Mathematical Optimization in Classification and Regression Trees

Emilio Carrizosa, Cristina Molero del Rio, Dolores Romero Morales*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Classification and regression trees, as well as their variants, are off-the-shelf methods in Machine Learning. In this paper, we review recent contributions within the Continuous Optimization and the Mixed-Integer Linear Optimization paradigms to develop novel formulations in this research area. We compare those in terms of the nature of the decision variables and the constraints required, as well as the optimization algorithms proposed. We illustrate how these powerful formulations enhance the flexibility of tree models, being better suited to incorporate desirable properties such as cost-sensitivity, explainability, and fairness, and to deal with complex data, such as functional data.
Original languageEnglish
Issue number1
Pages (from-to)5-33
Number of pages29
Publication statusPublished - Apr 2021


  • Classification and Regression Trees
  • Tree ensembles
  • Mixed-integer linear optimization
  • Continuous nonlinear optimization
  • Sparsity
  • Explainability

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