A Reciprocity Between Tree Ensemble Optimization and Multilinear Optimization

Jongeun Kim (), Jean-Philippe P. Richard () and Mohit Tawarmalani ()
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Jongeun Kim: Department of Industrial and Systems Engineering, University of Minnesota-Twin Cities, Minneapolis, Minnesota 55455
Jean-Philippe P. Richard: Department of Industrial and Systems Engineering, University of Minnesota-Twin Cities, Minneapolis, Minnesota 55455
Mohit Tawarmalani: Mitchell E. Daniels, Jr. School of Business, Purdue University, West Lafayette, Indiana 47907

Operations Research, 2025, vol. 73, issue 5, 2610-2626

Abstract: In this paper, we establish a low-degree polynomially-sized reduction between tree ensemble optimization and optimization of multilinear functions over a Cartesian product of simplices. We use this insight to derive new formulations for tree ensemble optimization problems and to obtain new convex hull results for multilinear polytopes. A computational experiment on multicommodity transportation problems with costs modeled using tree ensembles shows the practical advantage of our formulation relative to existing formulations of tree ensembles and other piecewise-linear modeling techniques.

Keywords: Optimization; tree ensemble optimization; multilinear polytopes; convexification; decision trees (search for similar items in EconPapers)
Date: 2025
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