Memetic Algorithms

ByAnup Kulkarni(08305045)Prashanth Kamle(08305006)

Instructor: Prof. Pushpak Bhattacharyya

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Overview

Philosophy Behind Memetics Genetic Algorithm – Intuition and Structure Genetic Algorithm Operators Memetic Algorithms

TSP Using Memetic Algorithm

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Genes and biological evolution

A gene is a unit of biological information transferred from one generation to another.

Genes determine our physical traits, what you look like, what you inherit from either one of your parents.

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Biological Evolution

• Natural Selection

• Survival of The Fittest

• Origin of New Species

Examples of Biological Evolution and Natural

AdaptationGills in Pisces

Frog Skin

Hollow Bones in Birds

Biological Evolution of Human• Characteristic Thumb

• Erect Vertebral Column

• Lower Jaw

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Biological Evolution Cultural

Evolution..??

Source: www.wikipedia.org

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Biological Evolution Meme..!!!

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Meme

“the basic unit of cultural transmission, or imitation”

- Richard Dawkins

“an element of culture that may be considered to be passed on by non-genetic means”

- English Oxford Dictionary

Examples of Meme

FashionLatest trends are ideas of fashion designers

ScienceScientists sharing their thoughts

LiteratureNovel, poetry

MusicEven birds are found to imitate songs of other birds!!!

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Genes and Memes, where they are similar

Genes propagate biologically from chromosome to chromosome

Memes propagate from brain to brain via imitation

Survival of fittest in meme Concept of God is survived though no scientific

evidence is present

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Genes and Memes, where they differ

Genes are pre-decided Genes are static through generations, memes

can be changed! Memes allow improvement

After learning language, we contribute to it through literature

New heuristics to 8-puzzle problem solved in class We use this property to improve genetic

algorithms

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Genetic Algorithm

solves (typically optimization) problems by combining features of complete solutions to create new populations of solutions.

applicable when it is hard or unreasonable to try to completely identify a subproblem hierarchical structure or to approach the problem via an exact approach.

Genetic Algorithm

Initialize population PopInitialize population Pop

Return the best solution in PopReturn the best solution in Pop

While not stop criterion do

While not stop criterion do

Evaluate PopEvaluate Pop

Evaluate PopEvaluate Pop

Recombine Parents Recombine Parents

Select Parents from PopSelect Parents from Pop

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Crossover

Purpose: to combine features of feasible solutions already visited in order to provide new potential candidate solutions with better objective function value.

Mechanism that restarts the search by “exploring” the space “between” solutions.

offspringparents

0 0 0 0 0 0 0

1 1 1 1 1 1 1

0 0 0 1 1 1 1

1 1 1 0 0 0 0

Mutation

■ Purpose: to introduce new characteristics in the population by random modifications.

■ Explores the “neighborhood” of a solution.

mutated gene value

1 1 1 1 1 1 1 before

1 1 1 0 1 1 1 after

Memetic Algorithm

Initialize population PopInitialize population Pop

Return the best solution in PopReturn the best solution in Pop

While not stop criterion do

While not stop criterion do

Evaluate PopEvaluate Pop

Evaluate PopEvaluate Pop

Recombine Parents Recombine Parents

Select Parents from PopSelect Parents from Pop

Optimize Pop(Local search)Optimize Pop(Local search)

Optimize Pop(Local search)Optimize Pop(Local search)

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Solving the Traveling salesman problem with a

Memetic Algorithm

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Memetic Algo for TSP-representation

Array pop stores population Size of pop=P No of cities=N Tour represented as 1234....N Fitness function-cost of the tour

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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TSP - Crossover

Distance Preserving Crossover

d(p1,p2) = d(p1,child) = d(p2,child)

d(x, y) = #edges not common in x and y

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Distance Preserving Crossover

Source: B. Freisleben et al, “New Genetic Local Search Operators for the Traveling Salesman Problem”

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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2-OPT Search

Delete any two edges Insert other two edges which will result in

new tour 1

3

2

5

4

6

1

2

3

4

5

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Memetic AlgorithmInitialize population PopInitialize population Pop

Return the best solution in PopReturn the best solution in Pop

While not stop criterion do

While not stop criterion do

Evaluate PopEvaluate Pop

Evaluate PopEvaluate Pop

Recombine Parents Recombine Parents

Select Parents from PopSelect Parents from Pop

Optimize Pop(Local search)Optimize Pop(Local search)

Optimize Pop(Local search)Optimize Pop(Local search)

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Performance

Source: Slides of A.E. Eiben and J.E. Smith, Introduction to Evolutionary ComputingHybridisation with other techniques: Memetic Algorithms

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Conclusion

A genetic algorithm promises convergence but not optimality.

But we are assured of exponential convergence, possibly at different optimal chromosomes.

Do very well in identifying the regions where those optima lie.

Optimal solution=Genetic Algo + Local Search

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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References

R. Dawkins, “The Selfish Gene – new edition”, Oxford University Press, 1989 pp 189-201

David E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1st edition, Addison-Wesley Longman Publishing Co., 1989 pp 170-174

B. Freisleben and P. Merz, New Genetic Local Search Operators for the Traveling Salesman Problem. In H.-M. Voigt, W. Ebeling, I. Rechenberg, and H.-P. Schwefel, editors, Proceedings of the 4th Conference on Parallel Problem Solving from Nature - PPSN IV, pages 890--900. Springer, 1996

S. Lin and B. W. Kemighan, An effective heuristic algorithm for the Traveling Salesman problem, Operation Research 21 (1973) 498-516

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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?

Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay

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Thank you!