genetic algorithm.pdf

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IntroductionAlgorithm

TheoryWhy GA?

Applications

Genetic Algorithm

Saif Hasan Sagar Chordia Rahul Varshneya

February 6, 2012

GuidePushpak Bhattacharyya

1 / 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm

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TheoryWhy GA?

Applications

IntroductionHistoryMotivationTerminology

INTRODUCTION


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TheoryWhy GA?

Applications


Introduction

Genetic algorithms are a family of computational modelsbelonging to the class of evolutionary algorithms, part of

artificial intelligence


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TheoryWhy GA?

Applications


Introduction



These algorithms encode a potential solution to a specificproblem on a simple chromosome like data structure


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TheoryWhy GA?

Applications


Introduction



These algorithms encode a potential solution to a specificproblem on a simple chromosome like data structure

Uses techniques inspired by natural evolution such as

inheritance, mutation, selection and crossover


I t d ti

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TheoryWhy GA?

Applications


Introduction


artificial intelligenceThese algorithms encode a potential solution to a specificproblem on a simple chromosome like data structure

Uses techniques inspired by natural evolution such as

inheritance, mutation, selection and crossoverThey are often viewed as function optimizers


Introduction

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TheoryWhy GA?

Applications


History

First appeared in 1950s and early 1960s while biologists wereexplicitly seeking to the model of natural evolution


Introduction

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TheoryWhy GA?

Applications


History


Idea of inheritance and mutation introduced by Ingo

Rechenberg which is termed as evolution strategy (1965)


Introduction

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TheoryWhy GA?

Applications


History



Rechenberg which is termed as evolution strategy (1965)M.J. Walsh introduced evolutionary programming (1966)


IntroductionI d i

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TheoryWhy GA?

Applications


History




Later versions introduced population which leads to theGenetic Algorithms


IntroductionI t d ti

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AlgorithmTheory

Why GA?Applications


History




Later versions introduced population which leads to theGenetic Algorithms

In 1975 John Holland published book Adaptation in Naturaland Artificial System. This was the first book to representconcept of adaptive digital systems using mutation, selectionand crossover.


IntroductionIntroduction

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AlgorithmTheory

Why GA?Applications


Motivation

Evolution is very powerful theory since biological principles likecommon descent and selective breeding have been used forthe benefit of humans


Introduction Introduction

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AlgorithmTheory

Why GA?Applications


Motivation


Living organisms are consummate problem solvers. Theyexhibit a versatility that puts the best computer programs toshame.


Introduction Introduction

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AlgorithmTheory

Why GA?Applications


Motivation


Living organisms are consummate problem solvers. Theyexhibit a versatility that puts the best computer programs toshame.

Most organisms evolve by means of two primary processes:

natural selection and sexual reproduction. The first determineswhich members of population survive and reproduce, and thesecond ensures mixing and recombination among the genes of their offspring. Similar analogy is used in GA.


IntroductionAl i h

Introduction

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AlgorithmTheory

Why GA?Applications


Terminology

Search space/ State space : the space of all feasible solutions.


IntroductionAl ith

Introduction

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AlgorithmTheory

Why GA?Applications

HistoryMotivationTerminology

Terminology


Chromosome : a set of genes; a chromosome contains the

solution in form of genes.



Introduction

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AlgorithmTheory

Why GA?Applications


Terminology



solution in form of genes.Population : a set of solutions (or individuals/chromosomes).



Introduction

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AlgorithmTheory

Why GA?Applications


Terminology




Generation : the process of evaluation, selection,recombination and mutation.



IntroductionHi

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AlgorithmTheory

Why GA?Applications


Terminology




Generation : the process of evaluation, selection,recombination and mutation.

Fitness : the value assigned to an individual based on how faror close it is from the solution; greater the fitness value betterthe solution it contains.



