Upload
hilary-nicholson
View
232
Download
0
Tags:
Embed Size (px)
Citation preview
Memetic Algorithms
ByAnup Kulkarni(08305045)Prashanth K(08305006)
Instructor: Prof. Pushpak Bhattacharyya
Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
2
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
3
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
4
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
6
Biological Evolution Cultural
Evolution..??
Source: www.wikipedia.org
Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
7
Biological Evolution Meme..!!!
Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
8
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
10
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
11
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
12
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
14
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
17
Solving the Traveling salesman problem with a
Memetic Algorithm
Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
18
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
19
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
20
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
21
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
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
23
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
24
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
25
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
26
?
Anup Kulkarni and Prashanth K, Dept of CSE, IIT Bombay
27
Thank you!