genetic algorithms and genetic programming ehsan khoddam mohammadi
TRANSCRIPT
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GENETIC ALGORITHMS AND GENETIC
PROGRAMMING
Ehsan Khoddam Mohammadi
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DEFINITION OF THE GENETIC ALGORITHM (GA)
The genetic algorithm is a probabilistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation.
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Biological Background
• Chromosome (Genome)• Genes• Proteins (A T G C)• Trait• Allele• Natural Selection (survival of fittest)
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GA FLOWCHART
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Which problems could be solved by GA?
• Nonlinear dynamical systems - predicting, data analysis • Designing neural networks, both architecture and
weights • Robot trajectory • Evolving LISP programs (genetic programming) • Strategy planning • Finding shape of protein molecules • TSP and sequence scheduling • َ�All Optimization Problems (Knapsack,Graph coloring,
…)
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GA Operations
• Encodings• Initiate Population• Selection• Reproduction• Crossover (sexual reproduction)• Mutation
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GA Operations (Cont.)ENCODING(1/3)
• Fixed-Length encoding– 1D encoding: arrays, lists, strings,…– 2D encoding: matrices,graphs
• Variable-Length encoding– Tree encoding: binary parser trees like
postfix,infix,…
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GA Operations (Cont.)ENCODING (2/3)
• Permutation Encoding :– Map Coloring problem , TSP,…– Array in size of regions, each cell has an integer
corresponding to available colors.R=1 G=2 B=3 W=4
• Binary Encoding:– Knapsack problem, equation solving ()
Chromosome A 101100101100101011100101 Chromosome B 111111100000110000011111
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GA Operations (Cont.)ENCODING (3/3)
• Tree encoding– Genetic programming, finding function of given
values (elementry system identification)
( + x ( / 5 y ) ) ( do_until step wall )
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GA Operations (Cont.)SELECTION (1/3)
• In GA ,the object is to Maximizing or Minimizing fitness values of population of Chromes.
• Fitness Function should be applicable to any Chromes (bounded).
• Mostly a positive number, showing a distance between present state to goal state.
• In NP-Complete or partially defined problems should relatively be computed .
• Two important parameters :– Population diversity (exploring new areas)– Selective pressure ( degree to which better individuals
are favoured)
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GA Operations (Cont.)SELECTION (2/3)
• Roulette Wheel Selection (improved by Ranking) – [Sum] Calculate sum of all chromosome fitnesses in population - sum S. – [Select] Generate random number from interval (0,S) - r. – [Loop] Go through the population and sum fitnesses from 0 - sum s. When the
sum s is greater then r, stop and return the chromosome where you are
• Not suitable for highly variance populations• Using RANK Selection
– The worst will have fitness 1, second worst 2 etc. and the best will have fitness N (number of chromosomes in population).
– Converge Slowly
1 2
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GA Operations (Cont.)SELECTION (3/3)
• Steady-state Selection (threshold)– Fittest just survived
• Elitism– Fittest selected, for others we use other selection
manners• Boltzmann Selection
– P(E)=exp(-E/kT), like SA. Number of selections reduces in order of growing of age
• Tournament Selection
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F.Nitzche
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GA Operations (Cont.)REPRODUCTION(1/1)
• Reproduction rate• Selected gene transfers directly to new
Generation without any change.
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GA Operations (Cont.)CROSSOVER(1/1)
• CROSSOVER rate• Single Child
– Single-Point11001011+11011111 = 11001111
– Multi-Point
– Uniform– Arithmetic
11001011 + 11011111 = 11001001 (AND)
• Multi Children
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GA Operations (Cont.)MUTATION(1/1)
• Mutation rate• Inversion
• Deletion and Regeneration• …
For TSP is proved that some kind of mutation causes to most efficient solution
11001001 => 10001001
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GA EXTENTIONS (part 1)
• GENETIC PROGRAMMING– solve a problem without explicitly programming– Writing program to compute X^2+X+1
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GENETIC PROGRAMMING
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Genetic Programming (1/4)PREPARATORY STEPS
Objective: Find a computer program with one input (independent variable X) whose output equals the given data
1 Terminal set: T = {X, Random-Constants}
2 Function set: F = {+, -, *, %}
3 Fitness: The sum of the absolute value of the differences between the candidate program’s output and the given data (computed over numerous values of the independent variable x from –1.0 to +1.0)
4 Parameters: Population size M = 4
5 Termination: An individual emerges whose sum of absolute errors is less than 0.1
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Genetic Programming (2/4)initial population
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Genetic Programming (3/4)FITNESS OF THE 4 INDIVIDUALS IN GEN 0
x + 1 x2 + 1 2 x
0.67 1.00 1.70 2.67
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GENETIC PROGRAMMING (4/4)
Copy of (a)
Mutant of (c) picking “2” as mutation point
First offspring of crossover of (a) and (b) picking “+” of parent (a) and left-most “x” of parent (b) as crossover points
Second offspring of crossover of (a) and (b) picking “+” of parent (a) and left-most “x” of parent (b) as crossover points
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REPRESENTATIONS
• Decision trees• If-then production
rules• Horn clauses• Neural nets• Bayesian
networks• Frames• Propositional logic
• Binary decision diagrams
• Formal grammars • Coefficients for
polynomials• Reinforcement
learning tables• Conceptual clusters • Classifier systems
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GA EXTENTIONS (part 2)
• Multi Modal GA• SOCIAL MODEL: religion based• Hybrid Methods ( associate with FL and ANN)• …
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REFRENCES• Neural Networks, Fuzzy Logic and Genetic
Algorithms ,Synthesis and ApplicationsS.RajasekaranG.A.Vijayalakshmi PaiPSG College of Technology,Coimbatore
• http://www.smi.stanford.edu/people/kozaDoctor John R. Koza Department of Electrical EngineeringSchool of EngineeringStanford UniversityStanford California 94305
• http://cs.felk.cvut.cz/~xobitko/ga/Marek Obitko, [email protected]
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