On the Locality of Standard Search Operators in Grammatical Evolution

  • Ann Thorhauer
  • Franz Rothlauf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8672)


Offspring should be similar to their parents and inherit their relevant properties. This general design principle of search operators in evolutionary algorithms is either known as locality or geometry of search operators, respectively. It takes a geometric perspective on search operators and suggests that the distance between an offspring and its parents should be less than or equal to the distance between both parents. This paper examines the locality of standard search operators used in grammatical evolution (GE) and genetic programming (GP) for binary tree problems. Both standard GE and GP search operators suffer from low locality since a substantial number of search steps result in an offspring whose distance to one of its parents is greater than the distance between both of its parents. Furthermore, the locality of standard GE search operators is higher than that of standard GP search operators, which allows more focused search in GE.


Grammatical evolution genetic programming locality geometric crossover random walk 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Byrne, J., O’Neill, M., McDermott, J., Brabazon, A.: An analysis of the behaviour of mutation in grammatical evolution. In: Esparcia-Alcázar, A.I., Ekárt, A., Silva, S., Dignum, S., Uyar, A.Ş. (eds.) EuroGP 2010. LNCS, vol. 6021, pp. 14–25. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Byrne, J., O’Neill, M., Brabazon, A.: Structural and nodal mutation in grammatical evolution. In: GECCO 2009: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pp. 1881–1882. ACM (2009)Google Scholar
  3. 3.
    Castle, T., Johnson, C.G.: Positional effect of crossover and mutation in grammatical evolution. In: Esparcia-Alcázar, A.I., Ekárt, A., Silva, S., Dignum, S., Uyar, A.Ş. (eds.) EuroGP 2010. LNCS, vol. 6021, pp. 26–37. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Doran, J., Michie, D.: Experiments with the graph traverser program. Proceedings of the Royal Society of London (A) 294, 235–259 (1966)CrossRefGoogle Scholar
  5. 5.
    Galván-López, E., McDermott, J., O’Neill, M., Brabazon, A.: Towards an understanding of locality in genetic programming. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, GECCO 2010, pp. 901–908. ACM, New York (2010)Google Scholar
  6. 6.
    Galván-López, E., McDermott, J., O’Neill, M., Brabazon, A.: Defining locality as a problem difficulty measure in genetic programming. Genetic Programming and Evolvable Machines 12(4), 365–401 (2011)CrossRefGoogle Scholar
  7. 7.
    Galvan-Lopez, E., O’Neill, M., Brabazon, A.: Towards understanding the effects of locality in gp. In: Eighth Mexican International Conference on Artificial Intelligence, MICAI 2009, pp. 9–14 (2009)Google Scholar
  8. 8.
    Goldberg, D.E., Korb, B., Deb, K.: Messy genetic algorithms: Motivation, analysis, and first results. Complex Systems 3(5), 493–530 (1989)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Hugosson, J., Hemberg, E., Brabazon, A., O’Neill, M.: An investigation of the mutation operator using different representations in grammatical evolution. In: 2nd International Symposium “Advances in Artificial Intelligence and Applications”, Wisla, Poland, October 15-17, vol. 2, pp. 409–419 (2007)Google Scholar
  10. 10.
    Koza, J.R.: Genetic programming: On the programming of computers by natural selection. MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  11. 11.
    Koza, J.R., Keane, M.A., Streeter, M.J., Mydlowec, W., Yu, J., Lanza, G.: Genetic Programming IV: Routine human-competitive machine intelligence. Springer, New York (2005)Google Scholar
  12. 12.
    Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions and reversals. Soviet Physics Doklady 10(8), 707–710 (1966); Doklady Akademii Nauk SSSR 163(4), 845–848 (1965)Google Scholar
  13. 13.
    Liepins, G.E., Vose, M.D.: Representational issues in genetic optimization. Journal of Experimental and Theoretical Artificial Intelligence 2, 101–115 (1990)CrossRefGoogle Scholar
  14. 14.
    Moraglio, A.: Towards a Geometric Unification of Evolutionary Algorithms. PhD thesis, Department of Computer Science, University of Essex (November 2007)Google Scholar
  15. 15.
    Moraglio, A., Poli, R.: Topological interpretation of crossover. In: Deb, K., Tari, Z. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 1377–1388. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    O’Neill, M., Ryan, C.: Grammatical evolution. IEEE Transactions on Evolutionary Computation 5(4), 349–358 (2001)CrossRefGoogle Scholar
  17. 17.
    Radcliffe, N.J.: Equivalence class analysis of genetic algorithms. Complex Systems 5(2), 183–205 (1991)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Rothlauf, F.: Distributed Autonomous Robotics Systems, 1st edn. STUDFUZZ, vol. 104. Springer, Heidelberg (2002)CrossRefzbMATHGoogle Scholar
  19. 19.
    Rothlauf, F.: Design of Modern Heuristics. Springer, Heidelberg (2011)Google Scholar
  20. 20.
    Rothlauf, F., Oetzel, M.: On the locality of grammatical evolution. In: Collet, P., Tomassini, M., Ebner, M., Gustafson, S., Ekárt, A. (eds.) EuroGP 2006. LNCS, vol. 3905, pp. 320–330. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    Ryan, C., Collins, J.J., Neill, M.O.: Grammatical evolution: Evolving programs for an arbitrary language. In: Banzhaf, W., Poli, R., Schoenauer, M., Fogarty, T.C. (eds.) EuroGP 1998. LNCS, vol. 1391, pp. 83–95. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  22. 22.
    Surry, P.D., Radcliffe, N.: Formal algorithms + formal representations = search strategies. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 366–375. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  23. 23.
    Uy, N.Q., Hoai, N.X., O’Neill, M., McKay, B.: The role of syntactic and semantic locality of crossover in genetic programming. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6239, pp. 533–542. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  24. 24.
    Uy, N.Q., O’Neill, M., Hoai, N.X., Mckay, B., Galván-López, E.: Semantic similarity based crossover in gp: The case for real-valued function regression. In: Collet, P., Monmarché, N., Legrand, P., Schoenauer, M., Lutton, E. (eds.) EA 2009. LNCS, vol. 5975, pp. 170–181. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Uy, N.Q., Hoai, N.X., O’Neill, M., McKay, R.I., Phong, D.N.: On the roles of semantic locality of crossover in genetic programming. Information Sciences 235, 195–213 (2013)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ann Thorhauer
    • 1
  • Franz Rothlauf
    • 1
  1. 1.University of MainzGermany

Personalised recommendations