Shape-Constrained Symbolic Regression with NSGA-III

Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This inclusion ensure that certain expected behavior is better reflected by the resulting models. The defined via constraints, which refer function form e.g. monotonicity, concavity, convexity or models image boundaries. In addition advantage of obtaining more robust and reliable due defining constraints over functions shape, use SCSR find are noise have a extrapolation behavior. paper presents mutlicriterial approach minimize approximation error as well constraint violations. Explicitly two algorithms NSGA-II NSGA-III implemented compared against each other in terms model quality runtime. Both capable dealing with multiple objectives, whereas established multi-objective performing on instances up-to 3 objectives. an extension algorithm was developed handle problems "many" objectives (more than objectives). executed selected set benchmark from physics textbooks. results indicate both able largely feasible solutions provides slight improvements quality. Moreover, improvement runtime can be observed using many-objective approach.