Abstract
A key ingredient in any successful genetic programming is robust initialisation. Many successful initialisation methods used in genetic programming have been adapted to use with grammatical evolution, to varying levels success. This paper examines the effectiveness of some of the most popular of these initialisation techniques on structured grammatical evolution. Namely, we investigate Sensible Initialisation and Probabilistic Tree Creation 2, as well as the standard initialisation procedure used in structured grammatical evolution, Grow. We also propose a novel procedure called Local Optimised Probabilistic Tree Creation 2, which runs a quick greedy optimisation on the trees created. We do this using using two different grammar specifications, both with and without protected operators, and using an error based and correlation based fitness function. We examine their performance, as well as the diversity of solutions they create, on 8 well-known benchmarks. We observe that Local Optimised Probabilistic Tree Creation 2 created the fittest, or joint fittest, initialisation populations on every benchmark considered, bar one. Local Optimised Probabilistic Tree Creation 2 remained the best initialisation procedure when the grammar specification was changed, confirming it’s robustness. This did not necessarily result in overall better runs, however, and SGE runs with below average initialisation performance were seen to overcome their “bad start”. The diversity of solutions, particularly fitness diversity, at the end of the run was lower for Local Optimised Probabilistic Tree Creation 2 and Probabilistic Tree Creation 2 than for both sensible initialisation and grow. Local Optimised Probabilistic Tree Creation 2 was seen to take between 8 and 20 times longer to create the initial population than the other methods. This article is an extension of a paper which originally appeared at the Grammatical Evolution Workshop held as part of GECCO 2023.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availibility
The code necessary for replication, along with all experimental results will appear online: https://github.com/nunolourenco/sge3.
Notes
https://github.com/nunolourenco/sge3.
References
A. Bartoli, A. De Lorenzo, E. Medvet, G. Squillero, Multi-level diversity promotion strategies for grammar-guided genetic programming. Appl. Soft Comput. 83, 105599 (2019)
P. Carvalho, J. Mégane, N. Lourenço, P. Machado, Context matters: adaptive mutation for grammars, in Genetic Programming. ed. by G. Pappa, M. Giacobini, Z. Vasicek (Springer Nature Switzerland, Cham, 2023), pp.117–132
R. Harper, Ge, explosive grammars and the lasting legacy of bad initialisation. In: IEEE Congress on Evolutionary Computation. pp. 1–8. IEEE (2010)
M. Keijzer, Improving symbolic regression with interval arithmetic and linear scaling, in Genetic Programming. ed. by C. Ryan, T. Soule, M. Keijzer, E. Tsang, R. Poli, E. Costa (Springer, Berlin, 2003), pp.70–82
J.R. Koza, Genetic programming as a means for programming computers by natural selection. Stat. Comput. 4, 87–112 (1994)
N. Lourenço, F.B. Pereira, E. Costa, SGE: a structured representation for grammatical evolution. In: International Conference on Artificial Evolution (Evolution Artificielle). pp. 136–148. Springer (2015)
N. Lourenço, F.B. Pereira, E. Costa, Unveiling the properties of structured grammatical evolution. Genet. Program Evol. Mach. 17, 251–289 (2016)
S. Luke, Two fast tree-creation algorithms for genetic programming. IEEE Trans. Evol. Comput. 4(3), 274–283 (2000)
E. Medvet, A comparative analysis of dynamic locality and redundancy in grammatical evolution. In: European Conference on Genetic Programming. pp. 326–342. Springer (2017)
