Using Shape Constraints for Improving Symbolic Regression Models
This addresses the need for data-driven models in engineering to have specific properties, but it is incremental as it builds on existing multi-objective algorithms for symbolic regression.
The paper tackles the problem of incorporating prior knowledge about function shape (e.g., positivity, monotonicity) into symbolic regression models to improve their extrapolation behavior, using multi-objective evolutionary algorithms like NSGA-II and MOEA/D with a soft-penalty approach, and shows that all tested algorithms successfully find models conforming to constraints.
We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever a data-driven model obtained from measurements must have certain properties (e.g. positivity, monotonicity or convexity/concavity). We implement shape constraints using a soft-penalty approach which uses multi-objective algorithms to minimize constraint violations and training error. We use the non-dominated sorting genetic algorithm (NSGA-II) as well as the multi-objective evolutionary algorithm based on decomposition (MOEA/D). We use a set of models from physics textbooks to test the algorithms and compare against earlier results with single-objective algorithms. The results show that all algorithms are able to find models which conform to all shape constraints. Using shape constraints helps to improve extrapolation behavior of the models.