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Crossover in Cartesian Genetic Programming: Evaluation of Two Phenotypic Methods

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Computational Intelligence (IJCCI 2021)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1119))

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Abstract

The tree-based representation model of Genetic Programming is commonly used with subtree crossover as the predominant genetic operator. In contrast, Cartesian Genetic Programming (CGP) is widely used merely with mutation for genetic variation. Compared to comprehensive and advanced knowledge about crossover in the field of tree-based Genetic Programming, the state of knowledge in CGP appears to be generally weak. Even if CGP was officially introduced over twenty years ago, the role of recombination in CGP has been recently considered to be still an open question. Promising steps have been taken in the last years, but the outcomes show that more studies are needed to evaluate crossover operators in CGP on a wider set of benchmark problems. In this work, we compare algorithms that utilize two phenotypic crossover operators for CGP, called subgraph and block crossover, to the traditional mutation-only approach. The results of our experiments on well-known symbolic regression, Boolean function, and images operator design problems demonstrate that the use of crossover-based algorithms can outperform the mutation-only CGP approach on well-known benchmark problems.

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References

  1. Atkinson, T., Plump, D., Stepney, S.: Evolving graphs by graph programming. In: Castelli, M., Sekanina, L., Zhang, M., Cagnoni, S., García-Sánchez, P. (eds.) EuroGP 2018. LNCS, vol. 10781, pp. 35–51. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77553-1_3. https://eprints.whiterose.ac.uk/126500/1/AtkinsonPlumpStepney.EuroGP.18.pdf

  2. Clegg, J., Walker, J.A., Miller, J.F.: A new crossover technique for cartesian genetic programming. In: Thierens, D., et al. (eds.) GECCO 2007: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, vol. 2, pp. 1580–1587. ACM Press, London, 7–11 July 2007. https://doi.org/10.1145/1276958.1277276. https://www.cs.bham.ac.uk/~wbl/biblio/gecco2007/docs/p1580.pdf

  3. Cramer, N.L.: A representation for the adaptive generation of simple sequential programs. In: Grefenstette, J.J. (ed.) Proceedings of an International Conference on Genetic Algorithms and the Applications, Carnegie-Mellon University, Pittsburgh, PA, USA, 24–26 July 1985, pp. 183–187 (1985). https://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/papers/icga1985/icga85_cramer.pdf

  4. Forsyth, R.: BEAGLE a Darwinian approach to pattern recognition. Kybernetes 10(3), 159–166 (1981). https://doi.org/10.1108/eb005587. https://www.richardsandesforsyth.net/pubs/beagle81.pdf

  5. Hicklin, J.: Application of the genetic algorithm to automatic program generation. Master’s thesis, University of Idaho (1986)

    Google Scholar 

  6. Husa, J., Kalkreuth, R.: A comparative study on crossover in cartesian genetic programming. In: Castelli, M., Sekanina, L., Zhang, M., Cagnoni, S., García-Sánchez, P. (eds.) EuroGP 2018. LNCS, vol. 10781, pp. 203–219. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77553-1_13

    Chapter  Google Scholar 

  7. Kalganova, T.: Evolutionary approach to design multiple-valued combinational circuits. In: Proceedings of the 4th International conference on Applications of Computer Systems (ACS 1997), Szczecin, Poland, pp. 333–339 (1997)

    Google Scholar 

  8. Kalkreuth, R.: Two new mutation techniques for cartesian genetic programming. In: Guervós, J.J.M., Garibaldi, J.M., Linares-Barranco, A., Madani, K., Warwick, K. (eds.) Proceedings of the 11th International Joint Conference on Computational Intelligence, IJCCI 2019, Vienna, Austria, 17–19 September 2019, pp. 82–92. ScitePress (2019). https://doi.org/10.5220/0008070100820092

  9. Kalkreuth, R.: A comprehensive study on subgraph crossover in cartesian genetic programming. In: Guervós, J.J.M., Garibaldi, J.M., Wagner, C., Bäck, T., Madani, K., Warwick, K. (eds.) Proceedings of the 12th International Joint Conference on Computational Intelligence, IJCCI 2020, Budapest, Hungary, 2–4 November 2020, pp. 59–70. SCITEPRESS (2020). https://doi.org/10.5220/0010110700590070

  10. Kalkreuth, R.: An empirical study on insertion and deletion mutation in cartesian genetic programming. In: Merelo, J.J., Garibaldi, J., Linares-Barranco, A., Warwick, K., Madani, K. (eds.) IJCCI 2019. SCI, vol. 922, pp. 85–114. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-70594-7_4

