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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

TheoryWhy GA?

Applications

IntroductionHistoryMotivationTerminology

INTRODUCTION

TheoryWhy GA?

Applications

Introduction

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

artificial intelligence

TheoryWhy GA?

Applications

Introduction

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

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

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

TheoryWhy GA?

Applications

History

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

Introduction

TheoryWhy GA?

Applications

History

Idea of inheritance and mutation introduced by Ingo

Rechenberg which is termed as evolution strategy (1965)

Introduction

TheoryWhy GA?

Applications

History

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

IntroductionI d i

TheoryWhy GA?

Applications

History

Later versions introduced population which leads to theGenetic Algorithms

IntroductionI t d ti

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

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

AlgorithmTheory

Why GA?Applications

Motivation

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

Introduction Introduction

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

AlgorithmTheory

Why GA?Applications

Terminology

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

IntroductionAl ith

Introduction

AlgorithmTheory

Why GA?Applications

HistoryMotivationTerminology

Terminology

Chromosome : a set of genes; a chromosome contains the

solution in form of genes.

Introduction

AlgorithmTheory

Why GA?Applications

Terminology

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

Introduction

AlgorithmTheory

Why GA?Applications

Terminology

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

IntroductionHi

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

AlgorithmTheory

Why GA?Applications

EncodingOperations of GAParameters of GA

ALGORITHM

AlgorithmEncoding

gTheory

Why GA?Applications

Algorithm

Psuedocode of Genetics Algorithm

AlgorithmEncoding

TheoryWhy GA?

Applications

Algorithm

Choose the initial population of individuals

AlgorithmEncoding

TheoryWhy GA?

Applications

Algorithm

Evaluate the fitness of each individual in population

AlgorithmEncoding

TheoryWhy GA?

Applications

Algorithm

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

AlgorithmEncoding

TheoryWhy GA?

Applications

gOperations of GAParameters of GA

Algorithm

Selection: Select the individuals with greater fitness forreproduction

Theory

AlgorithmEncoding

TheoryWhy GA?

Applications

gOperations of GAParameters of GA

Algorithm

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

Theory

AlgorithmEncoding

TheoryWhy GA?

Applications

Operations of GAParameters of GA

Algorithm

Mutation: Apply probabilistic mutation on new individuals

Theory

AlgorithmEncodingO f G

TheoryWhy GA?

Applications

Algorithm

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

Theory

AlgorithmEncodingO i f GA

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

yWhy GA?

Applications

Flow Chart

Theory

AlgorithmEncodingOperations of GA

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

Why GA?Applications

Encoding

Common approaches are:

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

IntroductionAlgorithmTheory

Wh GA?

Why GA?Applications

Encoding

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

Wh GA?

Why GA?Applications

Encoding

Tree Encoding : a tree structure represents the chromosome

Wh GA?

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)

Why GA?

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?

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

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

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

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?

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.

Why GA?

Encoding Examples

Permutation Encoding : Travelling Salesman Problem

Why GA?A li i

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.

Why GA?A li ti

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.

Why GA?Applications

Applications

Encoding Examples

Tree Encoding : Genetic Programming

Why GA?Applications

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

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.

Why GA?Applications

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

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

Operations of Genetic Algorithm

Genetic operators used in GA maintain genetic diversity.

TheoryWhy GA?

Applications

Genetic diversity or variation is a necessity for evolution.

TheoryWhy GA?

Applications

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

TheoryWhy GA?

Applications

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

Reproduction (or Selection)

TheoryWhy GA?

Applications

Reproduction (or Selection)Crossover (or Recombination)

TheoryWhy GA?

Applications

Reproduction (or Selection)Crossover (or Recombination)

Mutation

TheoryWhy GA?

Applications

Reproduction or Selection

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

TheoryWhy GA?

Applications

Problem : How to select these chromosomes ?

Introduction

AlgorithmTheory

Why GA?Applications

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

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

Why GA?Applications

Popular methods of selection include :

Introduction

AlgorithmTheory

Why GA?Applications

R d i S l i

Roulette-wheel selection

Introduction

AlgorithmTheory

Why GA?Applications

R d i S l i

Tournament selection

Introduction

AlgorithmTheory

Why GA?Applications

R d i S l i

Tournament selectionRank selection

Introduction

AlgorithmTheory

Why GA?Applications

R d ti S l ti

Steady-state selection

Introduction

AlgorithmTheory

Why GA?Applications

R d ti S l ti

Boltzmann selection

Introduction

AlgorithmTheory

Why GA?Applications

Boltzmann selection

Scaling selection

Introduction

AlgorithmTheory

Why GA?Applications

Roulette Wheel Selection

Roulette-Wheel Selection

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

Introduction

AlgorithmTheory

Why GA?Applications

Introduction

AlgorithmTheory

Why GA?Applications

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

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

Introduction

AlgorithmTheory

Why GA?Applications

Elitist Selection

Advantages :

Introduction

AlgorithmTheory

Why GA?Applications

Elitist Selection

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

Introduction

AlgorithmTheoryWhy GA?

Applications

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

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

Introduction

Applications

Crossover

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

Introduction

Applications

Crossover

Consider the two parents selected for crossover.

