Grammatical Evolution : Evolving Programs for an Arbitrary Language

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Grammatical Evolution Evolving Programs for an
Arbitrary Language

• C.Ryan, JJ Collins, M.O.NeillPresentation by
  Taeyoung Jeong

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Contents

• Backus Naur Form(BNF)
• Genetic Algorithm for Developing Software (GADS)
• Problems of GADS
• Review of GA
• Grammatical Evolution(GE)
• Examples

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Backus Naur Form(BNF)

• Notation forexpressing the grammar of a language
  in the form of production rules.
• Consists of terminals T, non-terminals N,
  starting symbol S, production rule P.

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BNF Example

• Nexpr,op,pre_op,varTsin,cos,tan,log,,-,,/,
  (,),XSltexprgt
• ltexprgtltexprgtltopgtltexprgt ( ltexprgt )
  ltpre_opgt ( ltexprgt ) ltvargt
• ltopgt , -, , /
• ltvargt X
• ltpre_opgtsin cos tan log

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Genetic Algorithm for Developing Software (GADS)

• Described in Evolving Caching Algorithms in C by
  GP by N.Paterson
• Uses linear chromosome, and each gene means an
  production rule applied.

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GADS by Example

• ltexprgtltexprgtltopgtltexprgt 0 ( ltexprgt ) 1
  ltpre_opgt ( ltexprgt ) 2 ltvargt 3
• ltopgt , -, , / 4,5,6,7
• ltvargt X 8
• ltpre_opgtsin cos 9,10 tan
  log 11,12 13 rules

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GADS Example continued

• Gene 156, 42, 112, 199, 250, 21 becomes 0, 3,
  8, 4, 3, 8 (by modular 13)
• ltexprgt ltexprgt ltopgt ltexprgt 0 ltvargt ltopgt
  ltexprgt 3 X ltopgt ltexprgt 8 X
  ltexprgt 4 X ltvargt 3 X X 8

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Problems of GADS 1

• After resolving chromosome, what if the
  non-terminal exists?ltexprgtltexprgtltopgtltexprgt....
  . XXXXXltopgtltexprgt applies default
  rule, like ltopgt, but unfortunate or misguided
  choice could harm the evolution.

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Problems of GADS 2

• There are several dont care symbols, that is,
  the rules that cannot be applied.
• S ltexprgt ?--- ltvgtx (?)
  ltexprgt ?--- ltegtltegtltogtltegt ltexprgtltopgtltexprgt
  ?- ltogt (?) ltexprgtltopgtltexprgt

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Dramatic Error Fair?

• ltvgtXltegtltegtltogtltegtltegtltvgtltvgtXltogtltegtltvgtltv
  gtX
• S gt XX

• ltegtltvgtltegtltegtltogtltegtltegtltvgtltvgtXltogtltegtltvgt
  ltvgtX
• S gt ltvgtby default rule, SX

• Dont care symbols mean nothing, but still
  important for resolving(?)

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Review of GA Representation

• Path representation chromosome describes the
  sequence
• ex) 3?1?4?7?5?2?6 (for TSP, or Job
  Processing)- only the relative position matters.

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Review of GA Representation

• Ordinal representation chromosome describes the
  number of position for each element.
• ex) 2, 6, 1, 3, 5, 7, 4 (12nd,26th,31st,43rd,
  55th,67th,74th) (for TSP, or Job
  Processing)- The gene and its place are both
  matters.

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Concept Protein Model

• What if, each gene means the rules actually
  applied? The position of each gene has
  meaning.
• What if, each gene can have a meaning for any
  choice of rules? No dont care symbol.

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Concept Protein Model

• A protein can be used in several cells or organs,
  but the use of it can be different place to
  place.(fat can be in the brain, in the
  stomach...)
• A gene can be placed in several places in
  chromosome, but the use of it can be different
  place to place.

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Grammatical Evolution(GE) Example

• If the first unresolved non-terminal symbol is
  ltexprgt, the gene means one of the following
  rules.ltexprgtltexprgtltopgtltexprgt 0 ( ltexprgt
  ) 1 ltpre_opgt ( ltexprgt ) 2 ltvargt 3

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GE example contd.

• ltopgt , -, , / for 0,1,2,3
• ltpre_opgtsin,cos,tan,log for 0,1,2,3
• ltvargt X is trivial no genes needed

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GE example contd.

• We got gene 156, 42, 112, 199, 250, 21
• Sltexprgt gene 1560(mod 4) ltegtltegtltogtltegt
• Sltegtltogtltegt gene 422(mod 4) ltegtltpgt(ltegt)
• Sltpgt(ltegt)ltogtltegt gene 1122(mod 4) ltpgttan
• Stan(ltegt)ltogtltegt gene 1993(mod 4) ltegtltvgtX

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GE example contd.

• We got gene 156, 42, 112, 199, 250, 21
• Stan(X)ltogtltegt gene 2502(mod 4) ltogt
• Stan(X)ltegt gene 211(mod 4) ltegt(ltegt)
• Stan(X)(ltegt) .....huh?

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What if we got non-terminal?

• Resolve it by default rules(same error!)
• Consider the gene invalid, putting HARD
  penalties on it.
• Reuse the genes read the genes again, and
  resolve it until it finishes. (or hits TO)Each
  gene generates the same protein, but the effect
  of that protein can be different, depending on
  where it is.

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GE in GA view

• In schema theorem, the shorter the schema is,
  the more possible it can alive while crossover.
• GE makes the chromosome more simple and short,
  decreasing the distance between the product
  rules. ? easy to survive!

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Operator Duplicate()

• Making a copy of a gene or genes.
• New gene can be placed next to the original gene,
  or the very different place.
• AOOOOOO if we duplicate O (eeoe, eO,
  o)AOOOOOOO

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Operator Prune() Introns
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Operator Prune()

• Too many introns GE dont necessarily use all
  the genesex) XXX uses 5 genes only
• Introns are also participate in crossover and
  mutation, and blocks the useful genes to be
  changed.
• Prune() is applied with a probability to any
  individuals, making it discard all its introns.

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Example Interpolation Problem
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Example Interpolation Problem
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Wrapper
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Results

• GE consistently discovered target function when
  both duplicate(), prune() employed.
• Tend to fixate on curve operators as sin(),
  exp(), as these gene rated a curve similar to the
  target function.
• Space constraint matters.
• Biasing individuals can help to find a shorter,
  effective solution.

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Conclusion

• GE has similar structures and aims to those of
  GP.
• GE has closer biological analogies to the nature
  than GP.
• Using BNF notation, GE can be used in multi-line
  function.