基于大语言模型的潜在感知实例生成的进化并行算法组合
Evolving Parallel Algorithm Portfolios via Potential-Aware Instance Generation with LLMs
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中文总结 AI 辅助
该研究针对LLM-ACP在少样本组合优化问题中泛化差的问题，提出PIAC框架，通过无需参考解的潜在增益指标和大语言模型生成多样实例，在TSP、CVRP上较基线实现显著性能提升。
中文摘要 AI 辅助
通过大语言模型（LLM）自动构建算法组合（LLM-ACP）在解决复杂组合优化问题时，实际少样本场景下泛化能力较差。实例与算法协同进化框架通过生成当前算法组合表现不佳的困难实例来扩展训练数据集，从而提升泛化能力，但该范式存在两个关键局限：评估实例硬度依赖高质量参考解，且单一生成模式限制了实例多样性。为克服这些局限，我们提出潜在感知实例与算法协同进化（PIAC）框架，核心贡献有两点：其一，提出潜在增益这一无需参考解的新指标，该指标通过扰动生成算法并评估其在生成问题实例上的改进潜力来估计泛化增益；其二，PIAC利用大语言模型合成多样的实例变异器，探索更广阔的问题-实例空间区域，进而提升算法组合的泛化能力。由于不同算法的扰动空间存在差异，我们在贪心构造算法（Greedy Constructive）、蚁群优化（Ant Colony Optimization）和引导局部搜索（Guided Local Search）算法主干上实例化该框架。对旅行商问题（TSP）和带容量约束的车辆路径问题（CVRP）在六种不同数据分布上的综合评估表明，PIAC始终优于最先进的LLM-ACP基线，其中TSP贪心构造算法组合实现了19.76%的相对提升。
英文摘要
The Automatic Construction of Portfolios via Large Language Models (LLM-ACP) suffers from poor generalization in practical few-shot scenarios when solving complex combinatorial optimization problems. Instance and algorithm co-evolution frameworks address this by expanding the training dataset with generated hard instances on which the current algorithm portfolio underperforms, thereby enhancing generalization. However, this paradigm faces two critical limitations: evaluating instance hardness relies on high-quality reference solutions, and single-mode generation patterns limit instance diversity. To overcome these limitations, we introduce the Potential-aware Instance and Algorithm Co-evolution (PIAC) framework. Our core contribution is twofold. First, we propose potential gain, a novel metric that eliminates the need for reference solutions. This metric estimates generalization gain by perturbing the generated algorithms and assessing their improvement potential on generated problem instances. Second, PIAC leverages LLMs to synthesize diverse instance mutators, exploring a broader region of the problem-instance space and thereby enhancing the portfolio's generalization capabilities. Given that perturbation spaces vary across different algorithms, we instantiate our framework on Greedy Constructive, Ant Colony Optimization, and Guided Local Search algorithmic backbones. Comprehensive evaluations on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) across six distinct data distributions demonstrate that PIAC consistently outperforms state-of-the-art LLM-ACP baselines, notably achieving a 19.76% relative improvement for TSP Greedy Constructive portfolios.
发表机构
- Southern University of Science and Technology（南方科技大学）
- Zhongguancun Academy（中关村学院）
机构由 AI 辅助整理，请以论文原文为准。
