Evolving Simple Symbolic Regression Models
by Multi-Objective Genetic Programming
Michael Kommenda, Gabriel Kronberger, Michael Affenzeller,
Stephan M. Winkler, and Bogdan Burlacu
Abstract In this chapter we examine how multi-objective genetic programming
can be used to perform symbolic regression and compare its performance to single-
objective genetic programming. Multi-objective optimization is implemented by
using a slightly adapted version of NSGA-II, where the optimization objectives
are the model’s prediction accuracy and its complexity. As the model complexity
is explicitly defined as an objective, the evolved symbolic regression models are
simpler and more parsimonious when compared to models generated by a single-
objective algorithm. Furthermore, we define a new complexity measure that includes
syntactical and semantic information about the model, while still being efficiently
computed, and demonstrate its performance on several benchmark problems. As a
result of the multi-objective approach the appropriate model length and the functions
included in the models are automatically determined without the necessity to specify
them a-priori.
Keywords Symbolic regression • Complexity measures • Multi-objective
optimization • Genetic programming • NSGA-II
1 Introduction
Symbolic regression is the task of finding mathematical formulas that model the
relationship between several independent and one dependent variable. A distin-
guishing feature of symbolic regression is that no assumption about the model
structure needs to be made a-priori, because the algorithm automatically determines
M. Kommenda () • M. Affenzeller • B. Burlacu
Heuristic and Evolutionary Algorithms Laboratory, University of Applied Sciences Upper
Austria, Softwarepark 11, 4232 Hagenberg, Austria
Institute for Formal Models and Verification, Johannes Kepler University,
Altenberger Straße 69, 4040 Linz, Austria
e-mail:[email protected]
G. Kronberger • S.M. Winkler
Heuristic and Evolutionary Algorithms Laboratory, University of Applied Sciences Upper
Austria, Softwarepark 11, 4232 Hagenberg, Austria
© Springer International Publishing Switzerland 2016
R. Riolo et al. (eds.),Genetic Programming Theory and Practice XIII,
Genetic and Evolutionary Computation, DOI 10.1007/978-3-319-34223-8_1
1