Reinforcement Learning for Variable Selection in a Branch and Bound Algorithm
This addresses the efficiency of commercial solvers for optimization problems, representing an incremental advancement by adapting RL techniques to a specific domain.
The paper tackles the problem of improving branching strategies in Branch and Bound algorithms for mixed integer linear programs by learning a new strategy from scratch using Reinforcement Learning, resulting in a method that generalizes well to new instances.
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.