AlgorithmE di

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AlgorithmTheory

Why GA?Applications

EncodingOperations of GAParameters of GA

ALGORITHM



AlgorithmEncoding

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gTheory

Why GA?Applications


Algorithm

Psuedocode of Genetics Algorithm



AlgorithmEncoding

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TheoryWhy GA?

Applications


Algorithm


Choose the initial population of individuals



AlgorithmEncoding

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TheoryWhy GA?

Applications


Algorithm



Evaluate the fitness of each individual in population



Th

AlgorithmEncoding

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TheoryWhy GA?

Applications


Algorithm



Evaluate the fitness of each individual in populationRepeat until termination condition satisfied:



Th

AlgorithmEncoding

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TheoryWhy GA?

Applications

gOperations of GAParameters of GA

Algorithm




Selection: Select the individuals with greater fitness forreproduction



Theory

AlgorithmEncoding

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TheoryWhy GA?

Applications

gOperations of GAParameters of GA

Algorithm




Selection: Select the individuals with greater fitness forreproductionCrossover: Breed new individuals through crossover



Theory

AlgorithmEncoding

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TheoryWhy GA?

Applications

Operations of GAParameters of GA

Algorithm





Mutation: Apply probabilistic mutation on new individuals



Theory

AlgorithmEncodingO f G

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TheoryWhy GA?

Applications


Algorithm





Mutation: Apply probabilistic mutation on new individualsForm a new population with these offsprings.



Theory

AlgorithmEncodingO i f GA

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TheoryWhy GA?

Applications


Algorithm



Evaluate the fitness of each individual in population

Repeat until termination condition satisfied:


Mutation: Apply probabilistic mutation on new individualsForm a new population with these offsprings.

Terminate



Theory

AlgorithmEncodingO ti f GA

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yWhy GA?

Applications


Flow Chart



Theory

AlgorithmEncodingOperations of GA

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yWhy GA?

Applications


Encoding

Before a genetic algorithm can be put to work on any problem, amethod is needed to encode potential solutions to that problem ina form so that a computer can process.

10/ 42 Saif Hasan, Sagar Chordia, Rahul Varshneya Genetic Algorithm


Theory


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Why GA?Applications


Encoding


Common approaches are:

Binary Encoding : every chromosome is a string of 0 or 1


IntroductionAlgorithmTheory

Wh GA?


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Why GA?Applications


Encoding




Permutation Encoding : every chromosome is a string of numbers that represent position in a sequence



Wh GA?


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Why GA?Applications


Encoding





Tree Encoding : a tree structure represents the chromosome



Wh GA?


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Why GA?Applications

pParameters of GA

Encoding





Tree Encoding : a tree structure represents the chromosome

Value Encoding : every chromosome is a sequence of somevalues (real numbers, characters or objects)



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Why GA?Applications

Parameters of GA

Encoding Examples

Binary Encoding : Suppose we have a knapsack of capacity C and N items, then we can encode this problem as follows



Why GA?


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Why GA?Applications

Parameters of GA

Encoding Examples


Chromosome, in this case, is a string of 0s and 1s with N bits



Why GA?

AlgorithmEncodingOperations of GAP f GA

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Why GA?Applications

Parameters of GA

Encoding Examples



Represent item i of problem with i th

bit in the chromosome



Why GA?

AlgorithmEncodingOperations of GAP t f GA

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y GApplications

Parameters of GA

Encoding Examples




bit in the chromosomei th bit is 1 iff i th item has been selected, 0 otherwise.



Why GA?

AlgorithmEncodingOperations of GAParameters of GA

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yApplications

Parameters of GA

Encoding Examples




bit in the chromosomei th bit is 1 iff i th item has been selected, 0 otherwise.The set of all such chromosomes (2N ) is the solution space of the problem.



Why GA?


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ApplicationsParameters of GA

Encoding Examples




bit in the chromosomei th bit is 1 iff i th item has been selected, 0 otherwise.The set of all such chromosomes (2N ) is the solution space of the problem.

