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