Presented by:Gaurav Khandelwal08BCE131

Genetic Algorithm

• General introduction to Genetic Algorithms (GA’s)

• Biological background

• Cell

• Chromosomes

• Origin of species

• Natural selection

• Genetic Algorithm

• Search space

• Basic algorithm

• Coding

• Examples

Overview

• Genetic algorithms (GA’s) are technique to solve problems which need optimization

• GA’s are a subclass of Evolutionary Computing

• GA’s are based on Darwin’s theory of evolution

• History of GA’s• Evolutionary computing evolved in the 1960’s.

• GA’s were created by John Holland in the mid-70’s.

General Introduction to GA’s

• 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(Cell)

• 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 genes for one property is called: allele

• Every gene has an unique position on the chromosome: locus

Biological Background(Chromosomes)

• 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(Genetics)

• Reproduction of genetical information

• Mitosis

• Meiosis

• Mitosis is copying the same genetic information to new offspring: there is no exchange of information

• Meiosis is the basis of the sexual reproduction

• During reproduction “errors ” occur

• Due to these “errors” genetic variation exists

• Most important “errors” are:Recombination(cross-over)

mutation

Biological Background(Reproduction)

• The origin of species: “Preservation of favourable variations 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.

• Important aspects in natural selection are:• adaptation to the environment• isolation of populations in different groups which cannot

mutually mate

Biological background(Natural-selection)

Genetics + Algorithm = Genetic Algorithm

Genetic Algorithm is robust and probabilistic search algorithm based on the mechanics of natural selection and genetics

Genetic Algorithm follows the principle of “Survival of the Fittest” laid down by Charles Darwin

Random search method

Genetic Algorithms

• Most often one is looking for the best solution in a specific subset of solutions

• This subset is called the search space (or state space)

• Every point in the search space is a possible solution

• Therefore every point has a fitness value, depending on the problem definition

• GA’s are used to search the search space for the bestsolution, e.g. a minimum

Genetic Algorithm-Search space

• Starting with a subset of n randomly chosen solutions from the search space (i.e. chromosomes). This is the population

• This population is used to produce a next generation of individuals by reproduction

• Individuals with a higher fitness have more chance to reproduce (i.e. natural selection)

Genetic algorithm-Basic algorithm

START : Create random population of n chromosomes

1 FITNESS : Evaluate fitness f(x) of each chromosome in the population

2 NEW POPULATION

0 SELECTION : Based on f(x)

1 RECOMBINATION : Cross-over chromosomes

2 MUTATION : Mutate chromosomes

3 ACCEPTATION : Reject or accept new one

3 REPLACE : Replace old with new population: the new

generation

4 TEST : Test problem criterium

5 LOOP : Continue step 1 – 4 until criterium is satisfied

Genetic Algorithm-Basis algorithm

• Outline of basis algorithm

• Chromosomes are encoded by bitstrings

• Every bitstring therefore is a solution but not necisseraly the best solution

• The way bitstrings can code differs from problem to problem

Genetic Algorithm-Coding

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Recombination (cross-over) can when using bitstrings schematically be represented:

Using a specific cross-over point

Genetic Algorithm-Coding

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• Mutation prevents the algorithm to be trapped in a local minimum

• In the bitstring approach mutation is simpy the flipping of one of the bits

Genetic Algorithm-Coding

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• Both recombination and mutation depend a lot on the exact definition of the problem and the choice of representing the chromosomes (e.g. no bitstrings)

• Different encodings can be used:

• Binary encoding

• Permutation encoding

• Value encoding

• Tree encoding

• Focus in this presentation stays with binary encoding

Genetic Algorithm-Coding

We require small finger and long feet.Gene are encoded as first two gene represent finger

characteristic and other two represent feet characteristic.We have population size four. Here 0 represent small and 1 represent longIdeal gene:

Example

0 0 1 1

1 0 0 00 1 0 0

0 1 0 1 0 0 1 0

A B

C D

Now fitness:

We apply crossover and mutation for optimum sol.

Example

Name Fitness

A 1

B 1

C 2

D 3

Crossover:

Example

Name Received gene

Genome Fitness

A’ A(0,1)+D(1,0)

A’(0,1,1,0) 2

B’ B(1,0)+D(1,0)

B’(1,0,1,0) 2

C’ D(0,0)+C(0,1)

C’(0,0,0,1) 3

D’ D D’(0,0,1,0) 3

Mutation:

Example

Name Gene Genome Fitness

A’ A’(0,1,1,0) A’’(0,0,1,0) 3

B’ B’(1,0,1,0) B’’(1,0,1,1) 3

C’ C’(0,0,0,1) C’’(0,0,1,1) 4

D’ D’(0,0,1,0) D’’(0,0,1,0) 3

Find a tour of a given set of cities so that • each city is visited only once• the total distance traveled is minimized

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

1) London 3) Dunedin 5) Beijing 7) Tokyo

2) Venice 4) Singapore 6) Phoenix 8) Victoria

CityList1 (3 5 7 2 1 6 4 8)

CityList2 (2 5 7 6 8 1 3 4)

Example(Travel salesman problem)

Representation

Crossover combines inversion and recombination:

Parent1 (1 2 3 4 5 6 7 8 9)

Parent2 (9 3 7 8 2 6 5 1 4)

Child (9 3 2 4 5 6 7 1 8)

This operator is called the partial crossover.

Example(Travel salesman problem)

Crossover

Mutation involves reordering of the list:

* *Before: (9 3 2 4 5 6 7 1 8)

After: (9 3 2 7 5 6 4 1 8)

Example(Travel salesman problem)

Mutation

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TSP Example: 30 cities

TSP Example: 30 cities Solution (Distance = 941)

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TSP30 (Performance = 941)

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TSP30 (Performance = 652)

TSP Example: 30 citiesSolution (Distance = 652)

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TSP30 Solution (Performance = 420)

TSP Example: 30 citiesBest solution(Distance = 420)

Concept is easy to understand

Supports multi-objective optimization

Good for “noisy” environments

Answer gets better with time

Inherently parallel; easily distributed

Advantages of Genetic algorithms

Genetic algorithm applications in controls which are

performed in real time are limited because of random

solutions and convergence.

Certain optimisation problems (they are called variant

problems) cannot be solved by means of genetic algorithms. This occurs due to poorly known fitness functions

Disadvantage of Genetic algorithm

Management ApplicationsSchedulingControl VLSI DesignIdentification & Pattern recognition

Application of GA

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