Chromosome 1: 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1

Chromosome 2: 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1The example shown above has 24 items (and therefore 24 bits)with item1 selected in both chromosome 1 and 2 whereasitem2 is selected in chromosome 2 but not in chromosome 1.



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Encoding Examples

Permutation Encoding : Travelling Salesman Problem



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Encoding Examples


Problem descripition : There are cities and given distancesbetween them. Travelling salesman has to visit all of them, but

he doesn’t want to travel more than necessary. Find asequence of cities with a minimal travelled distance.



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Applications

Encoding Examples


Problem descripition : There are cities and given distancesbetween them. Travelling salesman has to visit all of them, but

he doesn’t want to travel more than necessary. Find asequence of cities with a minimal travelled distance.

Chromosome A: 1 5 3 2 6 4 7 9 8

Chromosome B: 8 5 6 7 2 3 1 4 9

Encoding : Here, encoded chromosomes describe the order of

cities the salesman visits. For example, in chromosome A, thesalesman visits city-1 followed by city-5 followed by city-3 andso on.



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Applications

Encoding Examples

Tree Encoding : Genetic Programming



Why GA?Applications


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Applications

Encoding Examples


In tree encoding, every chromosome is a tree of some objects,such as functions or commands in programming language.



Why GA?Applications


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Applications

Encoding Examples


In tree encoding, every chromosome is a tree of some objects,such as functions or commands in programming language.Tree encoding is useful for evolving programs or any otherstructures that can be encoded in trees.



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Applications

Encoding Examples


In tree encoding, every chromosome is a tree of some objects,such as functions or commands in programming language.Tree encoding is useful for evolving programs or any otherstructures that can be encoded in trees.The crossover and mutation can be done relatively easy way .



TheoryWhy GA?

Applications


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pp

Encoding Examples


In tree encoding, every chromosome is a tree of some objects,such as functions or commands in programming language.Tree encoding is useful for evolving programs or any otherstructures that can be encoded in trees.The crossover and mutation can be done relatively easy way .

Image courtesy: http://www.myreaders.info/09 Genetic Algorithms.pdf



TheoryWhy GA?

Applications


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Operations of Genetic Algorithm

Genetic operators used in GA maintain genetic diversity.



TheoryWhy GA?

Applications


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Genetic diversity or variation is a necessity for evolution.



TheoryWhy GA?

Applications


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Genetic diversity or variation is a necessity for evolution.Genetic operators are analogous to those which occur in thenatural world:



TheoryWhy GA?

Applications


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Genetic operators are analogous to those which occur in thenatural world:

Reproduction (or Selection)



TheoryWhy GA?

Applications


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Reproduction (or Selection)Crossover (or Recombination)



TheoryWhy GA?

Applications


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Reproduction (or Selection)Crossover (or Recombination)

Mutation



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Applications


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Reproduction or Selection

Concept : From the population, the chromosomes are selectedto be parents to crossover and produce offspring.



TheoryWhy GA?

Applications


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Problem : How to select these chromosomes ?


Introduction

AlgorithmTheory

Why GA?Applications


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Hint : According to Charles Darwin’s evolution theory”survival of the fittest” - the best ones should survive andcreate new offspring.


Introduction

AlgorithmTheory

Why GA?Applications


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Hint : According to Charles Darwin’s evolution theory”survival of the fittest” - the best ones should survive andcreate new offspring.

Solution : Fitness function quantifies the optimality of a

solution (chromosome) so that a particular solution may beranked against all the other solutions. The function depictsthe closeness of a given ’solution’ to the desired result.


