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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jongeun Kim & Sven Leyffer & Prasanna Balaprakash, 2023. "Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1383-1403, November.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:6:p:1383-1403
    DOI: 10.1287/ijoc.2022.0050
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