Abstract
Parent selection algorithms (selection schemes) steer populations through a problem’s search space, often trading off between exploitation and exploration. Understanding how selection schemes affect exploitation and exploration within a search space is crucial to tackling increasingly challenging problems. Here, we introduce an “exploration diagnostic” that diagnoses a selection scheme’s capacity for search space exploration. We use our exploration diagnostic to investigate the exploratory capacity of lexicase selection and several of its variants: epsilon lexicase, down-sampled lexicase, cohort lexicase, and novelty-lexicase. We verify that lexicase selection out-explores tournament selection, and we show that lexicase selection’s exploratory capacity can be sensitive to the ratio between population size and the number of test cases used for evaluating candidate solutions. Additionally, we find that relaxing lexicase’s elitism with epsilon lexicase can further improve exploration. Both down-sampling and cohort lexicase—two techniques for applying random subsampling to test cases—degrade lexicase’s exploratory capacity; however, we find that cohort partitioning better preserves lexicase’s exploratory capacity than down-sampling. Finally, we find evidence that novelty-lexicase’s addition of novelty test cases can degrade lexicase’s capacity for exploration. Overall, our findings provide hypotheses for further exploration and actionable insights and recommendations for using lexicase selection. Additionally, this work demonstrates the value of selection scheme diagnostics as a complement to more conventional benchmarking approaches to selection scheme analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aenugu, S., Spector, L.: Lexicase selection in learning classifier systems. In: Proceedings of the Genetic and Evolutionary Computation Conference on - GECCO ’19, pp. 356–364. ACM Press, Prague, Czech Republic (2019)
Ahlmann-Eltze, C., Patil, I.: ggsignif: significance brackets for ggplot2. R package version 0.6.2. https://CRAN.R-project.org/package=ggsignif (2020)
Allaire, J., Xie, Y., McPherson, J., Luraschi, J., Ushey, K., Atkins, A., Wickham, H., Cheng, J., Chang, W., Iannone, R.: rmarkdown: dynamic documents for R. R package version 2.6. https://github.com/rstudio/rmarkdown (2020)
Dolson, E., Lalejini, A., Jorgensen, S., Ofria, C.: Interpreting the tape of life: ancestry-based analyses provide insights and intuition about evolutionary dynamics. Artif. Life 26, 58–79 (2020)
Dolson, E.L., Banzhaf, W., Ofria, C.: Ecological theory provides insights about evolutionary computation. preprint, PeerJ Preprints. https://peerj.com/preprints/27315 (2018). https://doi.org/10.7287/peerj.preprints.27315v1
Eiben, A.E., Schippers, C.A.: On evolutionary exploration and exploitation. Fundamenta Informaticae 35(1–4), 35–50 (1998)
Ferguson, A.J., Hernandez, J.G., Junghans, D., Lalejini, A., Dolson, E., Ofria, C.: Characterizing the effects of random subsampling on lexicase selection. In: Banzhaf, W., Goodman, E., Sheneman, L., Trujillo, L. (eds.) Genetic Programming Theory and Practice XVII, pp. 1–23. Springer (2020)
Garnier, S.: viridis: default color maps from matplotlib. R package version 0.5.1. https://github.com/sjmgarnier/viridis (2018)
Harrell Jr., F.E.: Hmisc: harrell miscellaneous. R package version 4.4-2. https://CRAN.R-project.org/package=Hmisc (2020)
Helmuth, T., Abdelhady, A.: Benchmarking parent selection for program synthesis by genetic programming. In: Proceedings of the 2020 Genetic and Evolutionary Computation Conference Companion, pp. 237–238 (2020)
Helmuth, T., Kelly, P.: PSB2: the second program synthesis benchmark suite. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 785–794. ACM, Lille France (2021)