Introduction

AlgorithmTheory

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Popular methods of selection include :


Introduction

AlgorithmTheory

Why GA?Applications


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Roulette-wheel selection


Introduction

AlgorithmTheory

Why GA?Applications


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Tournament selection


Introduction

AlgorithmTheory

Why GA?Applications


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Tournament selectionRank selection


Introduction

AlgorithmTheory

Why GA?Applications


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Steady-state selection


Introduction

AlgorithmTheory

Why GA?Applications


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Boltzmann selection


Introduction

AlgorithmTheory

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Boltzmann selection

Scaling selection


Introduction

AlgorithmTheory

Why GA?Applications


Roulette Wheel Selection

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Roulette-Wheel Selection

Concept : the chance of an individual’s being selected isproportional to its fitness, greater or less than its competitors’fitness.


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AlgorithmTheory

Why GA?Applications



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Introduction

AlgorithmTheory

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Implementation : Probability of selection of i th individual is:p i = f i

ΣN j =1f j

where f i :fitness of i th individual, N : number of individuals



Introduction

AlgorithmTheory

Why GA?Applications


Elitist Selection

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Elitist Selection

Concept : Most fit members of each generation areguaranteed to be selected for next generation.


Introduction

AlgorithmTheory

Why GA?Applications


Elitist Selection

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Elitist Selection


Advantages :


Introduction

AlgorithmTheory

Why GA?Applications


Elitist Selection

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Elitist Selection


Advantages :Ensures that the best solution found so far is not lost due tocrossover and mutation.


Introduction

AlgorithmTheoryWhy GA?

Applications


Elitist Selection

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Elitist Selection


Advantages :Ensures that the best solution found so far is not lost due tocrossover and mutation.Speeds up convergence once a good solution has beendiscovered.


Introduction


Applications


Crossover

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Crossover

Concept : Selects genes from parent chromosomes, combinesthem and creates a new offspring.


Introduction


Applications


Crossover

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Crossover


Idea : New chromosome may be better than both of theparents if it takes the best characteristics from each of them


Introduction


Applications


Crossover

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Consider the two parents selected for crossover.


Introduction


Applications


Crossover

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Interchange the parents chromosomes after crossover points.The offsprings produced are :



Introduction


Applications

Algorithm


Crossover

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The Crossover operators are of many types.


Introduction


Applications

Algorithm


Crossover

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Single-Point crossover


Introduction


Applications

Algorithm


Crossover

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Single-Point crossoverTwo Point crossover


Introduction


Applications

Algorithm


Crossover

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Single-Point crossoverTwo Point crossoverUniform crossover


Introduction


Applications

Algorithm


Crossover

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Single-Point crossoverTwo Point crossoverUniform crossoverArithmetic crossover


Introduction


Applications

Algorithm


Crossover

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Which Crossover operator is to be selected is based onchromosome encoding


Introduction


Applications

Algorithm


Crossover

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Specific crossover made for a specific problem can improveperformance of the genetic algorithm

20/ 42 Saif Hasan Sagar Chordia Rahul Varshneya Genetic Algorithm

Introduction


Applications

Algorithm


Crossover

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Specific crossover made for a specific problem can improveperformance of the genetic algorithm

Some research suggests more than two “parents” are better toreproduce a good quality chromosome (Eiben, A.E. et al (1994),

Ting, Chuan-Kang (2005))


Introduction


Applications

Algorithm


Two-Point Crossover

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Operation : randomly select two crossover points within achromosome, then interchange the two parent chromosomesbetween these points to produce two new offspring.Consider the two parents selected for crossover.


Introduction


Applications

Algorithm


Uniform Crossover

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Operation : mixing ratio decides the contribution of eachparent to the gene values in the offspring chromosomes.

Advantage : allows the parent chromosomes to be mixed atthe gene level rather than the segment level


If the mixing ratio is 0.5 approximately, then the possible set of

offsprings after crossover would be :



Introduction


Applications

Algorithm


Mutation

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Concept : Mutation alters one or more gene values in achromosome from its initial state.



TheoryWhy GA?

Applications

Algorithm


Mutation

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Advantages :



TheoryWhy GA?

Applications

Algorithm


Mutation

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Advantages :

Mutation can generate new genes values not already present in

sample space which can lead to better solution.



TheoryWhy GA?

