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Complexity Measures for Multi-objective Symbolic Regression

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9520)


Multi-objective symbolic regression has the advantage that while the accuracy of the learned models is maximized, the complexity is automatically adapted and need not be specified a-priori. The result of the optimization is not a single solution anymore, but a whole Pareto-front describing the trade-off between accuracy and complexity.

In this contribution we study which complexity measures are most appropriately used in symbolic regression when performing multi- objective optimization with NSGA-II. Furthermore, we present a novel complexity measure that includes semantic information based on the function symbols occurring in the models and test its effects on several benchmark datasets. Results comparing multiple complexity measures are presented in terms of the achieved accuracy and model length to illustrate how the search direction of the algorithm is affected.


  • Symbolic regression
  • Complexity measures
  • Multi-objective optimization
  • Genetic programming

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The 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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Correspondence to Michael Kommenda .

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Kommenda, M., Beham, A., Affenzeller, M., Kronberger, G. (2015). Complexity Measures for Multi-objective Symbolic Regression. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham.

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