Skip to main content
SpringerLink
Log in

Memetic Semantic Genetic Programming for Symbolic Regression

  • Conference paper
  • First Online:
Genetic Programming (EuroGP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13986))

Included in the following conference series:

Abstract

This paper describes a new memetic semantic algorithm for symbolic regression (SR). While memetic computation offers a way to encode domain knowledge into a population-based process, semantic-based algorithms allow one to improve them locally to achieve a desired output. Hence, combining memetic and semantic enables us to (a) enhance the exploration and exploitation features of genetic programming (GP) and (b) discover short symbolic expressions that are easy to understand and interpret without losing the expressivity characteristics of symbolic regression. Experimental results show that our proposed memetic semantic algorithm can outperform traditional evolutionary and non-evolutionary methods on several real-world symbolic regression problems, paving a new direction to handle both the bloating and generalization endeavors of genetic programming.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    We are focusing in this work on the specific case of SR, but \(X_i\) and \(y_i\) could belong to some other spaces, for instance, discrete spaces in the case of classification or boolean functions.

  2. 2.

    Though other types of hybridization between evolutionary computation (EC) and local search have been proposed, like using the local search as pre- or post-processor, as a mutation operator, among others that are beyond the focus of this work.

References

  1. Bleuler, S., Brack, M., Thiele, L., Zitzler, E.: Multiobjective genetic programming: reducing bloat using SPEA2. In: Congress on Evolutionary Computation, vol. 1, pp. 536–543 (2001)

    Google Scholar 

  2. Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)

    Article  MATH  Google Scholar 

  3. Castelli, M., Trujillo, L., Vanneschi, L., Silva, S., Z-Flores, E., Legrand, P.: Geometric semantic genetic programming with local search. In: Annual Conference on Genetic and Evolutionary Computation, pp. 999–1006 (2015)

    Google Scholar 

  4. Chen, Q., Xue, B., Niu, B., Zhang, M.: Improving generalisation of genetic programming for high-dimensional symbolic regression with feature selection. In: IEEE Congress on Evolutionary Computation, pp. 3793–3800 (2016)

    Google Scholar 

  5. Chen, Q., Zhang, M., Xue, B.: Geometric semantic genetic programming with perpendicular crossover and random segment mutation for symbolic regression. In: Shi, Y., et al. (eds.) SEAL 2017. LNCS, vol. 10593, pp. 422–434. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68759-9_35

    Chapter  Google Scholar 

  6. Chen, X., Ong, Y.S., Lim, M.H., Tan, K.C.: A multi-facet survey on memetic computation. IEEE Trans. Evol. Comput. 15(5), 591–607 (2011)

    Article  Google Scholar 

  7. Dawkins, R.: The Selfish Gene. Oxford University Press, Oxford (1976)

    Google Scholar 

  8. Ferreira, J., Pedemonte, M., Torres, A.I.: A genetic programming approach for construction of surrogate models. In: Computer Aided Chemical Engineering, vol. 47, pp. 451–456. Elsevier (2019)

    Google Scholar 

  9. Ffrancon, R., Schoenauer, M.: Memetic semantic genetic programming. In: Annual Conference on Genetic and Evolutionary Computation, pp. 1023–1030 (2015)

    Google Scholar 

  10. Fortin, F.A., De Rainville, F.M., Gardner, M.A.G., Parizeau, M., Gagné, C.: DEAP: evolutionary algorithms made easy. J. Mach. Learn. Res. 13(1), 2171–2175 (2012)

    MathSciNet  Google Scholar 

  11. Keijzer, M.: Improving symbolic regression with interval arithmetic and linear scaling. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 70–82. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36599-0_7

    Chapter  Google Scholar 

  12. Keijzer, M.: Scaled symbolic regression. Genet. Program Evolvable Mach. 5(3), 259–269 (2004)

    Article  Google Scholar 

  13. Korns, M.F.: A baseline symbolic regression algorithm. In: Riolo, R., Vladislavleva, E., Ritchie, M., Moore, J. (eds.) Genetic Programming Theory and Practice X. Genetic and Evolutionary Computation, pp. 117–137. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-6846-2_9

    Chapter  Google Scholar 

  14. Koza, J.R.: Genetic Programming: On the Programming of Computers by means of Natural Evolution. MIT Press, Massachusetts (1992)

    MATH  Google Scholar 

  15. Krawiec, K.: Semantic genetic programming. In: Krawiec, K. (ed.) Behavioral Program Synthesis with Genetic Programming. SCI, vol. 618, pp. 55–66. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-27565-9_5

    Chapter  Google Scholar 

  16. Krawiec, K., Lichocki, P.: Approximating geometric crossover in semantic space. In: 11th Annual conference on Genetic and Evolutionary Computation, pp. 987–994 (2009)

    Google Scholar 

  17. Krawiec, K., Pawlak, T.: Approximating geometric crossover by semantic backpropagation. In: 15th Annual Conference on Genetic and Evolutionary Computation, pp. 941–948 (2013)

    Google Scholar 

  18. Langdon, W.B., Poli, R.: Genetic programming bloat with dynamic fitness. In: Banzhaf, W., Poli, R., Schoenauer, M., Fogarty, T.C. (eds.) EuroGP 1998. LNCS, vol. 1391, pp. 97–112. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055931

