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

TL;DR

This paper addresses solving diverse text-attributed combinatorial optimization problems by bridging large language models with a Transformer-based solution generator. It introduces the LNCS framework, which freezes the LLM while the Transformer learns solution construction from LLM-derived embeddings of text descriptions (TAIs). A novel training scheme, conflict gradients erasing reinforcement learning (CGERL), mitigates multi-task gradient conflicts to enable end-to-end learning across multiple COPs. Empirical results across multiple COPs show LNCS achieving state-of-the-art performance among LLM-based approaches and strong generalization to new tasks and sizes, highlighting a practical, unified approach for real-world COP applications.

Abstract

To advance capabilities of large language models (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.

Figures (4)

• Figure 1: The illustration of the proposed framework. [Blue part]: The LLM is frozen and takes as input the TAI for different COPs, producing task embedding and initial node embedding. [Orange part]: The encoder of the trainable solution generator processes the embedding through the attention blocks and produces instance embeddings, which is further used to construct solutions by a decoder.
• Figure 2: The cosine similarities between gradients of loss functions for 5 COPs (with $n=50$). The gradients are calculated during training the LNCS by 2000 batches, following the vanilla averaged REINFORCE.
• Figure 3: Performance comparison (with $n=50$) of the LNCS under different settings: (a) different LLMs (b) different training algorithms. The smaller the shadow area is, the better the corresponding setting performs.
• Figure 4: Results by fine-tuning and learning from scratch for (a) VRPB50 and (b) MISP100.