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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note that multiple programs can contribute to the same phenotype as specified by its behavior.
References
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
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)
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
Brameier, M., Banzhaf, W.: Linear Genetic Programming. Springer, Heidelberg (2007). https://doi.org/10.1007/978-0-387-31030-5
Dingle, K., Camargo, C., Louis, A.: Input-output maps are strongly biased towards simple outputs. Nat. Commun. 9, 761 (2018)
Dingle, K., Novev, J., Ahnert, S., Louis, A.: Predicting phenotype transition probabilities via conditional algorithmic probability approximations. J. Roy. Soc. Interface (2023)
Dingle, K., Valle Perez, G., Louis, A.: Generic predictions of output probability based on complexities of inputs and outputs. Sci. Rep. 10, 4415 (2020)
Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exp. 21(11), 1129–1164 (1991)
Gao, J., Li, D., Havlin, S.: From a single network to a network of networks. Natl. Sci. Rev. 1, 346–356 (2014)
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)
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
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)
Kimura, M.: The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge (1983)
Lobkovsky, A.E., Wolf, Y.I., Koonin, E.V.: Predictability of evolutionary trajectories in fitness landscapes. PLoS Comput. Biol. 7(12), e1002302 (2011)
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
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)
Reidys, C., Stadler, P., Schuster, P.: Generic properties of combinatory maps: neutral networks of RNA secondary structures. Bull. Math. Biol. 59, 339–397 (1997)
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
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
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)