Uniform Linear Transformation with Repair and Alternation in Genetic Programming

  • Lee Spector
  • Thomas Helmuth
Part of the Genetic and Evolutionary Computation book series (GEVO)


Several genetic programming researchers have argued for the utility of genetic operators that act uniformly. By “act uniformly” we mean two specific things: that the probability of an inherited program component being modified during inheritance is independent of the size and shape of the parent programs beyond the component in question; and that pairs of parents are combined in ways that allow arbitrary combinations of components from each parent to appear in the child. Uniform operators described in previous work have had limited utility, however, because of a mismatch between the relevant notions of uniformity and the hierarchical structure and variable sizes of many genetic programming representations. In this chapter we describe a new genetic operator, ULTRA, which incorporates aspects of both mutation and crossover and acts approximately uniformly across programs of variable sizes and structures. ULTRA treats hierarchical programs as linear sequences and includes a repair step to ensure that syntax constraints are satisfied after variation. We show that on the drug bioavailability and Pagie-1 benchmark problems ULTRA produces significant improvements both in problem-solving power and in program size relative to standard operators. Experiments with factorial regression and with the boolean 6-multiplexer problem demonstrate that ULTRA can manipulate programs that make use of hierarchical structure, but also that it is not always beneficial. The demonstrations evolve programs in the Push programming language, which makes repair particularly simple, but versions of the technique should be applicable in other genetic programming systems as well.


Uniform mutation Uniform crossover ULTRA Push PushGP Drug bioavailability problem Pagie-1 problem Factorial regression Boolean multiplexer problem 



Thanks to Micah Savitzky for exploratory work that later led to the ideas in this paper, to Emma Tosch and Kyle Harrington for discussions and code, to Josiah Erikson for systems support, and to Hampshire College for support for the Hampshire College Institute for Computational Intelligence. This material is based upon work supported by the National Science Foundation under Grant Nos. 1017817 and 1129139. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.


