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Gene Expression Programming: A New Adaptive Algorithm for Solving Problems

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Title: Gene Expression Programming: A New Adaptive Algorithm for Solving Problems


1
Gene Expression Programming A New Adaptive
Algorithm for Solving Problems
  • Vincent Chan
  • System Electronics Lab.
  • Seoul National University

2
Contents
  • Introduction
  • Overview of Gene Expression Algorithm
  • The genome of GEP individuals
  • Fitness functions and selection
  • Reproduction with modification
  • Example
  • Conclusion

3
Introduction to GEP
  • Similarities with GA,GP
  • Using populations of individuals
  • Seleting individuals accoding to fitness
  • Introduces genetic variation using
  • Genetic Operatrs.
  • Solving searching, sorting and etc. problems

4
Introduction to GEP
  • Difference among GEP,GA,GP resides in the nature
    of the individuals
  • Individuals
  • GA Linear strings of fixed length/Array of bits
  • GP Nonlinear entities of different sizes and
    shapes (Parse trees)/Tree-like representations
  • GEP
  • Encoded as linear strings of fixed length
  • Genome or chromosomes
  • Expressed as nonlinear entities of different size
    and shapes
  • Simple diagram representations or expression
    trees

5
Introduction to GEP
  • Advantages of GEP
  • Truly functional genotype/phenotype relationship
  • Enabled by GEP chromosomes organization
  • Translation from language of chromosomes to
    languages of ET(Expression trees)
  • Translation from genotype to phenotype

6
Overview of GEA
Create Chromosomes of initial Population
Replication
Mutation
IS transposition
Express Chromosomes
RIS transposition
Evaluate Fitness
1-point Recombination
Iterate or Terminate
End
2-point Recombination
Gene Recombination
Keep Best Program
Prepare New Programs of Next Generation
Select Programs
7
The genome of GEP individuals
  • Open reading frames and genes
  • Gene expression programming genes
  • Multigenic chromosomes
  • Expression trees and the phenotype
  • Information decoding translation
  • Interactins of sub-expression trees

8
Open Reading frames and genes
  • Structural Organization of GEP
  • Apply the biology idea
  • Gene begins with Start codon
  • Continues with amino acid codons
  • Ends at termination codons

9
Codon sequence and codon table
10
Example of ORFs
Algebraic Expression
Expression Tree (ET)
Genotype
11
GEP genes
  • A head and a tail
  • Head
  • Contains symbols representing both functions and
    terminals
  • Tail
  • Contains only terminals
  • Function
  • Elements from function set F
  • Terminal
  • Elements from the terminal set T

12
GEP genes
Tail
Head
Expression Tree (ET)
13
Multigenic chromosomes
  • More than one gene of equal length in GEP
    chromosomes
  • Sub-Ets

14
Expression trees and the phenotype
  • Information decoding translation
  • Interactons of sub-expression trees

15
Information decoding Translation
  • Expression of geneti information starts from
    translation
  • Transfer from a gene into an ET
  • In GEP gene--gtET is done directly
  • Single gene organism of gene
  • GEP chromosomes are composed of one or more ORFs
  • Single ET Multi-subunit ET
  • The whole organism is encoded in a linear genome.

16
Interactions of sub-expression trees
A Two-genic chromosome
Sub-Ets codified by each gene
The result of posttranslational linking
17
Fitness functions
  • Fitness functions
  • Symbolic regression/function finding is an
    improtant application of GEP
  • To find an expression that performs well for all
    fitness cases within a certain eror of the
    correct value.
  • Limit the range of selection to control the
    population of the result
  • How to decide the range/limitation?

18
Fitness functions
  • Best possible solution
  • With in a minimum error
  • A board limit for selection (20)
  • For evolutionary to get started
  • Then it could be reshaped by seletion and
    populations adaption
  • Finding better solutions --gt perfect solution

19
Selection (Same as GA)
  • Selecting individuals
  • According to fitness
  • By roulettewheel sampling Goldberg 1989
  • Or tournament selection
  • No scheme is perfect for any problem
  • Conclusion from the paper
  • For more complex problems it seems that
    roulettewheel selection with elitism is best

20
Reproduction with modification
  • Using result from fitness and selection
  • Reproduce with modification
  • Replication
  • Mutation
  • Transpositon and insertion sequence elements
  • Transpositon of insertion sequence elements
  • Root transposition
  • Recombination
  • One-point recombination
  • Two-point recombination

21
Examples of GEP in problem solving
  • Symbolic regression
  • Sequence inducton and th creation of constants
  • Block stacking
  • Evolving cellular automata rules for the
    density-classification problem
  • Boolean concept learing

22
Conclusions
  • Detailed implementation of GEP is explained
  • It could be applied in several different fields
    with advantage of running efficiently in a PC
  • GEP offers more opportunities for soloving more
    complex problems
  • Organization of chromosomes is originally
    introduced
  • GEP could present nature more faithfully(?), so
    it could be used as computer models of natural
    evolutionary processes.

23
  • Thank You!
  • ?????!
  • ????!
  • ???!
  • Danke schön!
  • C?m on!
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