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Relaxations of Lexicase Parent Selection

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Genetic Programming Theory and Practice XV

Part of the book series: Genetic and Evolutionary Computation ((GEVO))

Abstract

In a genetic programming system, the parent selection algorithm determines which programs in the evolving population will be used as the material out of which new programs will be constructed. The lexicase parent selection algorithm chooses a parent by considering all test cases, individually, one at a time, in a random order, to reduce the pool of possible parent programs. Lexicase selection is ordinarily strict, in that a program can only be selected if it has the best error in the entire population on the first test case considered, and the best error relative to all other programs that remain in the pool each time it is reduced. This strictness may exclude high-quality candidates from consideration for parenthood, and hence from exploration by the evolutionary process. In this chapter we describe and present results of four variants of lexicase selection that relax these strict constraints: epsilon lexicase selection, random threshold lexicase selection, MADCAP epsilon lexicase selection, and truncated lexicase selection. We present the results of experiments with genetic programming systems using these and other parent selection algorithms on symbolic regression and software synthesis problems. We also briefly discuss the relations between lexicase selection and work on many-objective optimization, and the implications of these considerations for future work on parent selection in genetic programming.

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Notes

  1. 1.

    So “MADCAP” = Median Absolute Deviation from the median, Cap Applied Probabilistically.

  2. 2.

    https://epistasislab.github.io/ellyn/.

References

  1. Anne Auger, Johannes Bader, Dimo Brockhoff, and Eckart Zitzler. Theory of the hypervolume indicator: optimal -distributions and the choice of the reference point. In Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms, pages 87–102. ACM, 2009.

    Google Scholar 

  2. Kalyanmoy Deb, Manikanth Mohan, and Shikhar Mishra. Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions. Evolutionary Computation, 13(4):501–525, December 2005.

    Google Scholar 

  3. Thomas Helmuth, Nicholas Freitag McPhee, and Lee Spector. Effects of lexicase and tournament selection on diversity recovery and maintenance. In Tobias Friedrich and et al., editors, GECCO ‘16 Companion: Proceedings of the Companion Publication of the 2016 Annual Conference on Genetic and Evolutionary Computation, pages 983–990, Denver, Colorado, USA, 20–24 July 2016. ACM.

    Google Scholar 

  4. Thomas Helmuth, Nicholas Freitag McPhee, and Lee Spector. The impact of hyperselection on lexicase selection. In Tobias Friedrich, editor, GECCO ‘16: Proceedings of the 2016 Annual Conference on Genetic and Evolutionary Computation, pages 717–724, Denver, USA, 20–24 July 2016. ACM. Nominated for best paper.

    Google Scholar 

  5. Thomas Helmuth, Nicholas Freitag McPhee, and Lee Spector. Lexicase selection for program synthesis: A diversity analysis. In Rick Riolo, William P. Worzel, M. Kotanchek, and A. Kordon, editors, Genetic Programming Theory and Practice XIII, Genetic and Evolutionary Computation, pages 151–167, Ann Arbor, USA, May 2016. Springer.

    Google Scholar 

  6. Thomas Helmuth and Lee Spector. General program synthesis benchmark suite. In Sara Silva and et al., editors, GECCO ‘15: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, pages 1039–1046, Madrid, Spain, 11–15 July 2015. ACM.

    Google Scholar 

  7. Thomas Helmuth, Lee Spector, and James Matheson. Solving uncompromising problems with lexicase selection. IEEE Transactions on Evolutionary Computation, 19(5):630–643, October 2015.

    Google Scholar 

  8. Krzysztof Krawiec and Una-May O’Reilly. Behavioral programming: A broader and more detailed take on semantic gp. In Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, GECCO ‘14, pages 935–942, New York, NY, USA, 2014. ACM.

    Google Scholar 

  9. Krzysztof Krawiec, Jerry Swan, and Una-May O’Reilly. Behavioral program synthesis: Insights and prospects. In Genetic Programming Theory and Practice XIII, Genetic and Evolutionary Computation. Springer, 2015.

    Google Scholar 

  10. William La Cava, Kourosh Danai, and Lee Spector. Inference of compact nonlinear dynamic models by epigenetic local search. Engineering Applications of Artificial Intelligence, 55:292–306, October 2016.

    Google Scholar 

  11. William La Cava, Thomas Helmuth, Lee Spector, and Jason H. Moore. 𝜖-Lexicase selection: a probabilistic and multi-objective analysis of lexicase selection in continuous domains. Evolutionary Computation, 1–28. https://doi.org/10.1162/evco_a_00224.

