introduction to genetic algorithms

Introduction toIntroduction toGenetic AlgorithmsGenetic Algorithms

Speaker:Speaker:

Moch. Rif’anMoch. Rif’an

[email protected]@ub.ac.id

What are genetic What are genetic algorithms?algorithms?

Genetic algorithms (GAs) is a search technique used in computing to find exact or approximate solutions to optimization and search problems.

Genetic algorithms are categorized as global search heuristics.

Genetic algorithms are a particular class of evolutionary algorithms (also known as evolutionary computation) that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover (also called recombination).

A short history of genetic A short history of genetic algorithmsalgorithms19541954 - computer simulations of evolution started by the - computer simulations of evolution started by the

work of work of Nils Aall BarricelliNils Aall Barricelli1960s 1960s -- Hans Bremermann Hans Bremermann published a series of papers published a series of papers

that adopted a population of solution to that adopted a population of solution to optimization problems optimization problems

1963 1963 - - BarricelliBarricelli had simulated the evolution of ability had simulated the evolution of ability to to play a simple gameplay a simple game

1970s 1970s - artificial evolution became a widely recognized - artificial evolution became a widely recognized optimization method optimization method

19701970 - the first books that described the used methods - the first books that described the used methods ((Fraser and BurnellFraser and Burnell))

1980s 1980s - The - The First International ConferenceFirst International Conference on Genetic on Genetic Algorithms, Pennsylvania; General Electric started Algorithms, Pennsylvania; General Electric started selling the world's first genetic algorithm product selling the world's first genetic algorithm product

1989 1989 - - Axcelis, Inc.Axcelis, Inc. released Evolver, the world's second released Evolver, the world's second GA product and the first for desktop computers GA product and the first for desktop computers

Genetic Algorithms - HistoryGenetic Algorithms - History

Pioneered by John Holland in the Pioneered by John Holland in the 1970’s1970’s

Got popular in the late 1980’sGot popular in the late 1980’s Based on ideas from Darwinian Based on ideas from Darwinian

EvolutionEvolution Can be used to solve a variety of Can be used to solve a variety of

problems that are not easy to solve problems that are not easy to solve using other techniquesusing other techniques

Biological Background (1) – The cell

• Every animal cell is a complex of many small “factories” working together

• The center of this all is the cell nucleus

• The nucleus contains the genetic information

Biological Background (2) – Chromosomes

• Genetic information is stored in the chromosomes

• Each chromosome is build of DNA

• Chromosomes in humans form pairs

• There are 23 pairs

• The chromosome is divided in parts: genes

• Genes code for properties

• The posibilities of the genesforone property is called: allele

• Every gene has an unique positionon the chromosome: locus

Biological Background (3) – Genetics

• The entire combination of genes is called genotype

• A genotype develops to a phenotype

• Alleles can be either dominant or recessive

• Dominant alleles will always express from the genotype to the fenotype

• Recessive alleles can survive in the population for many generations, without being expressed.

Biological Background (4) – Reproduction

• Reproduction of genetical information• Mitosis

• Meiosis

• Mitosis is copying the same genetic information to new

offspring: there is no exchange of

information

• Mitosis is the normal way ofgrowing of multicell structures,

like organs.


• Meiosis is the basis of sexual reproduction

• After meiotic division 2 gametesappear in the process

• In reproduction two gametesconjugate to a zygote wich

will become the new individual

• Hence genetic information is sharedbetween the parents in order to

create new offspring


• During reproduction “errors” occur

• Due to these “errors” genetic variation exists

• Most important “errors” are:

• Recombination (cross-over)

• Mutation

Biological Background (7) – Natural selection

• The origin of species: “Preservation of favourablevariations and rejection of unfavourable

variations.”

• There are more individuals born than can survive, so there is a continuous struggle for life.

• Individuals with an advantage have a greater chance for survive: survival of the fittest.

