1. GENETIC ALGORITHMS AND GENETIC PROGRAMMING Ehsan Khoddam Mohammadi

2. 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.

3. Biological Background Chromosome (Genome) Genes Proteins (A T G C) Trait Allele Natural Selection (survival of fittest)

4. GA FLOWCHART

5. 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,…)

6. GA Operations Encodings Initiate Population Selection Reproduction Crossover (sexual reproduction) Mutation

7. 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,…

8. 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

9. 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 )

10. 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)

11. 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 12

12. 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

13. F.Nitzche

14. GA Operations (Cont.) REPRODUCTION(1/1) Reproduction rate Selected gene transfers directly to new Generation without any change.

15. GA Operations (Cont.) CROSSOVER(1/1) CROSSOVER rate Single Child – Single-Point 11001011+11011111 = 11001111 – Multi-Point – Uniform – Arithmetic 11001011 + 11011111 = 11001001 (AND) Multi Children

16. 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

17. GA EXTENTIONS (part 1) GENETIC PROGRAMMING – solve a problem without explicitly programming – Writing program to compute X^2+X+1

18. GENETIC PROGRAMMING

19. Genetic Programming (1/4) PREPARATORY STEPS Objective:Find a computer program with one input (independent variable X ) whose output equals the given data 1Terminal set: T = {X, Random-Constants} 2Function set: F = {+, -, *, %} 3Fitness: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) 4Parameters:Population size M = 4 5Termination:An individual emerges whose sum of absolute errors is less than 0.1

20. Genetic Programming (2/4) initial population

21. Genetic Programming (3/4) FITNESS OF THE 4 INDIVIDUALS IN GEN 0 x + 1x 2 + 12x 0.671.001.702.67

22. 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

23. 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

24. GA EXTENTIONS (part 2) Multi Modal GA SOCIAL MODEL: religion based Hybrid Methods ( associate with FL and ANN) …

25. REFRENCES Neural Networks, Fuzzy Logic and Genetic Algorithms,Synthesis and Applications S.Rajasekaran G.A.Vijayalakshmi Pai PSG College of Technology,Coimbatore http://www.smi.stanford.edu/people/koza Doctor John R. Koza Department of Electrical Engineering School of Engineering Stanford University Stanford California 94305 http://cs.felk.cvut.cz/~xobitko/ga/ Marek Obitko, obitko@email.cz

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