📄 中文摘要
大型语言模型（LLM）通过自动化启发式生成，推动了组合优化领域的发展。LLM驱动启发式设计（LHD）过程不再依赖人工设计，而是利用LLM迭代生成和优化求解器以实现高性能。然而，现有的LHD框架面临两个关键限制：首先，仅基于最终质量的评估，即只根据最终结果对求解器进行排名，忽略了求解器在优化过程中的收敛行为、搜索效率和资源消耗等动态特性。这种“端点评估”无法捕捉求解器在不同阶段的表现差异，也难以识别其在特定问题结构上的优势或劣势。其次，现有方法生成的求解器往往缺乏针对特定问题领域的专业化能力。
📄 English Summary
Rethinking LLM-Driven Heuristic Design: Generating Efficient and Specialized Solvers via Dynamics-Aware Optimization
Large Language Models (LLMs) have advanced the field of Combinatorial Optimization through automated heuristic generation. The LLM-Driven Heuristic Design (LHD) process leverages LLMs to iteratively generate and refine solvers to achieve high performance, moving beyond manual design. However, existing LHD frameworks face two critical limitations. Firstly, they rely on endpoint-only evaluation, ranking solvers solely by their final solution quality. This approach neglects crucial dynamic characteristics of the optimization process, such as convergence behavior, search efficiency, and resource consumption. Such 'endpoint evaluation' fails to capture performance differences across various stages of the solver's execution and struggles to identify its strengths or weaknesses on specific problem structures. Secondly, solvers generated by current methods often lack specialized capabilities for particular problem domains. General-purpose LLMs, when generating heuristics, tend towards universal strategies, making it difficult for them to deeply exploit the inherent structures and constraints of a specific combinatorial optimization problem. This can lead to suboptimal performance when these solvers confront complex, domain-specific problems, failing to match the efficiency and precision of specialized solvers designed by domain experts. This research aims to address these limitations by introducing 'dynamics-aware optimization.' Dynamics-aware optimization emphasizes considering not only the final solution quality but also the solver's behavior across its entire optimization trajectory during heuristic generation and evaluation. This includes analyzing convergence speed, the balance between exploration and exploitation, robustness to different initial conditions, and scalability across various problem sizes.