Biological Background (8) – Natural selection

• Important aspects in natural selection are:

• adaptation to the environment

• isolation of populations in different groups which cannot mutually mate

• If small changes in the genotypes of individuals are expressed easily, especially in small populations, we speak of genetic drift

• Mathematical expresses as fitness: success in life

How GA are Different than How GA are Different than Traditional Search MethodsTraditional Search Methods

GAs work with a coding of the parameter GAs work with a coding of the parameter set, not the parameters themselves.set, not the parameters themselves.

GAs search from a population of points, GAs search from a population of points, not a single point.not a single point.

GAs use payoff information, not GAs use payoff information, not derivatives or auxiliary knowldege.derivatives or auxiliary knowldege.

GAs use probablistic transition rules, not GAs use probablistic transition rules, not deterministic rules.deterministic rules.

Evolution in the real worldEvolution in the real world Each cell of a living thing contains Each cell of a living thing contains chromosomeschromosomes - -

strings of strings of DNADNA Each chromosome contains a set of Each chromosome contains a set of genesgenes - blocks of DNA - blocks of DNA Each gene determines some aspect of the organism (like Each gene determines some aspect of the organism (like

eye colour)eye colour) A collection of genes is sometimes called a A collection of genes is sometimes called a genotypegenotype A collection of aspects (like eye colour) is sometimes A collection of aspects (like eye colour) is sometimes

called a called a phenotypephenotype Reproduction involves recombination of genes from Reproduction involves recombination of genes from

parents and then small amounts of parents and then small amounts of mutationmutation (errors) in (errors) in copying copying

The The fitnessfitness of an organism is how much it can reproduce of an organism is how much it can reproduce before it diesbefore it dies

Evolution based on “survival of the fittest”Evolution based on “survival of the fittest”

Start with a Dream…Start with a Dream…

Suppose you have a problemSuppose you have a problem You don’t know how to solve itYou don’t know how to solve it What can you do?What can you do? Can you use a computer to somehow Can you use a computer to somehow

find a solution for you?find a solution for you? This would be nice! Can it be done?This would be nice! Can it be done?

A dumb solutionA dumb solution

A “blind generate and test” algorithm:A “blind generate and test” algorithm:

RepeatRepeatGenerate a random possible solutionGenerate a random possible solution

Test the solution and see how good it isTest the solution and see how good it is

Until solution is good enoughUntil solution is good enough

Can we use this dumb idea?Can we use this dumb idea?

Sometimes - yes:Sometimes - yes: if there are only a few possible solutionsif there are only a few possible solutions and you have enough timeand you have enough time then such a method then such a method couldcould be used be used

For most problems - no:For most problems - no: many possible solutionsmany possible solutions with no time to try them allwith no time to try them all so this method so this method can notcan not be used be used

A “less-dumb” idea (GA)A “less-dumb” idea (GA)

Generate a Generate a setset of random solutions of random solutions

RepeatRepeatTest each solution in the set (rank them)Test each solution in the set (rank them)

Remove some bad solutions from setRemove some bad solutions from set

Duplicate some good solutions Duplicate some good solutions

make small changes to some of themmake small changes to some of them

Until best solution is good enoughUntil best solution is good enough

Silly Example - Drilling for Silly Example - Drilling for OilOil

Imagine you had to drill for oil somewhere Imagine you had to drill for oil somewhere along a single 1km desert roadalong a single 1km desert road

Problem: choose the best place on the Problem: choose the best place on the road that produces the most oil per dayroad that produces the most oil per day

We could represent each solution as a We could represent each solution as a position on the roadposition on the road

Say, a whole number between [0..1000]Say, a whole number between [0..1000]

Where to drill for oil?Where to drill for oil?

