Learning in Reformulation-Linearization Technique-Based Spatial Branching: Limitations of Strong Branching Imitation

Over the last few years, there has been a surge in the use of learning techniques to improve the performance of optimization algorithms. In particular, the learning of branching rules in mixed integer linear programming has received a lot of attention, with most methodologies based on strong branching imitation. Recently, some advances have been made as well in the context of nonlinear programming, with some methodologies focusing on learning to select the best branching rule among a predefined set of rules, leading to promising results. In this paper, we explore, in the nonlinear setting, the limits on the improvements that might be achieved by the above two approaches when using reformulation-linearization technique-based relaxations for solving polynomial optimization problems: learning to select the best variable (strong branching) and learning to select the best rule (rule selection). History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: Financial support from Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia [Grants ED431C-2021/24, MICIU/AEI/10.13039/501100011033, PID2020-116587GB-I00, and PID2021-124030NB-C32] is gratefully acknowledged. I. Gómez-Casares received financial support from the Spanish Ministry of Education [FPU Grant 20/01555]. B. Ghaddar received financial support from the Natural Sciences and Engineering Research Council of Canada [Discovery Grants RGPIN-2017-04185 and RGPIN-2025-04585] and the John Thompson Chair Fellowship. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0775 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0775 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .