Abstract
Several genetic programming researchers have argued for the utility of genetic operators that act uniformly. By “act uniformly” we mean two specific things: that the probability of an inherited program component being modified during inheritance is independent of the size and shape of the parent programs beyond the component in question; and that pairs of parents are combined in ways that allow arbitrary combinations of components from each parent to appear in the child. Uniform operators described in previous work have had limited utility, however, because of a mismatch between the relevant notions of uniformity and the hierarchical structure and variable sizes of many genetic programming representations. In this chapter we describe a new genetic operator, ULTRA, which incorporates aspects of both mutation and crossover and acts approximately uniformly across programs of variable sizes and structures. ULTRA treats hierarchical programs as linear sequences and includes a repair step to ensure that syntax constraints are satisfied after variation. We show that on the drug bioavailability and Pagie-1 benchmark problems ULTRA produces significant improvements both in problem-solving power and in program size relative to standard operators. Experiments with factorial regression and with the boolean 6-multiplexer problem demonstrate that ULTRA can manipulate programs that make use of hierarchical structure, but also that it is not always beneficial. The demonstrations evolve programs in the Push programming language, which makes repair particularly simple, but versions of the technique should be applicable in other genetic programming systems as well.
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Notes
- 1.
We make no claims here about the prevalence of “protection from crossover.” This is just one example of the effects that operator uniformity can have on program sizes and on genetic programming search efficacy; other effects may interact with other hypothesized causes of program bloat in other ways.
- 2.
- 3.
Recently, however, concern have been raised about the use of this problem; see http://jmmcd.net/2013/12/19/gp-needs-better-baselines.html
- 4.
- 5.
Note that this work gives an outdated description of ULTRA that does not pad the shorter program before alternation.
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Acknowledgements
Thanks to Micah Savitzky for exploratory work that later led to the ideas in this paper, to Emma Tosch and Kyle Harrington for discussions and code, to Josiah Erikson for systems support, and to Hampshire College for support for the Hampshire College Institute for Computational Intelligence. This material is based upon work supported by the National Science Foundation under Grant Nos. 1017817 and 1129139. 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.
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Spector, L., Helmuth, T. (2014). Uniform Linear Transformation with Repair and Alternation in Genetic Programming. In: Riolo, R., Moore, J., Kotanchek, M. (eds) Genetic Programming Theory and Practice XI. Genetic and Evolutionary Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0375-7_8
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