Many real-world problems can be formulated as a constrained Traveling Salesman Problem (TSP). However, the constraints are always complex and numerous, making the TSPs challenging to solve. When the number of complicated constraints grows, it is time-consuming for traditional heuristic algorithms to avoid illegitimate outcomes. Learning-based methods provide an alternative to solve TSPs in a soft manner, which also supports GPU acceleration to generate solutions quickly. Nevertheless, the soft manner inevitably results in difficulty solving hard-constrained problems with learning algorithms, and the conflicts between legality and optimality may substantially affect the optimality of the solution. To overcome this problem and to have an effective solution against hard constraints, we proposed a novel learning-based method that uses looking-ahead information as the feature to improve the legality of TSP with Time Windows (TSPTW) solutions. Besides, we constructed TSPTW datasets with hard constraints in order to accurately evaluate and benchmark the statistical performance of various approaches, which can serve the community for future research. With comprehensive experiments on diverse datasets, MUSLA outperforms existing baselines and shows generalizability potential.

翻译：许多现实世界问题可被形式化为带约束的旅行商问题（TSP）。然而，这些约束往往复杂且繁多，使得TSP求解颇具挑战。当复杂约束数量增加时，传统启发式算法需耗费大量时间以避免不合规结果。基于学习的方法提供了一种软性求解TSP的替代方案，其支持GPU加速以快速生成解。然而，软性方式不可避免地导致学习算法在求解硬约束问题时面临困难，且合法性与最优性之间的冲突可能显著影响解的最优性。为克服该问题并有效应对硬约束，我们提出了一种新颖的基于学习的方法，利用前瞻信息作为特征以提升带时间窗TSP（TSPTW）解的合法性。此外，我们构建了具有硬约束的TSPTW数据集，以准确评估和基准测试各类方法的统计性能，为后续研究提供社区支持。通过在多样化数据集上的综合实验，MUSLA优于现有基线方法，并展现出泛化潜力。