A generalized benders decomposition-based global optimization approach to symbolic regression for explicit surrogate modeling from limited data information

Jiawen Wei, Zhihong Yuan

Abstract: Solving noncovex Disjunctive Programming (DP) problems for representing symbolic regression trees to build explicit surrogate models from limited data information is challenging. This paper presents an effective global optimization approach to deal with these DPs. Piecewise McCormick envelope-based strategy is used to relax the nonconvex bilinear terms and nonconvex inequality constraints of the DP. A large-scale convex mixed integer nonlinear programing (MINLP) is then generated via the convex hull. A tailored linearization strategy further relaxes tightly all nonlinear terms in the convex MINLP to generate a mixed integer linear programming which is finally solved to global optimality by Generalized Benders Decomposition-based algorithm. Through testing three numerical simulations and Cetane number prediction, when compared to the monolithic approach of the state-of-the-art global optimization solvers such as BARON, the proposed approach is shown to reduce the solution time by up to two orders of magnitude and construct more accurate explicit surrogate models.