    Chapter  Google Scholar 

  19. Liu, D., Virgolin, M., Alderliesten, T., Bosman, P.A.N.: Evolvability degeneration in multi-objective genetic programming for symbolic regression. In: Genetic and Evolutionary Computation Conference, pp. 973–981 (2022)

    Google Scholar 

  20. Lundberg, S.M., Lee, S.I.: A unified approach to interpreting model predictions. In: NeurIPS, pp. 4768–4777 (2017)

    Google Scholar 

  21. Martins, J.F.B., Oliveira, L.O.V., Miranda, L.F., Casadei, F., Pappa, G.L.: Solving the exponential growth of symbolic regression trees in geometric semantic genetic programming. In: Genetic and Evolutionary Computation Conference, pp. 1151–1158 (2018)

    Google Scholar 

  22. McPhee, N.F., Ohs, B., Hutchison, T.: Semantic building blocks in genetic programming. In: O’Neill, M., et al. (eds.) EuroGP 2008. LNCS, vol. 4971, pp. 134–145. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78671-9_12

    Chapter  Google Scholar 

  23. Moraglio, A., Krawiec, K., Johnson, C.G.: Geometric semantic genetic programming. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012. LNCS, vol. 7491, pp. 21–31. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32937-1_3

    Chapter  Google Scholar 

  24. Moscato, P.: On evolution, search, optimization, genetic algorithms and martial arts: towards memetic algorithms. Technical report 826, Caltech Concurrent Computation Program, California Institute of Technology (1989)

    Google Scholar 

  25. Ni, J., Drieberg, R.H., Rockett, P.I.: The use of an analytic quotient operator in genetic programming. IEEE Trans. Evol. Comput. 17(1), 146–152 (2013)

    Article  Google Scholar 

  26. Ong, Y.S., Lim, M.H., Neri, F., Ishibuchi, H.: Special issue on emerging trends in soft computing: memetic algorithms. Soft. Comput. 13(8), 739–740 (2009)

    Article  Google Scholar 

  27. Pawlak, T.P., Wieloch, B., Krawiec, K.: Semantic backpropagation for designing search operators in genetic programming. IEEE Trans. Evol. Comput. 19(3), 326–340 (2014)

    Article  Google Scholar 

  28. Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)

    MathSciNet  MATH  Google Scholar 

  29. Ribeiro, M.T., Singh, S., Guestrin, C.: Why should I trust you? Explaining the predictions of any classifier. In: SIGKDD, pp. 1135–1144 (2016)

    Google Scholar 

  30. Sathia, V., Ganesh, V., Nanditale, S.R.T.: Accelerating genetic programming using GPUs (2021)

    Google Scholar 

  31. Schmidt, M., Lipson, H.: Distilling free-form natural laws from experimental data. Science 324(5923), 81–85 (2009)

    Article  Google Scholar 

  32. Sipper, M., Moore, J.H.: Symbolic-regression boosting. Genet. Program Evolvable Mach. 22(3), 357–381 (2021). https://doi.org/10.1007/s10710-021-09400-0

    Article  Google Scholar 

  33. Stephens, T.: Genetic programming in python with a scikit-learn inspired API: gplearn (2016). github.com/trevorstephens/gplearn

  34. Udrescu, S.M., Tegmark, M.: AI Feynman: a physics-inspired method for symbolic regression. Sci. Adv. 6(16), eaay2631 (2020)

    Google Scholar 

  35. Uy, N.Q., Hoai, N.X., O’Neill, M., McKay, R.I., Galván-López, E.: Semantically-based crossover in genetic programming: application to real-valued symbolic regression. Genet. Program Evolvable Mach. 12(2), 91–119 (2011)

    Article  Google Scholar 

  36. Virgolin, M., Alderliesten, T., Witteveen, C., Bosman, P.A.: Improving model-based genetic programming for symbolic regression of small expressions. Evol. Comput. 29(2), 211–237 (2021)

    Article  Google Scholar 

  37. White, D.R., et al.: Better GP benchmarks: community survey results and proposals. Genet. Program Evolvable Mach. 14(1), 3–29 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

This research was partially funded by the European Commission within the HORIZON program (TRUST-AI Project, Contract No. 952060).

Author information

Authors and Affiliations

  1. TAU, Inria Saclay, LISN, Univ. Paris-Saclay, Gif-sur-Yvette, France

    Alessandro Leite & Marc Schoenauer

Authors
  1. Alessandro Leite
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marc Schoenauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessandro Leite .

Editor information

Editors and Affiliations

  1. Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil

    Gisele Pappa

  2. Università degli studi di Torino, Turin, Italy

    Mario Giacobini

  3. Brno University of Technology, Brno, Czech Republic

    Zdenek Vasicek

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Leite, A., Schoenauer, M. (2023). Memetic Semantic Genetic Programming for Symbolic Regression. In: Pappa, G., Giacobini, M., Vasicek, Z. (eds) Genetic Programming. EuroGP 2023. Lecture Notes in Computer Science, vol 13986. Springer, Cham. https://doi.org/10.1007/978-3-031-29573-7_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-29573-7_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-29572-0

  • Online ISBN: 978-3-031-29573-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation