Genetic Algorithms

Introduction to
Genetic Algorithms

Karthik S
Undergraduate Student (Final Year)
Department of Computer Science and Engineering
National Institute of Technology, Tiruchirappalli

What is GA?
DARWINIAN SELECTION:
From a group of individuals the best will survive

Understanding a GA means understanding the simple, iterative processes that
underpin evolutionary change

GA is an algorithm which makes it easy to search a large search space

EXAMPLE: finding largest divisor of a big number

By implementing this Darwinian selection to the problem only the best
solutions will remain, thus narrowing the search space.

EVOLUTIONARY COMPUTING – BIOLOGY PERSPECTIVE
Origin of species from a common descent and descent of species, as well as
their change, multiplication and diversity over time.

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Where GAs can be used?
OPTIMIZATION:
Where there are large solutions to the problem but we have to find
the best one.
 best moves in chess
 mathematical problems
 financial problems

DISADVANTAGES
 GAs are very slow.
 They cannot always find the exact solution but they always find
best solution.

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Biological Background
 Chromosome: A set of genes. Chromosome contains the solution in
form of genes.
 Gene: A part of chromosome. A gene contains a part of solution. It
determines the solution. E.g. 16743 is a chromosome and 1, 6, 7, 4 and
3 are its genes.
 Individual: Same as chromosome.
 Population: No of individuals present with same length of
chromosome.
 Fitness: Fitness is the value assigned to an individual. It is based on
how far or close a individual is from the solution. Greater the fitness
value better the solution it contains.
 Fitness function: Fitness function is a function which assigns fitness
value to the individual. It is problem specific.
 Selection: Selecting individuals for creating the next generation.
 Recombination (or crossover): Genes from parents form in some way
the whole new chromosome.
 Mutation: Changing a random gene in an individual.

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General Algorithm of GA

START

Generate initial population.
Assign fitness function to all individuals.

DO UNTIL best solution is found

Select individuals from current generation
Create new offsprings with mutation and/or breeding
Compute new fitness for all individuals
Kill all unfit individuals to give space to new offsprings
Check if best solution is found

LOOP

END

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Selection
 Darwinian Survival of The Fittest
 More preference to better guys
 Ways to do:
◦ Roulette Wheel
◦ Tournament
◦ Truncation
 By itself, pick best

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Recombination (crossover)
 Combine bits and pieces of good parents
 Speculate on new, possibly better children
 By itself, a random shuffle

Given two chromosomes

10001001110010010
01010001001000011

Choose a random bit along the length, say at position 9, and swap all the
bits after that point

so the above become:

10001001101000011
01010001010010010

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Mutation
 Mutation is random alteration of a string
 Change a gene, small movement in the neighbourhood
 By itself, a random walk

Before: 10001001110010010

After: 10000001110110010

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Improvement / Innovation

IMPROVEMENT:

Selection Mutation

Local changes - hill climbing

INNOVATION:

Selection Recombination

Combine notions - invent

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Encoding
“Coding of the population for evolution process”

BINARY ENCODING:

Chromosome A 011010110110110101
Chromosome B 101001010100101001

PERMUTATION ENCODING:

Chromosome A 12345678
Chromosome B 83456127

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Example
The travelling salesman problem

Find a tour of given set of cities so that:
 each city is visited only once
 the total distance travelled is minimized

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TSP – Coding for 8 cities
Encoding using permutation encoding
1. Chennai 2. Trichy 3. Thanjavur 4. Madurai
5. Bangalore 6. Hyderabad 7. Coimbatore 8. Cochin

City Route 1: (12347856)
City Route 2: (65872134)

CROSSOVER:
(12347856)
(12346587)
(31246587)

MUTATION:
(12346587) (12846537)

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TSP – GA Process
 First, create a group of many random tours in what is called a
population. This algorithm uses a greedy initial population that
gives preference to linking cities that are close to each other.
 Second, pick 2 of the better (shorter) tours parents in the
population and combine them to make 2 new child tours.
Hopefully, these children tour will be better than either parent.
 A small percentage of the time, the child tours are mutated. This is
done to prevent all tours in the population from looking identical.
 The new child tours are inserted into the population replacing two
of the longer tours. The size of the population remains the same.
 New children tours are repeatedly created until the desired goal is
reached.

