TY - GEN
T1 - Shape-Constrained Symbolic Regression with NSGA-III.
AU - Haider, Christian
AU - Kronberger, Gabriel
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This inclusion allows to ensure that certain expected behavior is reflected by the resulting models. This specific behavior is defined by constraints which restrict the functional form e.g. monotonicity, concavity or model image boundaries. That allows finding more robust and reliable models in the specific case of highly noisy data or in extrapolation domains. This paper presents a multi-objective approach to minimize the approximation error as well as the constraint violations. Explicitly the two algorithms NSGA-II and NSGA-III are implemented and compared against each other in terms of model quality and runtime. Both algorithms are executed on a selected set of benchmark instances from physics textbooks. The results indicate that both algorithms are able to generate mostly feasible solutions and NSGA-III provides slight improvements in terms of model quality. Moreover, an improvement in runtime can be observed when using NSGA-III.
AB - Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This inclusion allows to ensure that certain expected behavior is reflected by the resulting models. This specific behavior is defined by constraints which restrict the functional form e.g. monotonicity, concavity or model image boundaries. That allows finding more robust and reliable models in the specific case of highly noisy data or in extrapolation domains. This paper presents a multi-objective approach to minimize the approximation error as well as the constraint violations. Explicitly the two algorithms NSGA-II and NSGA-III are implemented and compared against each other in terms of model quality and runtime. Both algorithms are executed on a selected set of benchmark instances from physics textbooks. The results indicate that both algorithms are able to generate mostly feasible solutions and NSGA-III provides slight improvements in terms of model quality. Moreover, an improvement in runtime can be observed when using NSGA-III.
KW - Many-objective optimization
KW - Shape-constraints
KW - Symbolic regression
UR - http://www.scopus.com/inward/record.url?scp=85151123397&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-25312-6_19
DO - 10.1007/978-3-031-25312-6_19
M3 - Conference contribution
SN - 9783031253119
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 164
EP - 172
BT - Computer Aided Systems Theory – EUROCAST 2022 - 18th International Conference, Revised Selected Papers
A2 - Moreno-Díaz, Roberto
A2 - Pichler, Franz
A2 - Quesada-Arencibia, Alexis
PB - Springer
T2 - 18th International Conference on Computer Aided Systems Theory, EUROCAST 2022
Y2 - 20 February 2022 through 25 February 2022
ER -