Reinforcement Learning for Variable Selection in a Branch and Bound Algorithm

TL;DR

This paper introduces FMSTS, a novel reinforcement learning approach that learns an optimized branching strategy for Branch and Bound algorithms in solving mixed integer linear programs, outperforming traditional heuristics.

Contribution

It presents the first application of reinforcement learning to fully optimize the branching strategy in Branch and Bound algorithms, including a new neural network architecture.

Findings

FMSTS generalizes well to new instances.

The learned strategy improves efficiency over traditional heuristics.

Insights for adapting RL techniques to Branch and Bound are provided.

Abstract

Mixed integer linear programs are commonly solved by Branch and Bound algorithms. A key factor of the efficiency of the most successful commercial solvers is their fine-tuned heuristics. In this paper, we leverage patterns in real-world instances to learn from scratch a new branching strategy optimised for a given problem and compare it with a commercial solver. We propose FMSTS, a novel Reinforcement Learning approach specifically designed for this task. The strength of our method lies in the consistency between a local value function and a global metric of interest. In addition, we provide insights for adapting known RL techniques to the Branch and Bound setting, and present a new neural network architecture inspired from the literature. To our knowledge, it is the first time Reinforcement Learning has been used to fully optimise the branching strategy. Computational experiments show that our method is appropriate and able to generalise well to new instances.