0 500 1000

Road

Solution2 = 900Solution1 = 300

Digging for OilDigging for Oil

The set of all possible solutions [0..1000] The set of all possible solutions [0..1000] is called the is called the search spacesearch space or or state spacestate space

In this case it’s just one number but it In this case it’s just one number but it could be many numbers or symbolscould be many numbers or symbols

Often GA’s code numbers in binary Often GA’s code numbers in binary producing a bitstring representing a producing a bitstring representing a solutionsolution

In our example we choose 10 bits which In our example we choose 10 bits which is enough to represent 0..1000is enough to represent 0..1000

Drilling for OilDrilling for Oil

0 1000

Road

Solution2 = 900 (1110000100)

Solution1 = 300 (0100101100)

O I

L

Location

305

Classes of Search TechniquesClasses of Search TechniquesSearch Techniqes

Calculus Base Techniqes

Guided random search techniqes

Enumerative Techniqes

BFSDFS Dynamic Programming

Tabu Search Hill Climbing

Simulated Anealing

Evolutionary Algorithms

Genetic Programming

Genetic Algorithms

Fibonacci Sort

Search SpaceSearch Space

For a simple function f(x) the search space is For a simple function f(x) the search space is one dimensional.one dimensional.

But by encoding several values into the But by encoding several values into the chromosome many dimensions can be chromosome many dimensions can be searched e.g. two dimensions f(x,y)searched e.g. two dimensions f(x,y)

Search space can be visualised as a surface Search space can be visualised as a surface or or fitness landscapefitness landscape in which fitness dictates in which fitness dictates heightheight

Each possible genotype is a point in the Each possible genotype is a point in the spacespace

A GA tries to move the points to better places A GA tries to move the points to better places (higher fitness) in the space(higher fitness) in the space

Fitness landscapesFitness landscapes

Search SpaceSearch Space

Obviously, the nature of the search Obviously, the nature of the search space dictates how a GA will performspace dictates how a GA will perform

A completely random space would A completely random space would be bad for a GAbe bad for a GA

Also GA’s can get stuck in local Also GA’s can get stuck in local maxima if search spaces contain lots maxima if search spaces contain lots of theseof these

Generally, spaces in which small Generally, spaces in which small improvements get closer to the improvements get closer to the global optimum are goodglobal optimum are good

GA AlgorithmGenerate a set of random solutions

RepeatTest each solution in the set (rank them)

Remove some bad solutions from set

Duplicate some good solutions

make small changes to some of them

Until best solution is good enough

The Evolutionary CycleThe Evolutionary Cycle

selection

population evaluation

modification

discard

deleted members

parents

modifiedoffspring

evaluated offspring

initiate & evaluate

A genetic algorithm maintains aA genetic algorithm maintains a population of candidate solutionspopulation of candidate solutions for for thethe problemproblem at hand,at hand,and makes it evolve byand makes it evolve byiteratively applyingiteratively applyinga set of stochastic operatorsa set of stochastic operators

VocabularyVocabulary

Gene – An single encoding of part of Gene – An single encoding of part of the solution space.the solution space.

Chromosome – A string of “Genes” Chromosome – A string of “Genes” that represents a solution.that represents a solution.

Population - The number of Population - The number of “Chromosomes” available to test.“Chromosomes” available to test.

Adding Sex - CrossoverAdding Sex - Crossover

Although it may work for simple search Although it may work for simple search spaces our algorithm is still very spaces our algorithm is still very simplesimple

It relies on random mutation to find a It relies on random mutation to find a good solutiongood solution

It has been found that by introducing It has been found that by introducing “sex” into the algorithm better results “sex” into the algorithm better results are obtainedare obtained

This is done by selecting two parents This is done by selecting two parents during reproduction and combining during reproduction and combining their genes to produce offspringtheir genes to produce offspring

Adding Sex - CrossoverAdding Sex - Crossover

Two high scoring “parent” bit Two high scoring “parent” bit strings (strings (chromosomes)chromosomes) are selected are selected and with some probability and with some probability (crossover rate) combined(crossover rate) combined

Producing two new Producing two new offspring offspring (bit (bit strings)strings)

Each offspring may then be Each offspring may then be changed randomly (changed randomly (mutationmutation))

MethodologyMethodology

Genetic algorithms are Genetic algorithms are implemented as a computer simulation implemented as a computer simulation in which a population of abstract in which a population of abstract representations (called chromosomes representations (called chromosomes or the genotype or the genome) of or the genotype or the genome) of candidate solutions (called individuals, candidate solutions (called individuals, creatures, or phenotypes) to an creatures, or phenotypes) to an optimization problem evolves toward optimization problem evolves toward better solutions. better solutions.

