Recently, applying neural networks to address combinatorial optimization problems (COPs) has attracted considerable research attention. The prevailing methods always train deep models independently on specific problems, lacking a unified framework for concurrently tackling various COPs. To this end, we propose a unified neural combinatorial optimization (UNCO) framework to solve different types of COPs by a single model. Specifically, we use natural language to formulate text-attributed instances for different COPs and encode them in the same embedding space by the large language model (LLM). The obtained embeddings are further advanced by an encoder-decoder model without any problem-specific modules, thereby facilitating a unified process of solution construction. We further adopt the conflict gradients erasing reinforcement learning (CGERL) algorithm to train the UNCO model, delivering better performance across different COPs than vanilla multi-objective learning. Experiments show that the UNCO model can solve multiple COPs after a single-session training, and achieves satisfactory performance that is comparable to several traditional or learning-based baselines. Instead of pursuing the best performance for each COP, we explore the synergy between tasks and few-shot generalization based on LLM to inspire future work.

翻译：近年来，应用神经网络解决组合优化问题引起了广泛的研究关注。主流方法通常针对特定问题独立训练深度模型，缺乏能够同时处理多种组合优化问题的统一框架。为此，我们提出一种统一的神经组合优化框架，旨在通过单一模型解决不同类型的组合优化问题。具体而言，我们使用自然语言为不同组合优化问题构建文本属性实例，并通过大语言模型将其编码至同一嵌入空间。所得嵌入进一步通过编码器-解码器模型进行增强，该模型不含任何问题特定模块，从而实现了解决方案构建的统一流程。我们进一步采用冲突梯度消除强化学习算法训练UNCO模型，其在多种组合优化问题上的表现均优于传统多目标学习方法。实验表明，UNCO模型经过单次训练即可求解多种组合优化问题，并取得与传统方法及基于学习的基线方法相当的性能。本研究不追求在每个组合优化问题上获得最优性能，而是探索任务间的协同效应以及基于大语言模型的少样本泛化能力，以期为未来研究提供启发。