Helmuth, T., McPhee, N.F., Spector, L.: Effects of Lexicase and tournament selection on diversity recovery and maintenance. In: Proceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion - GECCO ’16 Companion, pp. 983–990. ACM Press, Denver, Colorado, USA (2016)
Helmuth, T., McPhee, N.F., Spector, L.: Lexicase selection for program synthesis: a diversity analysis. In: Riolo, R., Worzel, W., Kotanchek, M., Kordon, A. (eds.) Genetic Programming Theory and Practice XIII, pp. 151–167. Springer International Publishing, Cham (2016)
Helmuth, T., Pantridge, E., Spector, L.: On the importance of specialists for lexicase selection. Genetic Programming and Evolvable Machines (2020)
Helmuth, T., Spector, L.: General program synthesis benchmark suite. In: Proceedings of the 2015 on Genetic and Evolutionary Computation Conference - GECCO ’15, pp. 1039–1046. ACM Press, Madrid, Spain (2015)
Helmuth, T., Spector, L.: Explaining and exploiting the advantages of down-sampled lexicase selection. In: The 2020 Conference on Artificial Life, pp. 341–349. MIT Press, Online (2020)
Helmuth, T., Spector, L.: Problem-solving benefits of down-sampled lexicase selection (2021). arXiv:2106.06085 [cs]
Helmuth, T., Spector, L., Matheson, J.: Solving uncompromising problems with lexicase selection. IEEE Trans. Evol. Comput. 19(5), 630–643 (2015). https://doi.org/10.1109/TEVC.2014.2362729
Hernandez, J.G., Lalejini, A., Dolson, E., Ofria, C.: Random subsampling improves performance in lexicase selection. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 2028–2031 (2019)
Hernandez, J.G., Lalejini, A., Ofria, C.: Supplemental Material GitHub Repository (2021). https://doi.org/10.5281/zenodo.5020769
Hooker, J.N.: Testing heuristics: we have it all wrong. J. Heuristics 1, 33–42 (1995)
Jundt, L., Helmuth, T.: Comparing and combining lexicase selection and novelty search. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1047–1055. ACM, Prague Czech Republic (2019)
Kassambara, A.: rstatix: pipe-friendly framework for basic statistical tests. R package version 0.7.0. https://rpkgs.datanovia.com/rstatix/ (2021)
La Cava, W., Helmuth, T., Spector, L., Moore, J.H.: A probabilistic and multi-objective analysis of lexicase selection and \(\epsilon \)-lexicase selection. Evol. Comput. 27, 377–402 (2019)
La Cava, W., Spector, L., Danai, K.: Epsilon-lexicase selection for regression. In: Proceedings of the Genetic and Evolutionary Computation Conference 2016, pp. 741–748 (2016)
Lalejini, A.M., Hernandez, J.G.: Experiment data. https://osf.io/xpjft/ (2021). https://doi.org/10.17605/OSF.IO/XPJFT
Lehman, J., Stanley, K.O.: Exploiting open-endedness to solve problems through the search for novelty. In: Proceedings of the Eleventh International Conference on Artificial Life (Alife XI). MIT Press (2008)
Lehman, J., Stanley, K.O.: Abandoning objectives: evolution through the search for novelty alone. Evol. Comput. 19, 189–223 (2011)
Metevier, B., Saini, A.K., Spector, L.: Lexicase selection beyond genetic programming. In: Banzhaf, W., Spector, L., Sheneman, L. (eds.) Genetic Programming Theory and Practice XVI. Genetic and Evolutionary Computation, pp. 123–136. Springer International Publishing, Cham (2019). https://doi.org/10.1007/978-3-030-04735-1_7
Moore, J.M., McKinley, P.K.: A comparison of multiobjective algorithms in evolving quadrupedal gaits. In: Tuci, E., Giagkos, A., Wilson, M., Hallam, J. (eds.) From Animals to Animats 14, vol. 9825, pp. 157–169. Springer International Publishing, Cham (2016)
Moore, J.M., Stanton, A.: Lexicase selection outperforms previous strategies for incremental evolution of virtual creature controllers. In: Proceedings of the 14th European Conference on Artificial Life ECAL 2017, pp. 290–297. MIT Press, Lyon, France (2017)