    Chapter  Google Scholar 

  11. Kalkreuth, R., Rudolph, G., Droschinsky, A.: A new subgraph crossover for cartesian genetic programming. In: McDermott, J., Castelli, M., Sekanina, L., Haasdijk, E., García-Sánchez, P. (eds.) EuroGP 2017. LNCS, vol. 10196, pp. 294–310. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-55696-3_19

    Chapter  Google Scholar 

  12. Kaufmann, P., Kalkreuth, R.: An empirical study on the parametrization of cartesian genetic programming. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO 2017, pp. 231–232. ACM, New York, NY, USA (2017). https://doi.org/10.1145/3067695.3075980

  13. Kaufmann, P., Kalkreuth, R.: Parametrizing cartesian genetic programming: an empirical study. In: Kern-Isberner, G., Fürnkranz, J., Thimm, M. (eds.) KI 2017. LNCS (LNAI), vol. 10505, pp. 316–322. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67190-1_26

    Chapter  Google Scholar 

  14. Koza, J.: Genetic programming: a paradigm for genetically breeding populations of computer programs to solve problems. Technical report STAN-CS-90-1314, Department of Computer Science, Stanford University, June 1990

    Google Scholar 

  15. Koza, J.R.: Genetic Programming: on the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, USA (1992). https://mitpress.mit.edu/books/genetic-programming

  16. Koza, J.R.: Genetic Programming II: Automatic Discovery of Reusable Programs. MIT Press, Cambridge Massachusetts, May 1994. https://www.genetic-programming.org/gpbook2toc.html

  17. Langdon, W.B., Poli, R.: Fitness causes bloat. In: Chawdhry, P.K., Roy, R., Pant, R.K. (eds.) Soft Computing in Engineering Design and Manufacturing, pp. 13–22. Springer, London, 23–27 June 1997. https://doi.org/10.1007/978-1-4471-0427-8_2. https://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/papers/WBL.bloat_wsc2.ps.gz

  18. Langdon, W.B., Soule, T., Poli, R., Foster, J.A.: The evolution of size and shape. In: Spector, L., Langdon, W.B., O’Reilly, U.M., Angeline, P.J. (eds.) Advances in Genetic Programming, vol. 3, Chap. 8, pp. 163–190. MIT Press, Cambridge, MA, USA, June 1999. https://www.cs.ucl.ac.uk/staff/W.Langdon/aigp3/ch08.pdf

  19. Luke, S.: ECJ then and now. In: Bosman, P.A.N. (ed.) Genetic and Evolutionary Computation Conference, Berlin, Germany, 15–19 July 2017, Companion Material Proceedings, pp. 1223–1230. ACM (2017). https://doi.org/10.1145/3067695.3082467

  20. McDermott, J., et al.: Genetic programming needs better benchmarks. In: Soule, T., et al. (eds.) GECCO 2012: Proceedings of the Fourteenth International Conference on Genetic and Evolutionary Computation Conference, pp. 791–798. ACM, Philadelphia, Pennsylvania, USA, 7–11 July 2012. https://doi.org/10.1145/2330163.2330273

  21. McPhee, N.F., Miller, J.D.: Accurate replication in genetic programming. In: Eshelman, L.J. (ed.) Proceedings of the 6th International Conference on Genetic Algorithms, Pittsburgh, PA, USA, 15–19 July 1995, pp. 303–309. Morgan Kaufmann (1995)

    Google Scholar 

  22. Mercer, R.E., Sampson, J.: Adaptive search using a reproductive meta-plan. Kybernetes (1978)

    Google Scholar 

  23. Miller, J.F., Thomson, P., Fogarty, T.: Designing electronic circuits using evolutionary algorithms. Arithmetic circuits: a case study. In: Genetic Algorithms and Evolution Strategies in Engineering and Computer Science, pp. 105–131. Wiley (1997)

    Google Scholar 

  24. Miller, J.F.: An empirical study of the efficiency of learning Boolean functions using a cartesian genetic programming approach. In: Banzhaf, W., et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference, vol. 2, pp. 1135–1142. Morgan Kaufmann, Orlando, Florida, USA, 13–17 July 1999. https://citeseer.ist.psu.edu/153431.html

  25. Miller, J.F., Smith, S.L.: Redundancy and computational efficiency in cartesian genetic programming. IEEE Trans. Evol. Comput. 10(2), 167–174 (2006). https://doi.org/10.1109/TEVC.2006.871253

    Article  Google Scholar 

  26. Miller, J.F., Thomson, P.: Cartesian genetic programming. In: Poli, R., et al. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 121–132. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-540-46239-2_9. https://www.elec.york.ac.uk/intsys/users/jfm7/cgp-eurogp2000.pdf

  27. Miller, J.F.: Cartesian genetic programming: its status and future. Genet. Program Evolvable Mach. 21(1), 129–168 (2020). https://doi.org/10.1007/s10710-019-09360-6

  28. Scott, E.O., Luke, S.: ECJ at 20: toward a general metaheuristics toolkit. In: López-Ibáñez, M., Auger, A., Stützle, T. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO 2019, Prague, Czech Republic, 13–17 July 2019, pp. 1391–1398. ACM (2019). https://doi.org/10.1145/3319619.3326865

  29. Sekanina, L.: Image filter design with evolvable hardware. In: Applications of Evolutionary Computing, EvoWorkshops 2002: EvoCOP, EvoIASP, EvoSTIM/EvoPLAN, Kinsale, Ireland, 3–4 April 2002, Proceedings, pp. 255–266 (2002). https://doi.org/10.1007/3-540-46004-7_26

  30. da Silva, J.E.H., Bernardino, H.: Cartesian genetic programming with crossover for designing combinational logic circuits. In: 7th Brazilian Conference on Intelligent Systems, BRACIS 2018, São Paulo, Brazil, 22–25 October 2018, pp. 145–150. IEEE Computer Society (2018). https://doi.org/10.1109/BRACIS.2018.00033

  31. Soule, T., Foster, J.A.: Removal bias: a new cause of code growth in tree based evolutionary programming. In: 1998 IEEE International Conference on Evolutionary Computation, pp. 781–786. IEEE Press, Anchorage, Alaska, USA, 5–9 May 1998. https://doi.org/10.1109/ICEC.1998.700151. https://citeseer.ist.psu.edu/313655.html

  32. Turner, A.J.: Improving crossover techniques in a genetic program. Master’s thesis, Department of Electronics, University of York (2012)

    Google Scholar 

  33. Turner, A.J., Miller, J.F.: Cartesian genetic programming encoded artificial neural networks: a comparison using three benchmarks. In: Blum, C., et al. (eds.) GECCO 2013: Proceeding of the Fifteenth Annual Conference on Genetic and Evolutionary Computation Conference, pp. 1005–1012. ACM, Amsterdam, The Netherlands, 6–10 July 2013. https://doi.org/10.1145/2463372.2463484

  34. Turner, A.J., Miller, J.F.: The importance of topology evolution in NeuroEvolution: a case study using cartesian genetic programming of artificial neural networks. In: Bramer, M., Petridis, M. (eds.) Research and Development in Intelligent Systems XXX, pp. 213–226. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-02621-3_15

    Chapter  Google Scholar 

  35. Turner, A.J., Miller, J.F.: Neutral genetic drift: an investigation using cartesian genetic programming. Genet. Program Evolvable Mach. 16(4), 531–558 (2015). https://doi.org/10.1007/s10710-015-9244-6

  36. White, D.R., et al.: Better GP benchmarks: community survey results and proposals. Genet. Program Evolvable Mach. 14(1), 3–29 (2013). https://doi.org/10.1007/s10710-012-9177-2

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, TU Dortmund University, Otto-Hahn-Straße 14, Dortmund, Germany

    Roman Kalkreuth

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  1. Roman Kalkreuth
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Correspondence to Roman Kalkreuth .

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Editors and Affiliations

  1. Jubilee Campus, University of Nottingham, Nottingham, UK

    Jonathan Garibaldi

  2. Computer Science, University of Nottingham, Nottingham, UK

    Christian Wagner

  3. Advanced Computer Science, Leiden University, Leiden, The Netherlands

    Thomas Bäck

  4. King’s College London, Strand, UK

    Hak-Keung Lam

  5. Paris 1 Panthéon-Sorbonne, SAMM University, Paris, France

    Marie Cottrell

  6. University of Paris-EST Créteil (UPEC), Créteil, France

    Kurosh Madani

  7. Vice Chancellors Office, Coventry University, Coventry, UK

    Kevin Warwick

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Kalkreuth, R. (2023). Crossover in Cartesian Genetic Programming: Evaluation of Two Phenotypic Methods. In: Garibaldi, J., et al. Computational Intelligence. IJCCI 2021. Studies in Computational Intelligence, vol 1119. Springer, Cham. https://doi.org/10.1007/978-3-031-46221-4_3

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