A typical genetic algorithm requires two things to be defined:

A genetic representation of the solution domain A fitness function to evaluate the solution domain

A standard representation of the solution is as an array of bits. Arrays of other types and structures can be used in essentially the same way.

The fitness function is defined over the genetic representation and measures the quality of the represented solution.

InitializationInitialization

Initially many individual Initially many individual solutions are randomly generated to solutions are randomly generated to form an initial population. The form an initial population. The population size depends on the population size depends on the nature of the problem (hundreds or nature of the problem (hundreds or thousands of possible solutions ). thousands of possible solutions ). Traditionally, the population is Traditionally, the population is generated randomly, covering the generated randomly, covering the entire range of possible solutions. entire range of possible solutions.

Selecting ParentsSelecting Parents

Many schemes are possible so long as Many schemes are possible so long as better scoring chromosomes more better scoring chromosomes more likely selectedlikely selected

Score is often termed the Score is often termed the fitnessfitness ““Roulette Wheel” selection can be Roulette Wheel” selection can be

used:used: Add up the fitness's of all chromosomesAdd up the fitness's of all chromosomes Generate a random number R in that rangeGenerate a random number R in that range Select the first chromosome in the Select the first chromosome in the

population that - when all previous fitness’s population that - when all previous fitness’s are added - gives you at least the value Rare added - gives you at least the value R

Example: Discrete Example: Discrete Representation (Binary Representation (Binary

alphabet)alphabet)

CHROMOSOMECHROMOSOME

GENEGENE

Representation of an individual can be using discrete values (binary, integer, or any other system with a discrete set of values). Following is an example of binary representation.


alphabet)alphabet)

8 bits Genotype8 bits Genotype Phenotype:• Integer

• Real Number

• Schedule

• ...

• Anything?


alphabet)alphabet)Phenotype could be integer numbersPhenotype could be integer numbers

Genotype:

1*21*27 7 + 0*2+ 0*26 6 + 1*2+ 1*25 5 + 0*2+ 0*24 4 + 0*2+ 0*23 3 + 0*2+ 0*22 2 + 1*2+ 1*21 1 + 1*2+ 1*200 ==

128 + 32 + 2 + 1 = 163128 + 32 + 2 + 1 = 163

= 163Phenotype:


alphabet)alphabet) Phenotype could be Real NumbersPhenotype could be Real Numbers

e.g. a number between 2.5 and 20.5 using 8 e.g. a number between 2.5 and 20.5 using 8 binary digitsbinary digits

9609.135.25.20256

1635.2 x

= 13.9609Genotype: Phenotype:


alphabet)alphabet) Phenotype could be a SchedulePhenotype could be a Schedule

e.g. 8 jobs, 2 time stepse.g. 8 jobs, 2 time steps

Genotype:

=

12345678

21211122

JobTime Step

Phenotype

SelectionSelection

During each successive generation, During each successive generation, a proportion of the existing population is a proportion of the existing population is selected to breed a new generation. selected to breed a new generation. Individual solutions are selected through Individual solutions are selected through a a fitness-basedfitness-based process, where fitter process, where fitter solutions are to be selected. Certain solutions are to be selected. Certain selection methods rate the fitness of selection methods rate the fitness of each solution and preferentially select each solution and preferentially select the best solutions. Other methods rate the best solutions. Other methods rate only a random sample of the population, only a random sample of the population, as this process may be very time-as this process may be very time-consuming.consuming.