Applications

Algorithm


Mutation

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Advantages :


sample space which can lead to better solution.Randomness introduced by mutation helps in searching forglobal optima solutions and not geting stuck in local optima.(premature convergence).



TheoryWhy GA?

Applications

Algorithm


Mutation

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Advantages :



Operators : Mutation operators are of many type :



TheoryWhy GA?

Applications

Algorithm


Mutation

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Advantages :




one simple way is, Flip Bit.



TheoryWhy GA?

Applications

Algorithm


Mutation

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Advantages :




one simple way is, Flip Bit.the others are Boundary, Uniform, and Gaussian.



TheoryWhy GA?

Applications

Algorithm


Mutation

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Advantages :




one simple way is, Flip Bit.the others are Boundary, Uniform, and Gaussian.

Operators are selected based on encoding of chromosomes.



TheoryWhy GA?

Applications

Algorithm


Flip Bit

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The mutation operator simply inverts the value of the chosengene i.e. 0 goes to 1 and 1 goes to 0.

Consider the two original offsprings selected for mutation.

The Mutated Off-spring produced are :




TheoryWhy GA?

Applications

Algorithm


Parameters of Genetic Algorithm

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There are three basic parameters of Genetic Algorithm.

25/ 42 Saif Hasa Saga Cho dia Rah l Va sh e a Ge etic Algo ith


TheoryWhy GA?

Applications

Algorithm



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Crossover Probability

25/ 42 S if H S Ch di R h l V h G ti Al ith


TheoryWhy GA?

Applications

Algorithm



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Crossover ProbabilityMutation Probability

25/ 42 S if H S Ch di R h l V h G ti Al ith


TheoryWhy GA?

Applications

Algorithm



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Crossover ProbabilityMutation Probability

Population Size



TheoryWhy GA?

Applications

Algorithm



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Definition : Crossover probability represents how oftencrossover is performed.



TheoryWhy GA?

Applications

Algorithm



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Constraint :



TheoryWhy GA?

Applications

Algorithm



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Constraint :

If the crossover rate is too high, high performance strings are

eliminated faster than selection can produce improvements.



TheoryWhy GA?

Applications

Algorithm



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Constraint :


eliminated faster than selection can produce improvements.A low crossover rate may cause stagnation due to the lowerexploration rate.



TheoryWhy GA?

Applications

Algorithm



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Constraint :



Solution : Crossover rate generally should be high, about80%-95%.



TheoryWhy GA?

Applications

Algorithm



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Constraint :



Solution : Crossover rate generally should be high, about80%-95%.Some results show that for some problems crossover rateabout 60% is the best.



TheoryWhy GA?

Applications

Algorithm


Mutation Probability

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Defintion : Mutation probability represents how oftenmutation is performed.



TheoryWhy GA?

Applications

Algorithm



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Constraints :



TheoryWhy GA?

Applications



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Constraints :

A very small mutation rate may lead to convergence to localoptima areas.



TheoryWhy GA?

Applications



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Constraints :

A very small mutation rate may lead to convergence to localoptima areas.A mutation rate that is too high results in almost randomsearch.



TheoryWhy GA?

Applications



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Constraints :

A very small mutation rate may lead to convergence to localoptima areas.A mutation rate that is too high results in almost randomsearch.

Solution :Best rates reported are about 0.5%-1%.



TheoryWhy GA?

Applications


Population Size

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Definition : Number of chromosomes in population (in onegeneration).



TheoryWhy GA?

Applications


Population Size

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Constraints :



TheoryWhy GA?Applications


Population Size

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Constraints :

Too few chromosomes implies GA have a few possibilities toperform crossover and only a small part of search space isexplored.





Population Size

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Constraints :

Too few chromosomes implies GA have a few possibilities toperform crossover and only a small part of search space isexplored.Too many chromosomes implies GA slows down.





Population Size

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Constraints :

Too few chromosomes implies GA have a few possibilities toperform crossover and only a small part of search space isexplored.Too many chromosomes implies GA slows down.

