Embedding Decision Trees and Random Forests in Constraint Programming

In past papers, we have introduced Empirical Model Learning (EML) as a method to enable Combinatorial Optimization on real world systems that are impervious to classical modeling approaches. The core idea in EML consists in embedding a Machine Learning model in a traditional combinatorial model. So far, the method has been demonstrated by using Neural Networks and Constraint Programming (CP). In this paper we add one more technique to the EML arsenal, by devising methods to embed Decision Trees (DTs) in CP. In particular, we propose three approaches: 1) a simple encoding based on meta-constraints; 2) a method using attribute discretization and a global table constraint; 3) an approach based on converting a DT into a Multi-valued Decision Diagram, which is then fed to an mdd constraint. We finally show how to embed in CP a Random Forest, a powerful type of ensemble classifier based on DTs. The proposed methods are compared in an experimental evaluation, highlighting their strengths and their weaknesses.