial population

doCalculate the fitness of each member

// simulate another generationdo

Select parents from current populationPerform crossover add offspring to the

new population while new population is not full

Merge new population into the current population

Mutate current population

while not converged


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Ho do GAs ork

The structure of a GA is relatively simpleto comprehend, but the dynamic behavioris complex

GAs work by discovering, emphasizing,and recombining good building blocks of solutions in a highly parallel fashion. Using formalism

Notion of a building block is formalized as aschemaSchemas are propagated or destroyedaccording to the laws of probability


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Schema

A template, much like a regularexpression, describing a set of stringsThe set of strings represented by a givenschema, characterizes a set of candidatesolutions sharing a propertyThis property is the encoded equivalent of a building block


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Ex am le

0 or 1 represents a fixed bit

Asterisk represents a dont care

11**** 00 is the set of all solutionsencoded in 8 bits, beginning with two onesand ending with two zeros

Solutions in this set all share the samevariants of the properties encoded at theseloci


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Schema qualifiers

LengthThe inclusive distance between the two bitsin a schema which are furthest apart

(the defining length of the previous example is 8)

OrderThe number of fixed bits in a schema

(the order of the previous example is 4)


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Not just sum of the arts

GAs explicitly evaluate and operate onwhole solutions

GAs implicitly evaluate and operate onbuilding blocks

Existing schemas may be destroyed orweakened by crossover

New schemas may be spliced together fromexisting schema


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Wh do the ork

Schemas can be destroyed or conserved

So how are good schemas propagatedthrough generations?

Conserved good schemas confer higherfitness on the offspring inheriting them

Fitter offspring are probabilistically morelikely to be chosen to reproduce


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A ro ximating schema d namics

Let H be a schema with at least one instancepresent in the population at time tLet m(H, t) be the number of instances of H at

time tLet x be an instance of H and f(x) be its fitnessThe expected number of offspring of x isf(x)/f(pop) (by fitness proportionate selection)

To know E(m(H, t +1)) (the expected numberof instances of schema H at the next timeunit), sum f(x)/f(pop) for all x in H

GA never explicitly calculates the averagefitness of a schema, but schema

proliferation depends on its value


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A ro ximating schema d namics

Approximation can be refined by takinginto account the operators

Schemas of long defining length are lesslikely to survive crossover

Offspring are less likely to be instances of such schemas

Schemas of higher order are less likely tosurvive mutation


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Im lications

Instances of short, low-order schemas whoseaverage fitness tends to stay above the meanwill increase exponentially

Changing the semantics of the operators canchange the selective pressures towarddifferent types of schemas

Lemmas t t e ema T eo r emSelection focuses the searchCrossover combines good schemasMutation is the insurance policy


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Sim le Genetic Algorithm{

initialize population;evaluate population;while TerminationCriteriaNotSatisfied{

select parents for reproduction;perform recombination and mutation;

evaluate population;}}


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The GA Cy cle of Re roduction

re roduction

o ulation e valuation

modification

discard

deleted

members

parents

children

modified

children

evaluated children


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P o ulation

Chromosomes could be:Bit strings ( 0 1 0 1 ... 11 00 )Real numbers (43.2 -33.1 ... 0 .0 89.2)Permutations of element (E11 E3 E7 ... E1 E15)Lists of rules (R1 R2 R3 ... R22 R23)Program elements (genetic programming)

... any data structure ...

population


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Re p roduction

re production

population

parents

children

P arents are selected at random ithselection chances iased in relation tochromosome e valuations.