J. Mégane, N.Lourenço, P. Machado, Probabilistic grammatical evolution. In: Genetic Programming: 24th European Conference, EuroGP 2021, Held as Part of EvoStar 2021, Virtual Event, April 7–9, 2021, Proceedings 24. pp. 198–213. Springer (2021)
A. Murphy, A. De Lima, D. Mota Dias, C. Ryan, Error and correlation as fitness functions for scaled symbolic regression in grammatical evolution. In: Proceedings of the Companion Conference on Genetic and Evolutionary Computation. pp. 607–610 (2023)
A. Murphy, N. Lourenço, A. Ventresque, Initialisation in structured grammatical evolution. In: Proceedings of the Companion Conference on Genetic and Evolutionary Computation. pp. 2022–2028 (2023)
A. Murphy, G. Murphy, D.M. Dias, J. Amaral, E. Naredo, C. Ryan, Human in the loop fuzzy pattern tree evolution. SN Comput. Sci. 3(2), 1–14 (2022)
A. Murphy, C. Ryan, Improving module identification and use in grammatical evolution, in IEEE Congress on Evolutionary Computation, CEC 2020 IEEE Computational Intelligence Society. ed. by Y. Jin (IEEE Press, New york, 2020)
A. Murphy, A. Youssef, K.K. Gupt, M.A. Raja, C.Ryan, Time is on the side of grammatical evolution. In: 2021 International Conference on Computer Communication and Informatics (ICCCI). pp. 1–7. IEEE (2021)
M. Nicolau, Understanding grammatical evolution: initialisation. Genet. Progr. Evol. Mach. 18(4), 467–507 (2017)
M. O’Neill, C. Ryan, M. Keijzer, M. Cattolico, Crossover in grammatical evolution. Genet. Progr. Evol. Mach. 4(1), 67–93 (2003). https://doi.org/10.1023/A:1021877127167
L. Pagie, P. Hogeweg, Evolutionary consequences of coevolving targets. Evol. Comput. 5(4), 401–418 (1997)
M.A. Raja, A. Murphy, C. Ryan, Gelab and hybrid optimization using grammatical evolution. In: International Conference on Intelligent Data Engineering and Automated Learning. pp. 292–303. Springer (2020)
F. Rothlauf, M. Oetzel, On the locality of grammatical evolution, in Genetic Programming. ed. by P. Collet, M. Tomassini, M. Ebner, S. Gustafson, A. Ekárt (Springer, Berlin, 2006), pp.320–330
C. Ryan, R.M.A. Azad, Sensible initialisation in grammatical evolution. In: GECCO. pp. 142–145. AAAI Menlo Park (2003)
C. Ryan, J.J. Collins, M.O. Neill, Grammatical evolution: evolving programs for an arbitrary language. In: European Conference on Genetic Programming. pp. 83–96. Springer (1998)
D.R. White, J. McDermott, M. Castelli, L. Manzoni, B.W. Goldman, G. Kronberger, W. Jaśkowski, U.M. O’Reilly, S. Luke, Better GP benchmarks: community survey results and proposals. Genet. Progr. Evol. Mach. 14(1), 3–29 (2013)
Acknowledgements
The first, second, and third authors were supported with the financial support of the Science Foundation Ireland grant 13/RC/2094_2. The third author is supported, in part, by Science Foundation Ireland grant 20/FFP-P/8818. The fourth author was supported by the project A4A: Audiology for All (CENTRO-01-0247-FEDER-047083) financed by the Operational Program for Competitiveness and Internationalisation of PORTUGAL 2020 through the European Regional Development Fund and within the scope of CISUC R&D Unit - UIDB/00326/2020 or project code UIDP/00326 2020.
Author information
Authors and Affiliations
Contributions
A.M. wrote the manuscript and conducted experiments. A.M. and N.L. conceptualized the experiments. M.M. performed data creation, formal analysis and visualisations. All authors reviewed and edited the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
A.M and M.M. are guest editors of this special issue. N.L. and A.V. have no Conflict of interest to declare.
Ethical approval
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Murphy, A., Mahdinejad, M., Ventresque, A. et al. An investigation into structured grammatical evolution initialisation. Genet Program Evolvable Mach 25, 24 (2024). https://doi.org/10.1007/s10710-024-09498-y
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10710-024-09498-y