Hierarchical Reinforcement Learning with Dynamic Meta Agent for Adaptive Cut Selection in Integer Programming with Applications to Sensor Network Design

Designing optimal sensor networks for industrial processes presents significant combinatorial challenges. These are often formulated as large-scale integer programming (IP) problems. Efficiently solving these IPs, particularly through cutting plane selection, remains a critical bottleneck, due to its complexity. Cutting plane selection is a fundamental technique in many IP solvers. It involves iteratively adding valid linear inequalities (cuts) to the problem formulation to eliminate noninteger solutions without removing any feasible integer solutions. This work proposes a hierarchical reinforcement learning (HRL) framework with dynamic agent allocation to enhance adaptive cutting plane selection for the solution of these problems. Using a two-level architecture powered by the Proximal Policy Optimization (PPO) backbone, the framework features a meta-agent that selects cutting strategies and allocates lower-level agents to refine LP relaxations. We evaluate the approach on challenging sensor network design problems and synthetic IP instances, comparing it to single-agent RL and traditional heuristics. Results show that HRL achieves higher cumulative rewards, improved success rates, and faster convergence, achieving over 25% and 60% time savings for Gomory and cover cuts, respectively, on these large instances, demonstrating its scalability and effectiveness in optimizing cut selection for real-world applications.