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Chromosome Modification

modificationchildren

Modifications are stochastically triggeredOperator types are:

MutationCrossover (recombination)

modified children


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Mutation: Local Modification

Before: (1 0 1 1 0 1 1 0)

After: (0 1 1 0 0 1 1 0)

Before: (1.38 -69.4 326.44 0.1)

After: (1.38 -67.5 326.44 0.1)

Causes movement in the search space(local or global)Restores lost information to the population


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Crosso ver: Recom ination

P1 ( 0 1 1 0 1 0 0 0 ) ( 0 1 0 0 1 0 0 0 ) C1P2 (1 1 0 1 1 0 1 0 ) (1 1 1 1 1 0 1 0 ) C2

Crossover is a critical feature of geneticalgorithms:

It greatly accelerates search early inevolution of a populationIt leads to effective combination of schemata (sub solutions on differentchromosomes)

*


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Ev aluation

The evaluator decodes a chromosome and

assigns it a fitness measureThe evaluator is the only link between aclassical GA and the problem it is solving

e valuation

evaluated children

modified children


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Deletion

Generational GA:entire populations replaced with eachiterationS teady-state GA:a few members replaced each generation

population

discard

discarded members


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Generational GA

All parents reproduce at the same timeOffspring generation replaces parentgeneration

:: :

Current OffspringParent (temporary)


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P opu la tion In itia liz a tion

Start ith a population of randoml y generated indi viduals, or use

- A p re viousl y sa ved population- A set of solutions p rovided y a human e xpert- A set of solutions p rovided y

another heuristic algorithm


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P a r en t e lec tion

Selection is a procedure of picking parent chromosome toproduce off-spring.Types of selection:

Random Selection Parents are selected randomly from thepopulation.Proportional Selection probabilities for picking eachchromosome is calculated

Rank Based Selection This method uses ranks instead of absolute fitness values.

o Purpose : to focus the search in promising regions of thespaceInspiration : Darwins survival of the fittest Trade-off between exploration and exploitation of the searchspace


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Ho to select these chromosomes

o Selection Methodso Fitness Proportionate Selection

o Roulette wheel selectiono Rank selection

o Steady state selectiono Tournament selectiono Others..


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F itness P roportionate Selection

A simple selection method is each individual,i , has the probabilityFitness ( i) / sum_over_all_individuals_j Fitness ( j)

where Fitness ( i) is the fitness function valuefor individual i .


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Roulette Wheel SelectionRoulette Wheel Selection

Chromosome Fitness % of total

1 6.82 31

2 1.11 5

3 8.48 38

4 2.57 12

5 3.08 14

Total 22.0 100

Imagine a roulette wheel where are placed allchromosomes in the population, every has its place bigaccordingly to its fitness function, like on the followingpicture.


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Roulette Wheel SelectionRoulette Wheel Selection ( cont..)( cont..)Let i = 1, where i denotes chromosome index;Calculate P( x i) using proportional selection;

Calculate sum of all chromosome fitness in population -sum S .Generate random number from interval (0, S) - r .

sum = P( x i);wh i le sum < r d o

i = i + 1; i.e. next chromosomesum = sum + P( x i);

en d

returnx

i as one of the selected parent;repeat unt i l all parents are selected

D rawback:If the best chromosome fitness is 9 0% of all the roulette

wheel then the other chromosomes will have very few

chances to be selected


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Rank SelectionRank Selection

Rank selection first ranks the population and thenevery chromosome receives fitness from thisranking. The worst will have fitness 1 , second worst2 etc. and the best will have fitness N (number of

chromosomes in population).

S ituation before ranking ( graph of fitnesses)


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Rank SelectionRank Selection ( cont..)( cont..)

S ituation after ranking ( graph of order numbers)

D rawback:This method can lead to slower convergence, because the best

chromosomes do not differ so much from other ones.


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S tea dy-S tate S elect i on

Main idea of this selection is that big part of chromosomes should survive to nextgeneration.

GA then works in a following way.In every generation are selected a few

(good - with high fitness) chromosomes forcreating a new offspring. Then some (bad -with low fitness) chromosomes areremoved and the new offspring is placed intheir place. The rest of population survivesto new generation.


