LMask: Learn to Solve Constrained Routing Problems with Lazy Masking

2025-05-23

AI Summary

This work addresses combinatorial routing optimization under complex constraints—such as time windows and draft limitations—by proposing LazyMask, a neural solving framework that synergistically integrates dynamic masking with backtracking. Methodologically, it introduces a novel *lazy masking* decoding strategy, incorporating backtracking budget control and refinement intensity adjustment. We theoretically establish feasibility guarantees and probabilistic optimality of the generated solutions, while the loss function explicitly penalizes constraint violations. Leveraging constraint-aware embedding, penalty-guided supervised training, and budget-constrained sampling during decoding, LazyMask achieves state-of-the-art (SOTA) feasibility rates and solution quality on the TSPTW and TSPDL benchmarks—significantly outperforming existing neural solvers in both robustness and efficacy.

Technology Category

• Constraint Satisfaction and Optimization: Search
• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Solves constrained routing problems with dynamic masking
• Ensures solution feasibility using lazy mask decoding
• Improves efficiency with backtracking budget and penalty

Innovation

• Dynamic masking for constrained routing solutions
• LazyMask decoding with backtracking mechanism
• Refinement intensity embedding reduces ambiguity