Example (selection1)Example (selection1)

Next we apply fitness proportionate selection with the roulette wheel method:

Area is Proportional to fitness value

Individual i will have a

probability to be chosen

i

if

if

)(

)(

21n

3

4

We repeat the extraction as many times as the number of individuals we need to have the same parent population size (6 in our case)

ReproductionReproductionThe next step is to generate a second The next step is to generate a second

generation population of solutions from those generation population of solutions from those selected through genetic operators: selected through genetic operators: crossover (also called recombination) and/or crossover (also called recombination) and/or mutation.mutation.

For each new solution, a pair of "parent" For each new solution, a pair of "parent" solutions is selected for breeding from the solutions is selected for breeding from the pool selected previously. By producing a pool selected previously. By producing a "child" solution using crossover and mutation, "child" solution using crossover and mutation, a new solution is created which shares many a new solution is created which shares many of the characteristics of its "parents". New of the characteristics of its "parents". New parents are selected for each child and the parents are selected for each child and the process continues until a new population of process continues until a new population of solutions of appropriate size is generated.solutions of appropriate size is generated.

TerminationTerminationThis generational process is repeated until a This generational process is repeated until a

termination condition has been reached:termination condition has been reached: A solution is found that satisfies minimum A solution is found that satisfies minimum

criteriacriteria Fixed number of generations reachedFixed number of generations reached Allocated budget (computation time/money) Allocated budget (computation time/money)

reachedreached The highest ranking solution's fitness is reaching The highest ranking solution's fitness is reaching

or has reached a plateau such that successive or has reached a plateau such that successive iterations no longer produce better resultsiterations no longer produce better results

Manual inspectionManual inspection Combinations of the above.Combinations of the above.

Example (initialization)Example (initialization) We toss a fair coin 60 times and get We toss a fair coin 60 times and get

the following initial population:the following initial population: ss1 = 11110101011 = 1111010101f f ((ss1) = 71) = 7 ss2 = 01110001012 = 0111000101f f ((ss2) = 52) = 5 ss3 = 11101101013 = 1110110101f f ((ss3) = 73) = 7 ss4 = 01000100114 = 0100010011f f ((ss4) = 44) = 4 ss5 = 11101111015 = 1110111101f f ((ss5) = 85) = 8 ss6 = 01001100006 = 0100110000f f ((ss6) = 36) = 3

Simple ExampleSimple Example f(x) = {MAX(xf(x) = {MAX(x22): 0 <= x <= 32 }): 0 <= x <= 32 } Encode Solution: Just use 5 bits (1 or 0).Encode Solution: Just use 5 bits (1 or 0). Generate initial population.Generate initial population.

Evaluate each solution against objective.Evaluate each solution against objective.

AA 00 11 11 00 11

BB 11 11 00 00 00

CC 00 11 00 00 00

DD 11 00 00 11 11

Sol.Sol. StringString FitnessFitness % of % of TotalTotal

AA 0110101101 169169 14.414.4

BB 1100011000 576576 49.249.2

CC 0100001000 6464 5.55.5

DD 1001110011 361361 30.930.9

Pseudo-code algorithmPseudo-code algorithm Choose initial populationChoose initial population Evaluate the fitness of each individual in the Evaluate the fitness of each individual in the

populationpopulation Repeat Repeat

• Select best-ranking individuals to reproduceSelect best-ranking individuals to reproduce• Breed new generation through crossover and Breed new generation through crossover and

mutation (genetic operations) and give birth to mutation (genetic operations) and give birth to offspringoffspring

• Evaluate the individual fitnesses of the offspringEvaluate the individual fitnesses of the offspring• Replace worst ranked part of population with Replace worst ranked part of population with

offspringoffspring Until terminationUntil termination

Simple Example (cont.)Simple Example (cont.)

