Lindong Liu

Kuan Xu, Li Shen, Lindong Liu

Column generation (CG) is a vital method to solve large-scale problems by dynamically generating variables. It has extensive applications in common combinatorial optimization, such as vehicle routing and scheduling problems, where each iteration step requires solving an NP-hard constrained shortest path problem. Although some heuristic methods for acceleration already exist, they are not versatile enough to solve different problems. In this work, we propose a reinforcement learning-based hyper-heuristic framework, dubbed RLHH, to enhance the performance of CG. RLHH is a selection module embedded in CG to accelerate convergence and get better integer solutions. In each CG iteration, the RL agent selects a low-level heuristic to construct a reduced network only containing the edges with a greater chance of being part of the optimal solution. In addition, we specify RLHH to solve two typical combinatorial optimization problems: Vehicle Routing Problem with Time Windows (VRPTW) and Bus Driver Scheduling Problem (BDSP). The total cost can be reduced by up to 27.9\% in VRPTW and 15.4\% in BDSP compared to the best lower-level heuristic in our tested scenarios, within equivalent or even less computational time. The proposed RLHH is the first RL-based CG method that outperforms traditional approaches in terms of solution quality, which can promote the application of CG in combinatorial optimization.

Lindong Liu, Zhixiong Jin, Seongjin Choi

High-resolution highway traffic state information is essential for Intelligent Transportation Systems, but typical traffic data acquired from loop detectors and probe vehicles are often too sparse and noisy to capture the detailed dynamics of traffic flow. We propose PMA-Diffusion, a physics-guided mask-aware diffusion framework that reconstructs unobserved highway speed fields from sparse, incomplete observations. Our approach trains a diffusion prior directly on sparsely observed speed fields using two mask-aware training strategies: Single-Mask and Double-Mask. At the inference phase, the physics-guided posterior sampler alternates reverse-diffusion updates, observation projection, and physics-guided projection based on adaptive anisotropic smoothing to reconstruct the missing speed fields. The proposed framework is tested on the I-24 MOTION dataset with varying visibility ratios. Even under severe sparsity, with only 5% visibility, PMA-Diffusion outperforms other baselines across three reconstruction error metrics. Furthermore, PMA-diffusion trained with sparse observation nearly matches the performance of the baseline model trained on fully observed speed fields. The results indicate that combining mask-aware diffusion priors with a physics-guided posterior sampler provides a reliable and flexible solution for traffic state estimation under realistic sensing sparsity.