Learning for Spatial Branching: An Algorithm Selection Approach
This work addresses a gap in applying machine learning to non-linear optimization, offering a domain-specific improvement for polynomial optimization problems.
The authors tackled the problem of improving spatial branching in non-linear optimization by developing a learning framework based on instance-specific features, which significantly outperformed standard branching rules in experiments on benchmark instances.
The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To bridge this gap, we develop a learning framework for spatial branching and show its efficacy in the context of the Reformulation-Linearization Technique for polynomial optimization problems. The proposed learning is performed offline, based on instance-specific features and with no computational overhead when solving new instances. Novel graph-based features are introduced, which turn out to play an important role for the learning. Experiments on different benchmark instances from the literature show that the learning-based branching rule significantly outperforms the standard rules.