Survival of the Fittest

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TSP – GA Process – Issues (1)
The two complex issues with using a Genetic Algorithm to solve the
Traveling Salesman Problem are the encoding of the tour and the crossover
algorithm that is used to combine the two parent tours to make the child
tours.

In this example, the crossover point is between the 3rd and 4th item in the
list. To create the children, every item in the parent's sequence after the
crossover point is swapped.

Parent 1 F A B | E C G D
Parent 2 D E A | C G B F
Child 1 F A B | C G B F
Child 1 D E A | E C G D

What is the issue here ???

We get invalid sequences as children

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TSP – GA Process – Issues (2)
The encoding cannot simply be the list of cities in the order they are
travelled. Other encoding methods have been created that solve the
crossover problem. Although these methods will not create invalid tours,
they do not take into account the fact that the tour "A B C D E F G" is the
same as "G F E D C B A". To solve the problem properly the crossover
algorithm will have to get much more complicated.

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Other Examples
THE MAXONE PROBLEM

• Suppose we want to maximize the number of ones in a string of l binary
digits

• We can think of it as maximizing the number of correct answers, each
encoded by 1, to l yes/no difficult questions

THE TARGET NUMBER PROBLEM

• Given the digits 0 through 9 and the operators +, -, * and /, find a
sequence that will represent a given target number. The operators will
be applied sequentially from left to right as you read.

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GA in Data Mining
• Used in Classification

EXAMPLE:

• Two Boolean attributes, A1 and A2, and two classes, C1 and C2

• IF A1 AND NOT A2 THEN C2
100
• IF NOT A1 AND NOT A2 THEN C1
001

• If an attribute has k values, where k > 2, then k bits may be used
to encode the attribute’s values.
• Classes can be encoded in a similar fashion.

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Classification Problem
• Associating a given input pattern with one of the distinct classes
• Patterns are specified by a number of features (representing
some measurements made on the objects that are being
classified) so it is natural to think of them as d-dimensional
vectors, where d is the number of different features
• This representation gives rise to a concept of feature space
• Classification - determining which of the regions a given pattern
falls into
• A decision rule determines a decision boundary which partitions
the feature space into regions associated with each class
• The goal is to design a decision rule which is easy to compute and
yields the smallest possible probability of misclassification of
input patterns from the feature space.

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Classification Problem - samples

classification

An overly classified decision boundary

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Discriminant Function
• Training set - finite sample of patterns with known class affiliations
• Use training sets to create decision boundaries
• Avoid over-fitting a training set by creating overly complex decision
boundaries
• Simplify the shape of the decision boundary which will, by
sacrificing performance on the training samples, improve the
performance on new patterns
• Different classifiers can be implemented by constructing an
appropriate discriminant function gi(x), where i is the class index. A
pattern x is associated with the class j such that gj(x)>gi(x) for every
i not equal to j

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A Linear Discriminant Function
• Linear discriminant function limits to two distinct classes
• f(x) = ω + ω+1
=1
where xi are the components of the feature vector and the
weights need to be adjusted to optimize the performance of
the classifier
HOW TO USE GA FOR CLASSIFICATION AND FINDING THE OPTIMAL
WEIGHTS

• In genetic algorithms, classification problem reduces to finding the
parameters of the optimum discriminant function defining the
boundary between classes
• Each chromosome has a number of genes equal to the number of
parameters used in the discriminant function
• The fitness function is the fraction of patterns properly classified by
applying the discriminant function parameterized by the
chromosome to a given testing set
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Advantages of GA
• Concepts are easy to understand
• Genetic Algorithms are intrinsically parallel.
• Always an answer; answer gets better with time
• Inherently parallel; easily distributed
• Less time required for some special applications
• Chances of getting optimal solution are more

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Limitations of GA
• The population considered for the evolution should be moderate
or suitable one for the problem (normally 20-30 or 50-100)
• Crossover rate should be 80%-95%
• Mutation rate should be low i.e. 0.5%-1% assumed as best
• The method of selection should be appropriate
• Writing of fitness function must be accurate

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Conclusion
• Genetic algorithms are rich in application across a large and
growing number of disciplines.
• Genetic Algorithms are used in Optimization and in Classification
in Data Mining
• Genetic algorithm has changed the way we do computer
programming.

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Genetic Algorithms

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Genetic Algorithms