Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

Jongeun Kim (), Sven Leyffer () and Prasanna Balaprakash ()
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Jongeun Kim: Industrial and Systems Engineering, University of Minnesota-Twin Cities, Minneapolis, Minnesota 55455
Sven Leyffer: Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439
Prasanna Balaprakash: Computing and Computational Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

INFORMS Journal on Computing, 2023, vol. 35, issue 6, 1383-1403

Abstract: In this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature.

Keywords: symbolic regression; mixed-integer nonlinear programming; local branching heuristic; expression tree (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:35:y:2023:i:6:p:1383-1403

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