  1. Crawford-Marks R, Spector L (2002) Size control via size fair genetic operators in the PushGP genetic programming system. In: GECCO 2002: proceedings of the genetic and evolutionary computation conference, New York. Morgan Kaufmann, pp 733–739Google Scholar
  2. D’haeseleer P (1994) Context preserving crossover in genetic programming. In: Proceedings of the 1994 IEEE world congress on computational intelligence, Orlando, vol 1. IEEE, pp 256–261Google Scholar
  3. Harper R (2012) Spatial co-evolution: quicker, fitter and less bloated. In: GECCO ’12: proceedings of the fourteenth international conference on genetic and evolutionary computation conference, Philadelphia. ACM, pp 759–766Google Scholar
  4. Helmuth T, Spector L (2013) Evolving a digital multiplier with the PushGP genetic programming system. In: Workshop on stack-based genetic programming, Amsterdam. ACM, pp 1627–1634Google Scholar
  5. Kennedy CJ, Giraud-Carrier C (1999) A depth controlling strategy for strongly typed evolutionary programming. In: Proceedings of the genetic and evolutionary computation conference, Orlando, vol 1. Morgan Kaufmann, pp 879–885Google Scholar
  6. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT, CambridgezbMATHGoogle Scholar
  7. Langdon WB (2000) Size fair and homologous tree genetic programming crossovers. Genet Program Evolvable Mach 1(1/2):95–119CrossRefzbMATHGoogle Scholar
  8. Langdon WB, Poli R (2002) Foundations of genetic programming. Springer.
  9. Luke S, Panait L (2002) Is the perfect the enemy of the good? In: GECCO 2002: proceedings of the genetic and evolutionary computation conference, New York. Morgan Kaufmann, pp 820–828Google Scholar
  10. Luke S, Panait L (2006) A comparison of bloat control methods for genetic programming. Evol Comput 14(3):309–344CrossRefGoogle Scholar
  11. McDermott J, White DR, Luke S, Manzoni L, Castelli M, Vanneschi L, Jaskowski W, Krawiec K, Harper R, De Jong K, O’Reilly UM (2012) Genetic programming needs better benchmarks. In: GECCO ’12: proceedings of the fourteenth international conference on genetic and evolutionary computation conference, Philadelphia. ACM, pp 791–798Google Scholar
  12. Moraglio A, Krawiec K, Johnson CG (2012) Geometric semantic genetic programming. In: Parallel problem solving from nature, PPSN XII (Part 1), Taormina. Lecture notes in computer science, vol 7491. Springer, pp 21–31Google Scholar
  13. Niehaus J, Banzhaf W (2003) More on computational effort statistics for genetic programming. In: Genetic programming, proceedings of EuroGP’2003, Essex. Lecture notes in computer science, vol 2610. Springer, pp 164–172Google Scholar
  14. O’Neill M, Ryan C (2001) Grammatical evolution. IEEE Trans Evol Comput 5(4):349–358. doi:10.1109/4235.942529CrossRefGoogle Scholar
  15. Page J, Poli R, Langdon WB (1998) Smooth uniform crossover with smooth point mutation in genetic programming: a preliminary study. Technical report CSRP-98-20, School of Computer Science, University of Birmingham.
  16. Pagie L, Hogeweg P (1997) Evolutionary consequences of coevolving targets. Evol Comput 5(4):401–418CrossRefGoogle Scholar
  17. Perkis T (1994) Stack-based genetic programming. In: Proceedings of the 1994 IEEE world congress on computational intelligence, Orlando, vol 1. IEEE, pp 148–153Google Scholar
  18. Poli R, Langdon WB (1998) On the search properties of different crossover operators in genetic programming. In: Genetic programming 1998: proceedings of the third annual conference, University of Wisconsin, Madison. Morgan Kaufmann, pp 293–301Google Scholar
  19. Poli R, Page J (2000) Solving high-order Boolean parity problems with smooth uniform crossover, sub-machine code GP and demes. Genet Program Evolvable Mach 1(1/2):37–56CrossRefzbMATHGoogle Scholar
  20. Poli R, Langdon WB, McPhee NF (2008) A field guide to genetic programming. Published via and freely available at,, (With contributions by J. R. Koza)
  21. Schoenauer M, Sebag M, Jouve F, Lamy B, Maitournam H (1996) Evolutionary identification of macro-mechanical models. In: Angeline PJ, Kinnear KE Jr (eds) Advances in genetic programming 2. MIT, Cambridge, chap 23, pp 467–488Google Scholar
  22. Semenkin E, Semenkina M (2012) Self-configuring genetic programming algorithm with modified uniform crossover. In: Proceedings of the 2012 IEEE congress on evolutionary computation, Brisbane, pp 2501–2506Google Scholar
  23. Silva S, Vanneschi L (2009) Operator equalisation, bloat and overfitting: a study on human oral bioavailability prediction. In: GECCO ’09: proceedings of the 11th annual conference on genetic and evolutionary computation, Montreal. ACM, pp 1115–1122Google Scholar
  24. Silva S, Vanneschi L (2010) State-of-the-art genetic programming for predicting human oral bioavailability of drugs. In: Advances in bioinformatics. Springer, 74:165–173. doi:10.1007/978-3-642-13214-8.
  25. Spector L (2001) Autoconstructive evolution: Push, PushGP, and pushpop. In: Proceedings of the genetic and evolutionary computation conference (GECCO-2001), San Francisco. Morgan Kaufmann, pp 137–146Google Scholar
  26. Spector L (2012) Assessment of problem modality by differential performance of lexicase selection in genetic programming: a preliminary report. In: 1st workshop on understanding problems (GECCO-UP), Philadelphia. ACM, pp 401–408Google Scholar
  27. Spector L, Robinson A (2002) Genetic programming and autoconstructive evolution with the Push programming language. Genet Program Evolvable Mach 3(1):7–40CrossRefzbMATHGoogle Scholar
  28. Spector L, Klein J, Keijzer M (2005) The push3 execution stack and the evolution of control. In: GECCO 2005: proceedings of the 2005 conference on genetic and evolutionary computation, Washington, vol 2. ACM, pp 1689–1696Google Scholar
  29. Van Belle T, Ackley DH (2002) Uniform subtree mutation. In: Foster JA, Lutton E, Miller J, Ryan C, Tettamanzi AGB (eds) Genetic programming, proceedings of the 5th European conference, EuroGP 2002, Kinsale. Lecture notes in computer science, vol 2278. Springer, pp 152–161Google Scholar
  30. White DR, McDermott J, Castelli M, Manzoni L, Goldman BW, Kronberger G, Jaskowski W, O’Reilly UM, Luke S (2013) Better GP benchmarks: community survey results and proposals. Genet Program Evolvable Mach 14(1):3–29CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Cognitive Science, Hampshire CollegeAmherstUSA
  2. 2.Computer Science, University of MassachusettsAmherstUSA

Personalised recommendations