Create next generation of solutionsCreate next generation of solutions Probability of “being a parent” depends on the Probability of “being a parent” depends on the

fitness.fitness. Ways for parents to create next generationWays for parents to create next generation

ReproductionReproduction Use a string again unmodified.Use a string again unmodified.

CrossoverCrossover Cut and paste portions of one string to another.Cut and paste portions of one string to another.

MutationMutation Randomly flip a bit.Randomly flip a bit.

COMBINATION of all of the above.COMBINATION of all of the above.

The Basic Genetic AlgorithmThe Basic Genetic Algorithm1.1. [Start] [Start] Generate random population of Generate random population of nn chromosomes (suitable chromosomes (suitable

solutions for the problem)solutions for the problem) 2.2. [Fitness] [Fitness] Evaluate the fitness Evaluate the fitness f(x) f(x) of each chromosome of each chromosome xx in the in the

population population 3.3. [New population] [New population] Create a new population by repeating Create a new population by repeating

following steps until the new population is completefollowing steps until the new population is complete 1.1. [Selection] [Selection] Select two parent chromosomes from a Select two parent chromosomes from a

population according to their fitness (the better fitness, the population according to their fitness (the better fitness, the bigger chance to be selected) bigger chance to be selected)

2.2. [Crossover] [Crossover] With a crossover probability cross over the With a crossover probability cross over the parents to form new offspring (children). If no crossover was parents to form new offspring (children). If no crossover was performed, offspring is the exact copy of parents.performed, offspring is the exact copy of parents.

3.3. [Mutation] [Mutation] With a mutation probability mutate new offspring With a mutation probability mutate new offspring at each locus (position in chromosome). at each locus (position in chromosome).

4.4. [Accepting] [Accepting] Place new offspring in the new populationPlace new offspring in the new population 4.4. [Replace] [Replace] Use new generated population for a further run of the Use new generated population for a further run of the

algorithm algorithm 5.5. [Test] [Test] If the end condition is satisfied, stop, and return the best If the end condition is satisfied, stop, and return the best

solution in current population solution in current population 6.6. [Loop] [Loop] Go to step 2 Go to step 2

Example of mutation (Negnevitsky, Pearson Example of mutation (Negnevitsky, Pearson Education, 2002)Education, 2002)

Original network3

4

5

y6

x22

-0.3

0.9-0.7

0.5

-0.8

-0.6x11

-0.2

0.1

0.4

0.1 -0.7 -0.6 0.5 -0.8-0.2 0.9

3

4

5

y6

x22

0.2

0.9-0.7

0.5

-0.8

-0.6x11

-0.2

0.1

-0.1

0.1 -0.7 -0.6 0.5 -0.8-0.2 0.9

Mutated network

0.4 -0.3 -0.1 0.2

Some GA Application TypesSome GA Application TypesDomain Application Types

Control gas pipeline, pole balancing, missile evasion, pursuit

Design semiconductor layout, aircraft design, keyboardconfiguration, communication networks

Scheduling manufacturing, facility scheduling, resource allocation

Robotics trajectory planning

Machine Learning designing neural networks, improving classificationalgorithms, classifier systems

Signal Processing filter design

Game Playing poker, checkers, prisoner’s dilemma

CombinatorialOptimization

set covering, travelling salesman, routing, bin packing,graph colouring and partitioning

ConclusionsConclusions

Question:Question: ‘If GAs are so smart, why ain’t they rich?’‘If GAs are so smart, why ain’t they rich?’

Answer:Answer: ‘Genetic algorithms ‘Genetic algorithms areare rich - rich in rich - rich in application across a large and growing application across a large and growing number of disciplines.’number of disciplines.’

- David E. Goldberg, - David E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Genetic Algorithms in Search, Optimization and Machine LearningLearning

introduction to genetic algorithms

Documents

genetic algorithms gas

errors genetic variation

genetic algorithm product

reproduction errors

reproduction meiosis

locusbiological background

mutationbiological background

basis of sexual reproduction