Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs

Large Neighborhood Search (LNS) is a combinatorial optimization heuristic that starts with an assignment of values for the variables to be optimized, and iteratively improves it by searching a large neighborhood around the current assignment. In this paper we consider a learning-based LNS approach for mixed integer programs (MIPs). We train a Neural Diving model to generate an initial assignment. Formulating the subsequent search steps as a Markov Decision Process, we train a Neural Neighborhood Selection policy to select a search neighborhood at each step, which is searched using a MIP solver to find the next assignment. The policy network is trained using imitation learning. We propose a target policy for imitation that is designed to select the neighborhood containing the optimal next assignment amongst all possible choices for the neighborhood of a specified size. Our approach matches or outperforms all the baselines on five diverse real-world MIP datasets with large-scale instances, including two production applications at a large technology company. It achieves 2 × to 37 . 8 × better average primal gap than the best baseline on three datasets at large running times.