  12. William La Cava, Lee Spector, and Kourosh Danai. Epsilon-lexicase selection for regression. In Tobias Friedrich, editor, GECCO ‘16: Proceedings of the 2016 Annual Conference on Genetic and Evolutionary Computation, pages 741–748, Denver, USA, 20–24 July 2016. ACM.

    Google Scholar 

  13. Miqing Li and Jinhua Zheng. Spread assessment for evolutionary multi-objective optimization. In International Conference on Evolutionary Multi-Criterion Optimization, pages 216–230. Springer, 2009.

    Google Scholar 

  14. M. Lichman. UCI machine learning repository, 2013.

    Google Scholar 

  15. Pawel Liskowski, Krzysztof Krawiec, Thomas Helmuth, and Lee Spector. Comparison of semantic-aware selection methods in genetic programming. In Colin Johnson, Krzysztof Krawiec, Alberto Moraglio, and Michael O’Neill, editors, GECCO 2015 Semantic Methods in Genetic Programming (SMGP’15) Workshop, pages 1301–1307, Madrid, Spain, 11–15 July 2015. ACM.

    Google Scholar 

  16. Samir W Mahfoud. Niching methods for genetic algorithms. PhD thesis, 1995.

    Google Scholar 

  17. Yuliana Martnez, Enrique Naredo, Leonardo Trujillo, Pierrick Legrand, and Uriel Lpez. A comparison of fitness-case sampling methods for genetic programming. Journal of Experimental & Theoretical Artificial Intelligence, 29(6):1203–1224, 2017.

    Google Scholar 

  18. Nicholas Freitag McPhee, Brian Ohs, and Tyler Hutchison. Semantic building blocks in genetic programming. In Proceedings of the 11th European Conference on Genetic Programming, EuroGP 2008, volume 4971 of Lecture Notes in Computer Science, pages 134–145, Naples, 26–28 March 2008. Springer.

    Google Scholar 

  19. Michael Schmidt and Hod Lipson. Age-fitness Pareto optimization. In Genetic Programming Theory and Practice VIII, pages 129–146. Springer, 2011.

    Google Scholar 

  20. Lee Spector. Assessment of problem modality by differential performance of lexicase selection in genetic programming: A preliminary report. In Kent McClymont and Ed Keedwell, editors, 1st workshop on Understanding Problems (GECCO-UP), pages 401–408, Philadelphia, Pennsylvania, USA, 7–11 July 2012. ACM.

    Google Scholar 

  21. Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), pages 267–288, 1996.

    Google Scholar 

  22. Sarah Anne Troise and Thomas Helmuth. Lexicase selection with weighted shuffle. In Genetic Programming Theory and Practice XV, Genetic and Evolutionary Computation, pages 89–103, Ann Arbor, USA, May 2017. Springer.

    Google Scholar 

  23. Tobias Wagner, Nicola Beume, and Boris Naujoks. Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization. In Evolutionary Multi-Criterion Optimization, pages 742–756. Springer, Berlin, Heidelberg, March 2007. https://doi.org/10.1007/978-3-540-70928-2_56.

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Acknowledgements

This material is based upon work supported by the National Science Foundation under Grants No. 1617087, 1129139 and 1331283. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Author information

Authors and Affiliations

  1. Hampshire College, Amherst, MA, USA

    Lee Spector

  2. Institute for Biomedical Informatics, University of Pennsylvania, Philadelphia, PA, USA

    William La Cava

  3. University of Massachusetts, Amherst, MA, USA

    Saul Shanabrook

  4. Hamilton College, Clinton, NY, USA

    Thomas Helmuth

  5. MassMutual, Amherst, MA, USA

    Edward Pantridge

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  1. Lee Spector
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  2. William La Cava
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  3. Saul Shanabrook
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  4. Thomas Helmuth
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  5. Edward Pantridge
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Correspondence to Lee Spector .

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Editors and Affiliations

  1. BEACON Center for the Study of Evolution in Action and Department of Computer Science, Michigan State University, East Lansing, Michigan, USA

    Wolfgang Banzhaf

  2. Institute for Biomedical Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, USA

    Randal S. Olson

  3. Institute for Biomedical Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, USA

    William Tozier

  4. Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan, USA

    Rick Riolo

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Spector, L., Cava, W.L., Shanabrook, S., Helmuth, T., Pantridge, E. (2018). Relaxations of Lexicase Parent Selection. In: Banzhaf, W., Olson, R., Tozier, W., Riolo, R. (eds) Genetic Programming Theory and Practice XV. Genetic and Evolutionary Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-90512-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-90512-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90511-2

  • Online ISBN: 978-3-319-90512-9

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