Solution : Good population size is about 20-30, however

sometimes sizes 50-100 are reported as best.




Schema and HyperPlane

Implicit ParallelismThe Schema Theorem

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Why Genetic Algorithms Work?







Schema - solution string with some blank fields

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geg: 01***********








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geg: 01***********

Solution is combination of these schemas. Schema representsa particular component of solution.








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geg: 01***********


Solution space : N-dimensional HyperCube








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eg: 01***********


Solution space : N-dimensional HyperCube

Schema : HyperPlane








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eg: 01***********


Solution space : N-dimensional HyperCubeSchema : HyperPlane

In 3D cube, 0** represent front face.








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eg: 01***********


Solution space : N-dimensional HyperCubeSchema : HyperPlane

In 3D cube, 0** represent front face.

There is competition between Schema with n bit values insame positions.e g:- 00*, 01*, 10*, 11* are competing

Winner is the schema with highest fitness.






Implicit Parallelism

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A solution string belongs to many HyperPlanes (2N −1).eg: 010 belongs to 0** , *1*, **0







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Single Evaluation of string leads to evaluation of different

hyperplanes in an implicitly parallel fashion (John Holland 1975

);







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Single Evaluation of string leads to evaluation of different

hyperplanes in an implicitly parallel fashion (John Holland 1975

);Evaluation of population of strings, samples far morehyperplanes as compared to number of strings contained inthe population.







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Single Evaluation of string leads to evaluation of differenthyperplanes in an implicitly parallel fashion (John Holland 1975 );

Evaluation of population of strings, samples far morehyperplanes as compared to number of strings contained inthe population.

These cumulative effects provides statistical information to

GA about any particular subset of hyperplanes.






The Schema Theorem

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TheoryWhy GA?

Applications

Schema and HyperPlaneImplicit ParallelismThe Schema Theorem

The Schema Theorem

The Schema Theorem (Holland 1992; Goldberg 1989)

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The Schema Theorem (Holland 1992; Goldberg 1989 ).It provides a lower bound on the change in the sample rate fora single hyperplane from generation t to generation t + 1.



TheoryWhy GA?

Applications


The Schema Theorem


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Equation:



TheoryWhy GA?

Applications


The Schema Theorem


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Equation:

Building Blocks Hypothesis (Holland, 1975; Gold-berg, 1989 )Low-order, highly-fit schemas recombine to form even betterschemas.

In Goldberg’s words, “we construct better and better stringsfrom the best partial solutions of past samplings”



TheoryWhy GA?

Applications

Advantages

Disadvantages

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WHY GA?



TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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Implicit Parallelism - Solution Space is explored in multipledirections (GoldBerg - GA in Search and Optimization)



TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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Nonlinear problems -Large Solution space, but GA areideal.(Forrest - 1993 Genetic Algorithm)



TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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Nonlinear problems -Large Solution space, but GA areideal.(Forrest - 1993 Genetic Algorithm)

Works on complex landscape (discontinuous, noisy, changingwith time) (John Koza - Genetic Programming IV 2004 )



TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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Dilemma of global optimum vs many local optima. GA strikeperfect balance (John Holland - Genetic Algorithm 1992 )



TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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GA can manipulate many parameters simultaneously (Forrest -

Genetic algorithms: principles of natural selection applied to computation.1993 )



TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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GA can manipulate many parameters simultaneously (Forrest -

Genetic algorithms: principles of natural selection applied to computation.1993 )

GA don’t have specific knowledge of problem. All possiblesearch pathways are considered in GA.(John Koza - Genetic

Programming III 1999 )



Theory

Why GA?Applications

Advantages

Disadvantages

Disadvantages

Computationally expensive and time consuming

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Theory

Why GA?Applications

Advantages

Disadvantages

Disadvantages


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Issues in representation of problem



