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On the Analysis of Simple Genetic Programming for Evolving Boolean Functions

  • Andrea Mambrini
  • Pietro S. OlivetoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9594)

Abstract

This work presents a first step towards a systematic time and space complexity analysis of genetic programming (GP) for evolving functions with desired input/output behaviour. Two simple GP algorithms, called (1+1) GP and (1+1) GP*, equipped with minimal function (F) and terminal (L) sets are considered for evolving two standard classes of Boolean functions. It is rigorously proved that both algorithms are efficient for the easy problem of evolving conjunctions of Boolean variables with the minimal sets. However, if an extra function (i.e. NOT) is added to F, then the algorithms require at least exponential time to evolve the conjunction of n variables. On the other hand, it is proved that both algorithms fail at evolving the difficult parity function in polynomial time with probability at least exponentially close to 1. Concerning generalisation, it is shown how the quality of the evolved conjunctions depends on the size of the training set s while the evolved exclusive disjunctions generalize equally badly independent of s.

Keywords

Genetic programming Theory Runtime analysis 

Notes

Acknowledgements

The authors would like to thank Alberto Moraglio for constructive discussions which initialised this work. Further preliminary discussions occurred at Dagstuhl Seminar N.15211. This work was supported by EPSRC under Grant n. EP/M004252/1.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of SheffieldSheffieldUK

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