Novel Loop Structures and the Evolution of Mathematical Algorithms

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  author =       "Mingxu Wan and Thomas Weise and Ke Tang",
  title =        "Novel Loop Structures and the Evolution of
                 Mathematical Algorithms",
  booktitle =    "Proceedings of the 14th European Conference on Genetic
                 Programming, EuroGP 2011",
  year =         "2011",
  month =        "27-29 " # apr,
  editor =       "Sara Silva and James A. Foster and Miguel Nicolau and 
                 Mario Giacobini and Penousal Machado",
  series =       "LNCS",
  volume =       "6621",
  publisher =    "Springer Verlag",
  address =      "Turin, Italy",
  pages =        "49--60",
  organisation = "EvoStar",
  keywords =     "genetic algorithms, genetic programming",
  isbn13 =       "978-3-642-20406-7",
  DOI =          "doi:10.1007/978-3-642-20407-4_5",
  abstract =     "In this paper, we analyse the capability of GP to
                 synthesise non-trivial, non-approximative, and
                 deterministic mathematical algorithms with
                 integer-valued results. Such algorithms usually involve
                 loop structures. We raise the question which
                 representation for loops would be most efficient. We
                 define five tree-based program representations which
                 realise the concept of loops in different ways,
                 including two novel methods which use the convergence
                 of variable values as implicit stopping criteria. Based
                 on experiments on four problems under three fitness
                 functions (error sum, hit rate, constant 1) we find
                 that GP can statistically significantly outperform
                 random walks. Still, evolving said algorithms seems to
                 be hard for GP and the success rates are not high.
                 Furthermore, we found that none of the program
                 representations could consistently outperform the
                 others, but the two novel methods with indirect
                 stopping criteria are used to a much higher degree than
                 the other three loop instructions.",
  notes =        "Part of \cite{Silva:2011:GP} EuroGP'2011 held in
                 conjunction with EvoCOP2011 EvoBIO2011 and

Genetic Programming entries for Mingxu Wan Thomas Weise Ke Tang