Policy-Guided Monte-Carlo Tree Search for CAD-Grounded PCB Routing

PCB routing has traditionally relied on hand-designed cost functions and iterative route improvement. Learning-based routers instead optimize routing decisions from data, but their policies remain amortized over the training distribution and cannot adapt their decisions to an unseen board at deployment. We propose PW-MCTS, a policy-guided Monte-Carlo tree search method that refines a pretrained routing policy at test time by comparing alternative trajectories over the compact, connection-level action space exposed by a CAD engine, using the policy as the prior and its critic for leaf evaluation. To make this search reliable on out-of-distribution boards, we fit a board-wise iterated Bellman calibration of the critic and gate the bootstrap on its held-out correlation. We further determinize the CAD engine so that the search can treat each node as a unique routing state, and improve search efficiency through incremental environment restoration, branch-packed and memoized inference, and invalid-action filtering. We evaluate on 50 open-source boards with a policy trained only on procedurally generated ones, separating trajectory quality from wall-clock efficiency. At equal draws, PW-MCTS raises clean pass from $34.2\%$ to $47.7\%$ and routability from $0.695$ to $0.805$. At equal time, where one search trajectory costs $17.9\times$ one policy rollout, policy sampling matches search in clean pass and routability. Implementation optimizations raise throughput by $9.95\times$ over the determinized engine, and budget, leaf-value, and cost analyses identify what must improve for this per-draw advantage to become a wall-clock advantage.