Neural Large Neighborhood Search

ravichandra addanki, Vinod Nair, Mohammad Alizadeh

Keywords: Reinforcement Learning, Combinatorial Optimization, Mixed Integer Programming, Graph Neural Networks, Large Neighborhood Search

Abstract: Large Neighborhood Search (LNS) is a combinatorial optimization technique that works iteratively starting from a poor solution, and at each iteration searches a large set of neighbors of the current solution to find a better one. The choice of the set of neighbors to search at each iteration is crucial for LNS to be effective, and successful applications rely on problem-specific neighborhood definitions that are difficult to develop. In this work we propose NLNS, a Deep Reinforcement Learning approach to automatically learn a strong neighborhood selection policy in LNS for a given input distribution of problems. NLNS works in tandem with an existing solver that searches in each neighborhood, guiding it towards optimal solutions efficiently. We demonstrate our approach on Mixed Integer Programs (MIPs). Results on several datasets show that it is possible to learn a neighbor selection policy that allows LNS to efficiently find good solutions. We also present results for integrating the learned policy in a state-of-the-art MIP solver based on the branch-and-bound algorithm to improve its performance.