Neuwirth, E.: RColorBrewer: colorbrewer palettes. R package version 1.1-2. https://CRAN.R-project.org/package=RColorBrewer (2014)
Ofria, C., Moreno, M.A., Dolson, E., Lalejini, A., Rodriguez-Papa, S., Fenton, J., Perry, K., Jorgensen, S., Hoffman, R., Miller, R., Edwards, O.B., Stredwick, J., G, N.C., Clemons, R., Vostinar, A., Moreno, R., Schossau, J., Zaman, L., Rainbow, D.: Empirical: a scientific software library for research, education, and public engagement (2020). https://doi.org/10.5281/zenodo.4141943
Orzechowski, P., La Cava, W., Moore, J.H.: Where are we now? A large benchmark study of recent symbolic regression methods. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1183–1190. ACM, Kyoto Japan (2018)
R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/ (2020)
Spector, L.: Assessment of problem modality by differential performance of lexicase selection in genetic programming: a preliminary report. In: Proceedings of the Fourteenth International Conference on Genetic and Evolutionary Computation Conference Companion - GECCO Companion ’12, p. 401. ACM Press, Philadelphia, Pennsylvania, USA (2012)
Spector, L., Cava, W.L., Shanabrook, S., Helmuth, T., Pantridge, E.: Relaxations of lexicase parent selection. In: Banzhaf, W., Olson, R.S., Tozier, W., Riolo, R. (eds.) Genetic Programming Theory and Practice XV, pp. 105–120. Springer International Publishing, Cham (2018)
Wickham, H.: tidyverse: easily install and load the Tidyverse. R package version 1.3.0. https://CRAN.R-project.org/package=tidyverse (2019)
Wickham, H., Chang, W., Henry, L., Pedersen, T.L., Takahashi, K., Wilke, C., Woo, K., Yutani, H., Dunnington, D.: ggplot2: create elegant data visualisations using the grammar of graphics. R package version 3.3.4. https://CRAN.R-project.org/package=ggplot2 (2021)
Wilke, C.O.: cowplot: Streamlined plot theme and plot annotations for ggplot2. R package version 1.1.0. https://wilkelab.org/cowplot/ (2020)
Xie, Y.: bookdown: authoring books and technical documents with R markdown. R package version 0.21. https://github.com/rstudio/bookdown (2020)
Xie, Y.: knitr: A General-Purpose Package for Dynamic Report Generation in R. R package version 1.30. https://yihui.org/knitr/ (2020)
Zhu, H.: kableExtra: construct complex table with kable and pipe syntax. R package version 1.3.4. https://CRAN.R-project.org/package=kableExtra (2021)
Acknowledgements
We thank members of the Michigan State University (MSU) Digital Evolution Laboratory for helpful comments and suggestions on this work. We thank the participants of the 2021 Genetic Programming in Theory and Practice workshop for lively discussion of our work. We especially thank Lee Spector for encouraging remarks and insightful feedback on our manuscript. MSU provided computational resources through the Institute for Cyber-Enabled Research. This work was supported in part by the National Science Foundation (NSF) through the BEACON Center (DBI-0939454) and a Graduate Research Fellowship to AL (DGE-1424871) and by the GEM Fellowship Program and Oak Ridge National Laboratory (ORNL). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of MSU, the NSF, GEM, or ORNL.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Hernandez, J.G., Lalejini, A., Ofria, C. (2022). An Exploration of Exploration: Measuring the Ability of Lexicase Selection to Find Obscure Pathways to Optimality. In: Banzhaf, W., Trujillo, L., Winkler, S., Worzel, B. (eds) Genetic Programming Theory and Practice XVIII. Genetic and Evolutionary Computation. Springer, Singapore. https://doi.org/10.1007/978-981-16-8113-4_5
Download citation
DOI: https://doi.org/10.1007/978-981-16-8113-4_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-8112-7
Online ISBN: 978-981-16-8113-4
eBook Packages: Computer ScienceComputer Science (R0)