Abstract
This chapter proposes a new model of tree-based Genetic Programming (GP) as a simple sampling algorithm that samples minimal schemata (subsets of the solution space) described by a single concrete node at a single position in the expression tree. We show that GP explores these schemata in the same way across three benchmarks, rapidly converging the population to a specific function at each position throughout the upper layers of the expression tree. This convergence is driven by covariance between membership of a simple schema and rank fitness. We model this process using Price’s theorem and provide empirical evidence to support our model. The chapter closes with an outline of a modification of the standard GP algorithm that reinforces this bias by converging populations to fit schemata in an accelerated way.
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WB acknowledges funding from the Koza Endowment provided by MSU.
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White, D.R., Fowler, B., Banzhaf, W., Barr, E.T. (2020). Modelling Genetic Programming as a Simple Sampling Algorithm. In: Banzhaf, W., Goodman, E., Sheneman, L., Trujillo, L., Worzel, B. (eds) Genetic Programming Theory and Practice XVII. Genetic and Evolutionary Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-39958-0_18
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