Theory

Why GA?Applications

Advantages

Disadvantages

Disadvantages


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Proper writing of fitness function



Theory

Why GA?Applications

Advantages

Disadvantages

Disadvantages


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Proper values of size of population, crossover and mutationrate



Theory

Why GA?Applications

Advantages

Disadvantages

Disadvantages


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Deceptive Fitness Function (Mitchell, Melanie 1996 )



Theory

Why GA?Applications

Advantages

Disadvantages

Disadvantages


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p y p g





Premature Convergence



Theory

Why GA?Applications

Advantages

Disadvantages

Disadvantages


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p y p g





Premature Convergence

No one mathematically perfect solution since problems of biological adaptation don’t have this issue.



Theory

Why GA?Applications

Applications

Aeronautics

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APPLICATIONS



Theory

Why GA?Applications

Applications

Aeronautics

Applications

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Image courtesy: http://www.google.com



Theory

Why GA?Applications

Applications

Aeronautics

Aeronautics

Multiple-objective genetics algorithm to design wing shape for

supersonic aircraft

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Theory

Why GA?Applications

ApplicationsAeronautics

Aeronautics


supersonic aircraft

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Four major considerations for wing design



Theory

Why GA?Applications


Aeronautics


supersonic aircraftF j id i f i d i

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Minimizing aerodynamic drag at supersonic cruising speeds



Theory

Why GA?Applications


Aeronautics


supersonic aircraftF j id i f i d i

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Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speeds



Theory

Why GA?Applications


Aeronautics


supersonic aircraftF j id ti f i d i

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Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speedsMinimizing aerodynamic load (bending force on wing)



Theory

Why GA?Applications


Aeronautics


supersonic aircraftF j id ti f i d i

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Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speedsMinimizing aerodynamic load (bending force on wing)Minimizing twisting moment of wing



Theory

Why GA?Applications


Aeronautics


supersonic aircraftFour major considerations for wing design

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Minimizing aerodynamic drag at supersonic cruising speedsMinimizing drag at subsonic speedsMinimizing aerodynamic load (bending force on wing)Minimizing twisting moment of wing

Objectives are mutually exclusive and optimizing themrequires tradeoff



Theory

Why GA?Applications


Aeronautics



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Minimizing twisting moment of wing


Chromosomes - 66 real valued numbers, with population size -

64 and simulated for 70 generations.



Theory

Why GA?Applications


Aeronautics



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Minimizing twisting moment of wing


Chromosomes - 66 real valued numbers, with population size -

64 and simulated for 70 generations.Evolved wing configurations outperformed existing humandesigned-wings



Theory

Why GA?Applications


References

Obayashi, Shigeru, Daisuke Sasaki, Yukihiro Takeguchi, and NaokiHirose. “Multiobjective evolutionary computation for supersonicwing shape optimization ” IEEE Transactions on Evolutionary

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wing-shape optimization. IEEE Transactions on EvolutionaryComputation, vol.4, no.2, p.182-187 (July 2000).

Genetic Programming : On the Programming of Computers byMeans of Natural Selection by John R. Koza

http://www.myreaders.info/09 Genetic Algorithms.pdf

http://www.obitko.com/tutorials/genetic-algorithms/search-space.php

http://www.talkorigins.org/faqs/genalg/genalg.html

http://en.wikipedia.org/wiki/Genetic algorithm

http://brainz.org/15-real-world-applications-genetic-algorithms/



Theory

Why GA?Applications


Conclusion

Large Appeal of Genetic Algorithms

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Theory

Why GA?Applications


Conclusion


Is it because of Performance?

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Theory

Why GA?Applications


Conclusion


Is it because of Performance?Or is it Aesthetic pleasing origins in theory of evolution ?

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p g g y



Theory

Why GA?Applications


Conclusion


Is it because of Performance?Or is it Aesthetic pleasing origins in theory of evolution ?

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Theory

Why GA?Applications


Questions

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Questions ?


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Documents

genetic algorithm.pdf