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Genetic Programming Theory and Practice XV pp 17–37Cite as

Schema Analysis in Tree-Based Genetic Programming

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

Abstract

In this chapter we adopt the concept of schemata from schema theory and use it to analyze population dynamics in genetic programming for symbolic regression. We define schemata as tree-based wildcard patterns and we empirically measure their frequencies in the population at each generation. Our methodology consists of two steps: in the first step we generate schemata based on genealogical information about crossover parents and their offspring, according to several possible schema definitions inspired from existing literature. In the second step, we calculate the matching individuals for each schema using a tree pattern matching algorithm. We test our approach on different problem instances and algorithmic flavors and we investigate the effects of different selection mechanisms on the identified schemata and their frequencies.

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Notes

  1. 1.

    The terms root parent and non-root parent refer to the two parents involved in a crossover operation: the root parent passes on to the child its entire rooted tree structure, with the exception of the subtree swapped by crossover at an arbitrary location (called a cutpoint) from the non-root parent.

  2. 2.

    To maintain low computational times, certain compromises had to be made in terms of population size and number of generations.

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Acknowledgements

The work described in this paper was done within the COMET Project Heuristic Optimization in Production and Logistics (HOPL), #843532 funded by the Austrian Research Promotion Agency (FFG).

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Authors and Affiliations

  1. Heuristic and Evolutionary Algorithms Laboratory, University of Applied Sciences Upper Austria, Hagenberg, Austria

    Bogdan Burlacu, Michael Affenzeller, Michael Kommenda & Stephan Winkler

  2. Institute for Formal Models and Verification, Johannes Kepler University, Linz, Austria

    Bogdan Burlacu, Michael Affenzeller, Michael Kommenda & Stephan Winkler

  3. Heuristic and Evolutionary Algorithms Laboratory, University of Applied Sciences Upper Austria, Hagenberg, Austria

    Gabriel Kronberger

Authors
  1. Bogdan Burlacu
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  2. Michael Affenzeller
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  3. Michael Kommenda
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  4. Gabriel Kronberger
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  5. Stephan Winkler
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Corresponding author

Correspondence to Bogdan Burlacu .

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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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Burlacu, B., Affenzeller, M., Kommenda, M., Kronberger, G., Winkler, S. (2018). Schema Analysis in Tree-Based Genetic Programming. 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_2

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  • DOI: https://doi.org/10.1007/978-3-319-90512-9_2

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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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