Shaodi Feng

Shaodi Feng, Zhuoyi Lin, Yaoxin Wu et al.

Recent research has demonstrated the effectiveness of large language models (LLMs) in solving combinatorial optimization problems (COPs) by representing tasks and instances in natural language. However, purely language-based approaches struggle to accurately capture complex relational structures inherent in many COPs, rendering them less effective at addressing medium-sized or larger instances. To address these limitations, we propose AlignOPT, a novel approach that aligns LLMs with graph neural solvers to learn a more generalizable neural COP heuristic. Specifically, AlignOPT leverages the semantic understanding capabilities of LLMs to encode textual descriptions of COPs and their instances, while concurrently exploiting graph neural solvers to explicitly model the underlying graph structures of COP instances. Our approach facilitates a robust integration and alignment between linguistic semantics and structural representations, enabling more accurate and scalable COP solutions. Experimental results demonstrate that AlignOPT achieves state-of-the-art results across diverse COPs, underscoring its effectiveness in aligning semantic and structural representations. In particular, AlignOPT demonstrates strong generalization, effectively extending to previously unseen COP instances.

Shaodi Feng, Zhuoyi Lin, Jianan Zhou et al.

Deep learning has been extensively explored to solve vehicle routing problems (VRPs), which yields a range of data-driven neural solvers with promising outcomes. However, most neural solvers are trained to tackle VRP instances in a relatively monotonous context, e.g., simplifying VRPs by using Euclidean distance between nodes and adhering to a single problem size, which harms their off-the-shelf application in different scenarios. To enhance their versatility, this paper presents a novel lifelong learning framework that incrementally trains a neural solver to manage VRPs in distinct contexts. Specifically, we propose a lifelong learner (LL), exploiting a Transformer network as the backbone, to solve a series of VRPs. The inter-context self-attention mechanism is proposed within LL to transfer the knowledge obtained from solving preceding VRPs into the succeeding ones. On top of that, we develop a dynamic context scheduler (DCS), employing the cross-context experience replay to further facilitate LL looking back on the attained policies of solving preceding VRPs. Extensive results on synthetic and benchmark instances (problem sizes up to 18k) show that our LL is capable of discovering effective policies for tackling generic VRPs in varying contexts, which outperforms other neural solvers and achieves the best performance for most VRPs.