Grammer Modelbased Program Evolution

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Grammer Model-based Program Evolution

• Shan Yin et al

KIM KANG IL
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Contents

• Introduction
• Model
• Experiments
• Discussion
• Conclusion

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Introduction

• Keep the building block from mutation or
  crossover
• Building block have useful information for
  finding a solution EDA
• Propose a model using the GP-style tree
  representation against conventional GA-style
  linear representation
• Stochastic context free Grammar model represents
  the building blocks

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Model

• Flow diagram

Evaluate and select
Sample SCFG Model to Obtain new Population
Learn SCFG model from the selected individual
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1 step Evaluate and select

• Give initial randomly chosen population
• On population , calculate the fitness for each
  individuals by the defined function
• find the one individual which have the best
  fitness value specification

S
R1(Exp)
R2(Exp)
R3(A)
R4(B)
R5(C)
R6(B)
R7(B)
S -gt R1(Exp) R2(Exp) R1(Exp) -gt R3(A)
R4(B) R2(Exp) -gt R5(C) R6(B) R7(B)
S -gt Exp Exp -gt A B C B B
Initial grammar
Changed grammar by initial individual
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2 step learn the model

• Use stochastic context free grammar
• Give probability for each production
• The sum of probability of Productions which have
  same LHS is 1
• The probability of productions which are used in
  elitist increase

S -gt R1(Exp) 0.5 R2(Exp) 0.5 R1(Exp) -gt
R3(A) R4(B) 1 R2(Exp) -gt R5(C) R6(B) R7(B) 1
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S -gt R1(Exp) R2(Exp) R1(Exp) -gt R3(A)
R4(B) R2(Exp) -gt R5(C) R6(B) R7(B)

• Problem just specification make the model
  converge to local minimum
• We have to give a process to generalize
• Merge the productions -generalization
• Find the smallest grammar MML

Merge R1 , R2
S -gt R1(Exp) R1(Exp) -gt R3(A) R4(B) -gt R5(C)
R6(B) R7(B)
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3 step - sample the model

• Through the probability table of the selected
  grammar, we generate new population

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Experiments

• Royal tree problem
• The arity is increased by 1 for each depth
• In this experiment, maximum depth is 6
• Terminal x
• Nonterminal a,b,c,d,e
• The fitness is 50 runs

• resemblance between perfect tree

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• Max problem
• Operator x,
• Terminal x
• Finding maximum value
• Depth limit to 7
• Maximum fitness is 65536
• 50runs

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Discussion

• Internal structure representation
• Parent child dependency
• Structural representation
• Locality local dependency with near node

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• Positional independency
• Dependent model PIPE
• Should preserve building block
• Various complexity of model
• Vs PIPE (Fixed model about the number of node or
  depth, etc)
• Fixed model might have a problem for expressing
  the dependency or more complex individuals

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Conclusion

• GMPE is a kind of EDA with GP using stochastic
  grammar
• Grammar can better preserve the building blocks
  than conventional GP