Learning Large Neighborhood Search Policy for Integer Programming

We propose a deep reinforcement learning (RL) method to learn large neighborhood search (LNS) policy for integer programming (IP). The RL policy is trained as the destroy operator to select a subset of variables at each step, which is reoptimized by an IP solver as the repair operator. However, the combinatorial number of variable subsets prevents direct application of typical RL algorithms. To tackle this challenge, we represent all subsets by factorizing them into binary decisions on each variable. We then design a neural network to learn policies for each variable in parallel, trained by a customized actor-critic algorithm. We evaluate the proposed method on four representative IP problems. Results show that it can find better solutions than SCIP in much less time, and significantly outperform other LNS baselines with the same runtime. Moreover, these advantages notably persist when the policies generalize to larger problems. Further experiments with Gurobi also reveal that our method can outperform this state-of-the-art commercial solver within the same time limit. Recently, a number of works apply deep (reinforcement) learning to automatically design heuristic algorithms, either in constructive or improving fashion. Different from construction heuristics that sequentially extend partial solutions to complete ones [4, 5, 6, 7, 8, 9, 10, 11] , learning improvement heuristics can often deliver high solution quality by iteratively reoptimizing an initial solution using * Wen Song is the corresponding author. 35th Conference on Neural Information Processing Systems (NeurIPS 2021).