Pushpak Bhattacharyya CSE Dept., IIT Bombay 8 th , 10 th March , 2011
Memetic Algorithms By Anup Kulkarni(08305045) Prashanth K(08305006) Instructor: Prof. Pushpak...
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Transcript of Memetic Algorithms By Anup Kulkarni(08305045) Prashanth K(08305006) Instructor: Prof. Pushpak...
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Memetic Algorithms
ByAnup Kulkarni(08305045)Prashanth K(08305006)
Instructor: Prof. Pushpak Bhattacharyya
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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
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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.
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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
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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
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Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
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Biological Evolution Cultural
Evolution..??
Source: www.wikipedia.org
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Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
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Biological Evolution Meme..!!!
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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
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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!!!
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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
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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
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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.
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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
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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
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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
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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)
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Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
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Solving the Traveling salesman problem with a
Memetic Algorithm
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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
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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
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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”
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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
6
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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)
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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
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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
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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
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Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
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?
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Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
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Thank you!