How the Combinatorics of Neutral Spaces Leads Genetic Programming to Discover Simple Solutions

1. Banzhaf, W.: Genotype-phenotype-mapping and neutral variation—a case study in genetic programming. In: International Conference on Parallel Problem Solving from Nature, pp. 322–332. Springer (1994)

   Google Scholar 

2. Banzhaf, W., Leier, A.: Evolution on neutral networks in genetic programming. In: Genetic Programming—Theory and Practice III, pp. 207–221. Springer (2006)

   Google Scholar 

3. Banzhaf, W., Nordin, P., Keller, R.E., Francone, F.: Genetic Programming—An Introduction. Morgan Kaufmann, Morgan Kaufmann Publishers 340 Pine Street, 6th Floor San Francisco, CA 94104 USA (1998)

   Google Scholar 

4. Brameier, M., Banzhaf, W.: Linear Genetic Programming. Springer (2007)

   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., 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 

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

   Google Scholar 

8. Hu, T., Banzhaf, W., Moore, J.H.: The effect of recombination on phenotypic exploration and robustness in evolution. Artif. Life 20(4), 457–470 (2014)

   Article  Google Scholar 

9. Hu, T., Ochoa, G., Banzhaf, W.: Phenotype search trajectory networks for linear genetic programming. In: Genetic Programming: 26th European Conference, EuroGP 2023, Held as Part of EvoStar 2023, Brno, Czech Republic, April 12–14, 2023, Proceedings, pp. 52–67. Springer (2023)

   Google Scholar 

10. Hu, T., Payne, J.L., Banzhaf, W., Moore, J.H.: Robustness, evolvability, and accessibility in linear genetic programming. In: European Conference on Genetic Programming, pp. 13–24. Springer (2011)

    Google Scholar 

11. 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. Gen. Program. Evol. Mach. 13, 305–337 (2012)

    Article  Google Scholar 

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

    Book  Google Scholar 

13. Koza, J.R.: Genetic Programming. MIT Press, 12th floor of One Broadway, in Cambridge, MA 02142 (1992)

    Google Scholar 

14. Langdon, W.B., Poli, R.: Foundations of genetic programming. Springer (2002)

    Google Scholar 

15. Lehman, J., et al.: The surprising creativity of digital evolution: a collection of anecdotes from the evolutionary computation and artificial life research communities. Artif. Life 26, 274–306 (2020)

    Article  Google Scholar 

16. Miller, J.F.: Cartesian genetic programming: its status and future. Gen. Program. Evol. Mach. 21, 129–168 (2020)

    Article  Google Scholar 

17. Ochoa, G., Malan, K.M., Blum, C.: Search trajectory networks of population-based algorithms in continuous spaces. In: European Conference on Applications of Evolutionary Computation. EvoApps, pp. 70–85. Springer International Publishing, Cham (2020)

    Google Scholar 

18. Ochoa, G., Malan, K.M., Blum, C.: Search trajectory networks: a tool for analysing and visualising the behaviour of metaheuristics. Appl. Soft Comput. 109, 107,492 (2021)

    Google Scholar 

19. 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  Google Scholar 

20. Sarti, S., Adair, J., Ochoa, G.: Neuroevolution trajectory networks of the behaviour space. In: European Conference on Applications of Evolutionary Computation, EvoApps, Lecture Notes in Computer Science, vol. 13224, pp. 685–703. Springer (2022). 10.1007/978-3-031-02462-7_43

    Google Scholar 

21. Sarti, S., Adair, J., Ochoa, G.: Neuroevolution trajectory networks of the behaviour space. In: European Conference on Applications of Evolutionary Computation, EvoApps, Lecture Notes in Computer Science, vol. 13224, pp. 685–703. Springer (2022)

    Google Scholar 

22. Schuster, P., Fontana, W., Stadler, P.F., Hofacker, I.L.: From sequences to shapes and back: a case study in RNA secondary structures. In: Proceedings of the Royal Society of London. Series B: Biological Sciences, vol. 255(1344), pp. 279–284 (1994)

    Google Scholar 

23. Vanneschi, L., Pirola, Y., Mauri, G., Tomassini, M., Collard, P., Verel, S.: A study of the neutrality of boolean function landscapes in genetic programming. Theor. Comput. Sci. 425, 34–57 (2012)

    Article  MathSciNet  Google Scholar 

24. Wigner, E.P.: The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl. Math. 13, 1–14 (1960)

    Article  Google Scholar 

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

    Google Scholar 

Download references