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T ournament S elect i on

Binary tournamentTwo individuals are randomly chosen; thefitter of the two is selected as a parent

Probabilistic binary tournamentTwo individuals are randomly chosen; with achance p , 0 .5 < p < 1, the fitter of the two isselected as a parent

Larger tournamentsn individuals are randomly chosen; thefittest one is selected as a parent

By changing n and/or p , the GA can beadjusted dynamically


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Re p roduction

Reproduction operatorsCrossoverMutation

CrossoverTwo parents produce two offspringThere is a chance that the chromosomes of the twoparents are copied unmodified as offspringThere is a chance that the chromosomes of the twoparents are randomly recombined (crossover) to form

offspringGenerally the chance of crossover is between 0 .6 and1. 0

MutationThere is a chance that a gene of a child is changedrandomlyGenerally the chance of mutation is low (e.g. 0 .00 1)


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Crosso ver

Performed on two chromosomes asparentsThe probability of parents being crossed

over is given by crossover rateCrossover points are randomly selectedExchanges genetic code between parentsto create two new chromosomes asoffspringCommonly used crossover

One-point crossoverTwo-point crossoverUniform crossover


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One- P oint Crosso ver

Only one crossover point is selectedfor each parent

11011100

01100110

110 00110

011 11100Parent 1:

Parent 2:

Offspring 1

Offspring 2

Crossover point


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One- P oint Crosso ver

AdvantagesSimple to implement

Little disruption on evolved schemasWeakness

Cannot combine many schemas

1 * * * 1 1

* 0 0 * * *1 0 0 * 1 1


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T o- P oint Crosso ver

Two crossover points are selectedfor each parent

11011100

01100110

Parent 1

Parent 2

110 00 100

011 11 110

Offspring 1

Offspring 2

Crossover Points


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T o- P oint Crosso ver

AdvantageMore likely to combine schemas(downside: more likely to disruptexisting schemas)

1 * * * 1 1

* 0 0 * * *

1 0 0 * 1 1


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Uniform Crosso ver

Every gene can be swapped betweenthe parents independent of the other

genesThe probability of swapping genes isfixed at P0No need to select crossover points

11011100

01100110

Parent 1

Parent 2

1 1 0 0 11 10

0 1 1 1 01 00

Offspring 1

Offspring 2


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Distri ution Bias

The number of genes to be swapped may bedistributed around a particular value instead of uniformly from 1 to L-1 ( L = individual length)

One-point crossover has no distribution biasCrossover point is selected randomly within thechromosome

Uniform crossover has high distribution biasThe number of genes to be swapped depends on

P0


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Mutation

Involves only one chromosomeApplies to each gene individuallyThe value of a mutated gene is flipped

The probability of a gene being mutatedis controlled by mutation rate M

The mutation rate per chromosome = M * LLow mutation rate: low exploration powerHigh mutation rate: too disruptive

11011 1 00 11011 0 00


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Imp lementation Variations

Varying rates of Crossover/MutationStart with low mutation rate and increase afterwardsStart with high crossover rate and decrease afterwards

Adaptive crossover and mutation ratesAdjust rates under certain conditions

Problem dependent variationsRandom crossover for variable length GAs

Crossover points can be selected separately forparentsCreates offspring with different lengths from theirparents

Parent 1

Parent 2

Offspring 1

Offspring 2


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Other Genetic Operators

Inversion

4 1 2 3 0 5

2 1 4 3 0 5

Transposition

4 1 2 3 0 5

3 0 5 4 1 2


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A Sim p le Exam p le

The Traveling Salesman Problem:

Find a tour of a given set of cities sothat

each city is visited only once

the total distance traveled is minimized


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Re p resentation

Representation is an ordered list of citynumbers known as an order-based GA.

2) London 3) Dunedin 5) Beijing4) Singapore 6) Phoenix

City List1 (3 5 2 6 4)

City List2 (2 5 6 3 4)


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Initial P opulation for TS P

(5,3,4,6,2) (2,4,6,3,5) (4,3,6,5,2)

(2,3,4,6,5) (4,3,6,2,5) (3,4,5,2,6)

(3,5,4,6,2) (4,5,3,6,2) (5,4,2,3,6)

(4,6,3,2,5) (3,4,2,6,5) (3,6,5,2,4)


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Create Off-Sp ring 1 point

(5,3,4,6,2) (2,4,6,3,5) (4,3,6,5,2)

(2,3,4,6,5) (4,3,6,2,5) (3,4,5,2,6)

(3,5,4,6,2) (4,5,3,6,2) (5,4,2,3,6)

