18 M. Kommenda et al.
objective genetic programming has been performed by utilizing NSGA-II with
slight adaptations to make it suitable for symbolic regression. Furthermore, we
defined a new complexity measure that combines syntactical information about the
evolved trees and the semantics of the occurring symbols.
Among the standard genetic programming algorithms the one with the strictest
size constraints worked best on the artificial problems, both in terms of the accuracy
and simplicity of the models. However, this is only the case if the length constraint
is large enough to generate models that could explain the data reasonably well. This
picture changes when comparing the results obtained on noisy problems, where
standard GP with larger size constraints works better. This indicates that the optimal
length constraint is problem dependent and cannot be known a-priori, thus multiple
values have to be tested during modeling.
Switching from single-objective to multi-objective genetic programming
removes the necessity for specifying a length constraint, because the complexity is
implicitly optimized during the algorithm execution. Additionally, we demonstrated
that by including semantics of the function symbols contained in the models, the
algorithm’s ability to determine the necessary complexity to model the data is
strengthened without worsening the accuracy of the evolved models.
AcknowledgementsThe 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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