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-Point11001011+11011111 = 11001111
– Multi-Point
– Uniform– Arithmetic
11001011 + 11011111 = 11001001 (AND)
• Multi Children
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
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 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
Genetic Programming (2/4)initial population
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
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 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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