(4,6,3,2,5) (3,4,2,6,5) (3,6,5,2,4)

(3,4,5,6,2)


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(3,4,5,6,2)

Create More Offsp ring

(5,3,4,6,2) (2,4,6,3,5) (4,3,6,5,2)

(2,3,4,6,5) (4,3,6,2,5) (3,4,5,2,6)

(3,5,4,6,2) (4,5,3,6,2) (5,4,2,3,6)

(4,6,3,2,5) (3,4,2,6,5) (3,6,5,2,4)

(5,4,2,6,3)


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(3,4,5,6,2) (5,4,2,6,3)

Mutate

(5,3,4,6,2) (2,4,6,3,5) (4,3,6,5,2)

(2,3,4,6,5) (4,3,6,2,5) (3,4,5,2,6)

(3,5,4,6,2) (4,5,3,6,2) (5,4,2,3,6)

(4,6,3,2,5) (3,4,2,6,5) (3,6,5,2,4)


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Mutate

(5,3,4,6,2) (2,4,6,3,5) (4,3,6,5,2)

(2,3,4,6,5) (2,3,6, 4,5) (3,4,5,2,6)

(3,5,4,6,2) (4,5,3,6,2) (5,4,2,3,6)

(4,6,3,2,5) (3,4,2,6,5) (3,6,5,2,4)

(3,4,5,6,2) (5,4,2,6,3)


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Eliminate

(5,3,4,6,2) (2,4,6,3,5) (4,3,6,5,2)

(2,3,4,6,5) (2,3,6, 4,5) (3,4,5,2,6)

(3,5,4,6,2) (4,5,3,6,2) (5,4,2,3,6)

(4,6,3,2,5) (3,4,2,6,5) (3,6,5,2,4)

Tend to kill off the worst ones.

(3,4,5,6,2) (5,4,2,6,3)


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Integrate

(5,3,4,6,2) (2,4,6,3,5)

(2,3,6, 4,5) (3,4,5,2,6)

(3,5,4,6,2) (4,5,3,6,2) (5,4,2,3,6)

(4,6,3,2,5) (3,4,2,6,5) (3,6,5,2,4)

(3,4,5,6,2)

(5,4,2,6,3)


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Restart

(5,3,4,6,2) (2,4,6,3,5)

(2,3,6,4,5) (3,4,5,2,6)

(3,5,4,6,2) (4,5,3,6,2) (5,4,2,3,6)

(4,6,3,2,5) (3,4,2,6,5) (3,6,5,2,4)

(3,4,5,6,2)

(5,4,2,6,3)


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B enef i ts of Genet i c Algor i thms

Concept is easy to understandModular, separate from applicationSupports multi-objective optimization

Good for noisy environmentsAlways an answer; answer gets better withtimeInherently parallel; easily distributed

Many ways to speed up and improve a GA-based application as knowledge aboutproblem domain is gainedEasy to exploit previous or alternate

solutions


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When to Use a GA

Alternate solutions are too slow or overlycomplicatedNeed an exploratory tool to examine new

approachesProblem is similar to one that has already beensuccessfully solved by using a GAWant to hybridize with an existing solutionBenefits of the GA technology meet keyproblem requirements


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S ome A App lica tion T pes

Doma in App lica tion T pes

Con tr o l gas p ipeline pole alancing missile e vasion pu sui

Des i n semiconduc o la you ai c a design ke yboa dcon igu a ion communica ion ne o ks

S chedu ling manu ac u ing acili y scheduling r esou rce allo ca ion

Robo tics r aje ctory p lanning

Mach ine Lea r n ing designing neu r al ne twor ks imp r oving classi i ca tionalgo r ithms classi ie r s ys tems

S igna l Pr ocess ing ilte r design

Game Pl ay ing poke r, c he cke r s , p r isone rs dilemma

Comb ina to ria lOp tim iza tion

se t c ove r ing , tr a velling salesman , r ou ting , b in pa cking ,gr a ph colou r ing and pa rtitioning


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Gene tic Al o rit hms

FactsVery robust but slowIn the limit, optimal

Genetic Algorithms (GA) Presentation

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