GENETIC ALGORITHMS AND GENETIC PROGRAMMING

Ehsan Khoddam Mohammadi

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.

Biological Background

• • • • • • Chromosome (Genome) Genes Proteins (A T G C) Trait Allele Natural Selection (survival of fittest)

GA FLOWCHART

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,…)

GA Operations

• • • • • • Encodings Initiate Population Selection Reproduction Crossover (sexual reproduction) Mutation

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,…

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

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 )

• • • • • 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)

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

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

F.Nitzche

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

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

GA Operations (Cont.) MUTATION(1/1) • • Mutation rate Inversion • • 11001001 => 10001001 Deletion and Regeneration … For TSP is proved that some kind of mutation causes to most efficient solution

GA EXTENTIONS (part 1)

• GENETIC PROGRAMMING – solve a problem without explicitly programming – Writing program to compute X^2+X+1

GENETIC PROGRAMMING

Genetic Programming (1/4) PREPARATORY STEPS

Objective: Find a computer program with one input (independent variable X ) whose output equals the given data

1 2 3

Terminal set: Function set: Fitness: T = {X, Random-Constants} F = {+, -, *, %} The sum of the absolute value of the differences between independent variable

x

the candidate program’s output and the given data (computed over numerous values of the from –1.0 to +1.0)

4

Parameters: Population size

M

= 4

Genetic Programming (2/4) initial population

Genetic Programming (3/4) FITNESS OF THE 4 INDIVIDUALS IN GEN 0

x

+ 1 0.67

x

2 + 1 1.00

2 1.70

x

2.67

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

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

GA EXTENTIONS (part 2)

• • • • Multi Modal GA SOCIAL MODEL: religion based Hybrid Methods ( associate with FL and ANN) …

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, [email protected]

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