Abstract
This chapter proposes a generic framework to build geometric dispersion (GD) operators for Geometric Semantic Genetic Programming in the context of symbolic regression, followed by two concrete instantiations of the framework: a multiplicative geometric dispersion operator and an additive geometric dispersion operator. These operators move individuals in the semantic space in order to balance the population around the target output in each dimension, with the objective of expanding the convex hull defined by the population to include the desired output vector. An experimental analysis was conducted in a testbed composed of sixteen datasets showing that dispersion operators can improve GSGP search and that the multiplicative version of the operator is overall better than the additive version.
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Notes
- 1.
The convex hull of a set of points is given by the set of all possible convex combinations of these points [18].
- 2.
Note that when \({\mathbf {x}}_i \in \mathbb {R}^d\) with d > 1 the vector I becomes a matrix with dimensions d × n. We allow an abuse of notation by representing the matrix as a vector with dimension n, where each element corresponds to a vector of dimension d.
- 3.
The coefficients of convex combinations can be found by means of Gaussian elimination [9].
- 4.
Oliveira et al. [15] presents the first geometric dispersion operator. However, this operator is a particular case of the framework presented in this paper. Hence, hereafter their operator is referred as multiplicative geometric dispersion (MGD) operator in contrast to the GD framework.
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Acknowledgements
The authors would like to thank CAPES, FAPEMIG, and CNPq (141985/ 2015-1) for their financial support.
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Oliveira, L.O.V.B., Otero, F.E.B., Pappa, G.L. (2018). A Generic Framework for Building Dispersion Operators in the Semantic Space. In: Riolo, R., Worzel, B., Goldman, B., Tozier, B. (eds) Genetic Programming Theory and Practice XIV. Genetic and Evolutionary Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-97088-2_12
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