Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimization

Abstract: To advance capabilities of LLMs in solving combinatorial optimization problems (COPs), this paper presents the Language-based Neural COP Solver (LNCS), a novel framework that is unified for the end-to-end resolution of diverse text-attributed COPs. LNCS leverages LLMs to encode problem instances into a unified semantic space, and integrates their embeddings with a Transformer-based solution generator to produce high-quality solutions. By training the solution generator with conflict-free multi-task reinforcement learning, LNCS effectively enhances LLM performance in tackling COPs of varying types and sizes, achieving state-of-the-art results across diverse problems. Extensive experiments validate the effectiveness and generalizability of the LNCS, highlighting its potential as a unified and practical framework for real-world COP applications.