Scalable Solution of the Stochastic Multi-path Traveling Salesman Problem via Neural Networks

The traveling salesman problem (TSP) is a canonical NP-hard combinatorial optimization benchmark that tests the representational capacity and generalization of neural solvers. While non-autoregressive (NAR) approaches offer parallel inference, they often lack sufficient geometric inductive bias and stable training signals, leading to degraded performance under cross-scale and cross-distribution shifts. We propose GeoRouteNet, a geometry-enhanced NAR neural solver for Euclidean TSP. On the model side, GeoRouteNet incorporates centered node features, learnable radial distance basis functions, distance-aware graph attention with explicit edge messaging, LayerNorm-SwiGLU feed-forward blocks, and cross-layer attentive residual mixing. On the training side, we design multi-candidate self-comparison reinforcement learning (MCS-RL), which samples multiple candidate tours per instance, constructs adaptive baselines from greedy and peer candidates, and adds winner-candidate guidance with annealed entropy regularization. On 10,000 random TSP50 instances, GeoRouteNet achieves a 0.32% optimality gap under Beam-1000 decoding. On TSP100, the gap is 1.26%. On 27 stratified TSPLIB EUC_2D instances, the overall gap drops from 17.12% (NAR4TSP reproduction) to 3.60%, while batch inference throughput substantially exceeds that of Concorde and LKH3. Ablation studies confirm that geometric structure enhancement and multi-candidate training are complementary: structure improvements dominate cross-distribution gains, while MCS-RL further stabilizes solution quality when paired with a strong geometric encoder.

Neural combinatorial optimization (NCO) offers a promising alternative to traditional heuristic-based methods for solving complex graph optimization problems by proposing to learn heuristics through data. This class of problems frequently arises in automation, as it can be used to model a variety of applications. While NCO has been extensively studied for deterministic combinatorial optimization problems, there are only a few works that aim to solve stochastic combinatorial optimization problems. In this work, we present N(CO)$^2$: Neural Combinatorial Optimization with Chance cOnstraints to solve the Stochastic Orienteering Problem (SOP) without the use of hand-crafted heuristics. By integrating a reinforcement learning (RL) framework, the model optimizes path selection under uncertainty, effectively balancing exploration and exploitation. Empirical results demonstrate that our method generalizes well across diverse SOP instances, achieving competitive performance compared to the state-of-the-art mixed-integer linear program (MILP) for the task. The proposed approach reduces human effort in heuristic design while enabling adaptive and efficient decision-making in uncertain environments.

In modern intelligent transportation systems (ITS), particularly in freight transportation and logistics, real-time route planning is crucial. It presents unique challenges driven by high uncertainty in service requests, where the number of service customers can vary drastically, ranging from hundreds to thousands. Existing neural methods struggle to maintain performance under such significant variations, which severely limits their practical applicability. To address this crucial shortcoming, this work proposes a novel Instance-Conditioned Adaptation Model (ICAM) designed for better large-scale generalization. In particular, we design a simple yet efficient instance-conditioned adaptation function that adjusts the policy based on the specific geometry and density of the current traffic scenario to improve model adaptability with minimal computational overhead. Furthermore, we propose a powerful yet low-complexity instance-conditioned adaptation module to generate better solutions for instances across various scales. Extensive experiments on synthetic, benchmark, and real-world instances demonstrate that ICAM can consistently achieve promising generalization performance across four widely studied large-scale route planning scenarios. Notably, our proposed method delivers high-quality solutions with remarkably fast inference speed, providing a scalable and efficient solution for real-time intelligent transportation operations. Our code is available at https://github.com/CIAM-Group/ICAM.