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.

Original languageEnglish
Number of pages9
Publication statusPublished - 2022


  • Many-objective optimization
  • Shape-constraints
  • Symbolic regression


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