LMask: Learn to Solve Constrained Routing Problems with Lazy Masking

TL;DR

LMask is a learning framework that uses lazy masking and backtracking to efficiently generate feasible solutions for complex constrained routing problems, achieving state-of-the-art results.

Contribution

It introduces LazyMask decoding with backtracking and refinement embedding, providing theoretical guarantees and improved performance on constrained routing benchmarks.

Findings

LMask achieves higher feasibility rates than existing neural methods.

LMask produces better solution quality on TSPTW and TSPDL.

The approach reduces sampling costs through backtracking budget and penalty mechanisms.

Abstract

Routing problems are canonical combinatorial optimization tasks with wide-ranging applications in logistics, transportation, and supply chain management. However, solving these problems becomes significantly more challenging when complex constraints are involved. In this paper, we propose LMask, a novel learning framework that utilizes dynamic masking to generate high-quality feasible solutions for constrained routing problems. LMask introduces the LazyMask decoding method, which lazily refines feasibility masks with the backtracking mechanism. In addition, it employs the refinement intensity embedding to encode the search trace into the model, mitigating representation ambiguities induced by backtracking. To further reduce sampling cost, LMask sets a backtracking budget during decoding, while constraint violations are penalized in the loss function during training to counteract infeasibility caused by this budget. We provide theoretical guarantees for the validity and probabilistic optimality of our approach. Extensive experiments on the traveling salesman problem with time windows (TSPTW) and TSP with draft limits (TSPDL) demonstrate that LMask achieves state-of-the-art feasibility rates and solution quality, outperforming existing neural methods.