Skip to main content

Phenotype Search Trajectory Networks for Linear Genetic Programming

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

Abstract

In this study, we visualise the search trajectories of a genetic programming system as graph-based models, where nodes are genotypes/phenotypes and edges represent their mutational transitions. We also quantitatively measure the characteristics of phenotypes including their genotypic abundance (the requirement for neutrality) and Kolmogorov complexity. We connect these quantified metrics with search trajectory visualisations, and find that more complex phenotypes are under-represented by fewer genotypes and are harder for evolution to discover. Less complex phenotypes, on the other hand, are over-represented by genotypes, are easier to find, and frequently serve as stepping-stones for evolution.

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

Access this chapter

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.

    Note that multiple programs can contribute to the same phenotype as specified by its behavior.

References

  1. Banzhaf, W.: Genotype-phenotype-mapping and neutral variation—a case study in genetic programming. In: Davidor, Y., Schwefel, H.-P., Männer, R. (eds.) PPSN 1994. LNCS, vol. 866, pp. 322–332. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-58484-6_276

    Chapter  Google Scholar 

  2. Banzhaf, W., Leier, A.: Evolution on neutral networks in genetic programming. In: Yu, T., Riolo, R., Worzel, B. (eds.) Genetic Programming – Theory and Practice III, pp. 207–221. Kluwer (2006)

    Google Scholar 

  3. Barrick, J.E.: Limits to predicting evolution: insights from a long-term experiment with Escherichia coli. In: Evolution in Action: Past, Present and Future. GEC, pp. 63–76. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-39831-6_7

    Chapter  Google Scholar 

  4. Brameier, M., Banzhaf, W.: Linear Genetic Programming. Springer, Heidelberg (2007). https://doi.org/10.1007/978-0-387-31030-5

    Book  MATH  Google Scholar 

  5. Dingle, K., Camargo, C., Louis, A.: Input-output maps are strongly biased towards simple outputs. Nat. Commun. 9, 761 (2018)

    Article  Google Scholar 

  6. Dingle, K., Novev, J., Ahnert, S., Louis, A.: Predicting phenotype transition probabilities via conditional algorithmic probability approximations. J. Roy. Soc. Interface (2023)

    Google Scholar 

  7. Dingle, K., Valle Perez, G., Louis, A.: Generic predictions of output probability based on complexities of inputs and outputs. Sci. Rep. 10, 4415 (2020)

    Article  Google Scholar 

  8. Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exp. 21(11), 1129–1164 (1991)

    Article  Google Scholar 

  9. Gao, J., Li, D., Havlin, S.: From a single network to a network of networks. Natl. Sci. Rev. 1, 346–356 (2014)

    Article  Google Scholar 

  10. Hu, T., Banzhaf, W.: Neutrality and variability: two sides of evolvability in linear genetic programming. In: Rothlauf, F., et al. (eds.) Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pp. 963–970 (2009)

    Google Scholar 

  11. Hu, T., Payne, J.L., Banzhaf, W., Moore, J.H.: Robustness, evolvability, and accessibility in linear genetic programming. In: Silva, S., Foster, J.A., Nicolau, M., Machado, P., Giacobini, M. (eds.) EuroGP 2011. LNCS, vol. 6621, pp. 13–24. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20407-4_2

    Chapter  Google Scholar 

  12. Hu, T., Payne, J.L., Banzhaf, W., Moore, J.H.: Evolutionary dynamics on multiple scales: a quantitative analysis of the interplay between genotype, phenotype, and fitness in linear genetic programming. Genet. Program. Evol. Mach. 13, 305–337 (2012)

    Article  Google Scholar 

  13. Kimura, M.: The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge (1983)

    Book  Google Scholar 

  14. Lobkovsky, A.E., Wolf, Y.I., Koonin, E.V.: Predictability of evolutionary trajectories in fitness landscapes. PLoS Comput. Biol. 7(12), e1002302 (2011)

    Article  Google Scholar 

  15. Ochoa, G., Malan, K.M., Blum, C.: Search trajectory networks of population-based algorithms in continuous spaces. In: Castillo, P.A., Jiménez Laredo, J.L., Fernández de Vega, F. (eds.) EvoApplications 2020. LNCS, vol. 12104, pp. 70–85. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-43722-0_5

    Chapter  Google Scholar 

  16. Ochoa, G., Malan, K.M., Blum, C.: Search trajectory networks: a tool for analysing and visualising the behaviour of metaheuristics. Appl. Soft Comput. 109, 107492 (2021)

    Article  Google Scholar 

  17. Reidys, C., Stadler, P., Schuster, P.: Generic properties of combinatory maps: neutral networks of RNA secondary structures. Bull. Math. Biol. 59, 339–397 (1997)

    Article  MATH  Google Scholar 

  18. Sarti, S., Adair, J., Ochoa, G.: Neuroevolution trajectory networks of the behaviour space. In: Jiménez Laredo, J.L., Hidalgo, J.I., Babaagba, K.O. (eds.) EvoApplications 2022. LNCS, vol. 13224, pp. 685–703. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-02462-7_43

    Chapter  Google Scholar 

  19. Wright, A.H., Laue, C.L.: Evolvability and complexity properties of the digital circuit genotype-phenotype map. In: Proceedings of the Annual Conference on Genetic and Evolutionary Computation, pp. 840–848 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ting Hu .

Editor information

Editors and Affiliations

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

Hu, T., Ochoa, G., Banzhaf, W. (2023). Phenotype Search Trajectory Networks for Linear Genetic Programming. 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_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-29573-7_4

  • 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