Neural Combinatorial Optimization for Time-Dependent Traveling Salesman Problem

The Time-Dependent Traveling Salesman Problem (TDTSP) extends the classical TSP by allowing dynamic edge weights that vary with departure time, reflecting real-world scenarios such as transportation networks, where travel times fluctuate due to congestion patterns. TDTSP violates symmetry, triangle inequality, and cyclic invariance properties of classical TSP, creating unique computational challenges. In this paper, we propose a neural model that extends MatNet from static asymmetric TSP to time-dependent settings by using an adjacency tensor to capture temporal variations, followed by a time-aware decoder. Our architecture addresses the unique challenge of asymmetry and triangle inequality violations that change dynamically over time. Beyond architectural innovations, our research reveals a critical evaluation insight: many practical TDTSP instances maintain the same optimal solution regardless of time-dependent edge weights. This exposes a fundamental limitation in current evaluation practices for TDTSP that rely solely on average travel time metrics across all instances. Such metrics fail to effectively distinguish between methods that genuinely capture temporal dynamics and those that merely perform well on static routing problems. Instead, we present extensive experiments on real-world datasets, evaluating our approach on both entire datasets and specifically filtered instances where temporal dependencies alter the optimal solution. Results show that our method achieves state-of-the-art average optimality gap on full instances and significant travel-time reduction on instances where time-aware routing saves time. These results demonstrate state-of-the-art ability to identify and exploit temporal dependencies, setting new standards for evaluating time-dependent routing problems.