Learning for Spatial Branching: An Algorithm Selection Approach

TL;DR

This paper introduces a machine learning framework for spatial branching in non-linear optimization, demonstrating significant performance improvements over standard rules through novel graph-based features and offline training.

Contribution

It develops a new learning approach for spatial branching in non-linear optimization, filling a gap in the application of ML to such problems.

Findings

Learning-based branching outperforms standard rules.

Graph-based features are crucial for effective learning.

No additional computational overhead during solving.

Abstract

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.