Introduction

Applications

Crossover

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

Introduction

Applications

Algorithm

Crossover

The Crossover operators are of many types.

Introduction

Applications

Algorithm

Crossover

Single-Point crossover

Introduction

Applications

Algorithm

Crossover

Single-Point crossoverTwo Point crossover

Introduction

Applications

Algorithm

Crossover

Single-Point crossoverTwo Point crossoverUniform crossover

Introduction

Applications

Algorithm

Crossover

Single-Point crossoverTwo Point crossoverUniform crossoverArithmetic crossover

Introduction

Applications

Algorithm

Crossover

Which Crossover operator is to be selected is based onchromosome encoding

Introduction

Applications

Algorithm

Crossover

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

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

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

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

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

TheoryWhy GA?

Applications

Algorithm

Mutation

Advantages :

TheoryWhy GA?

Applications

Algorithm

Mutation

Advantages :

Mutation can generate new genes values not already present in

sample space which can lead to better solution.

TheoryWhy GA?

Applications

Algorithm

Mutation

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

Advantages :

Operators : Mutation operators are of many type :

TheoryWhy GA?

Applications

Algorithm

Mutation

Advantages :

one simple way is, Flip Bit.

TheoryWhy GA?

Applications

Algorithm

Mutation

Advantages :

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

TheoryWhy GA?

Applications

Algorithm

Mutation

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

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

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

Crossover Probability

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

TheoryWhy GA?

Applications

Algorithm

Crossover ProbabilityMutation Probability

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

TheoryWhy GA?

Applications

Algorithm

Crossover ProbabilityMutation Probability

Population Size

TheoryWhy GA?

Applications

Algorithm

Definition : Crossover probability represents how oftencrossover is performed.

TheoryWhy GA?

Applications

Algorithm

Constraint :

TheoryWhy GA?

Applications

Algorithm

Constraint :

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

eliminated faster than selection can produce improvements.

TheoryWhy GA?

Applications

Algorithm

Constraint :

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

TheoryWhy GA?

Applications

Algorithm

Constraint :

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

TheoryWhy GA?

Applications

Algorithm

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

Defintion : Mutation probability represents how oftenmutation is performed.

TheoryWhy GA?

Applications

Algorithm

Constraints :

TheoryWhy GA?

Applications

Constraints :

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

TheoryWhy GA?

Applications

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

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

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

TheoryWhy GA?

Applications

Population Size

Constraints :

TheoryWhy GA?Applications

Population Size

Constraints :

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

Population Size

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

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

Why Genetic Algorithms Work?

Schema - solution string with some blank fields

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

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

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

Solution space : N-dimensional HyperCube

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

Solution space : N-dimensional HyperCube

Schema : HyperPlane

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

Solution space : N-dimensional HyperCubeSchema : HyperPlane

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

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

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

Single Evaluation of string leads to evaluation of different

hyperplanes in an implicitly parallel fashion (John Holland 1975

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.

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

TheoryWhy GA?

Applications

Schema and HyperPlaneImplicit ParallelismThe Schema Theorem

The Schema Theorem

The Schema Theorem (Holland 1992; Goldberg 1989)

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

Equation:

TheoryWhy GA?

Applications

The Schema Theorem

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

WHY GA?

TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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

TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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

TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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

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

TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

GA can manipulate many parameters simultaneously (Forrest -

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

TheoryWhy GA?

Applications

Advantages

Disadvantages

Advantages

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

Computationally expensive and time consuming

Theory

Why GA?Applications

Advantages

Disadvantages

Issues in representation of problem

Theory

Why GA?Applications

Advantages

Disadvantages

Proper writing of fitness function

Theory

Why GA?Applications

Advantages

Disadvantages

Proper values of size of population, crossover and mutationrate

Theory

Why GA?Applications

Advantages

Disadvantages

Deceptive Fitness Function (Mitchell, Melanie 1996 )

Theory

Why GA?Applications

Advantages

Disadvantages

p y p g

Premature Convergence

Theory

Why GA?Applications

Advantages

Disadvantages

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

APPLICATIONS

Theory

Why GA?Applications

Applications

Aeronautics

Applications

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

Theory

Why GA?Applications

Applications

Aeronautics

Multiple-objective genetics algorithm to design wing shape for

supersonic aircraft

Theory

Why GA?Applications

ApplicationsAeronautics

Aeronautics

supersonic aircraft

Four major considerations for wing design

Theory

Why GA?Applications

Aeronautics

supersonic aircraftF j id i f i d i

Minimizing aerodynamic drag at supersonic cruising speeds

Theory

Why GA?Applications

Aeronautics

supersonic aircraftF j id i f i d i

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

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

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

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

Minimizing twisting moment of wing

Chromosomes - 66 real valued numbers, with population size -

64 and simulated for 70 generations.

Theory

Why GA?Applications

Aeronautics

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

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

Theory

Why GA?Applications

Conclusion

Is it because of Performance?

Theory

Why GA?Applications

Conclusion

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

p g g y

Theory

Why GA?Applications

Conclusion

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

Theory

Why GA?Applications

Questions

Questions ?

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