基于大语言模型引导的进化搜索的约束模型重构以提升求解器效率
LLM-Guided Evolutionary Search for Constraint Model Reformulation to Improve Solver Efficiency
AI总结：
本研究提出LLM引导的进化框架，引入PDR策略保留多样化上下文，在8个CSPLib问题上验证迭代重构可提升求解速度，且多样化上下文策略和验证选择均能增强加速效果。
AI中文摘要：
组合问题出现在众多工业应用中。常见方法是将这些问题形式化为声明式约束模型，随后可编译为多种后端求解器并由其求解。近期研究显示，大语言模型（LLMs）可从自然语言生成正确模型，但即便模型正确，求解成本仍可能很高，因为性能对建模选择敏感。本研究探讨LLMs能否自动化面向性能的模型重构。受自动启发式设计（AHD）启发，我们采用进化框架，其中LLM提出候选重构方案，经验证并与用户定义的基准模型对比。我们比较适配AHD的搜索策略，这些策略控制哪些先前尝试、指令和测得反馈进入每个提示。现有保留策略优先考虑新近性或性能，但未明确多样化上下文。为填补这一空白，我们引入简档多样化保留（PDR），其对实例级运行时向量应用最大边际相关性（MMR）以保留行为多样化的尝试。我们基于验证集的最终模型选择，在8个CSPLib问题上系统评估这些策略。结果表明：（i）迭代重构可产生显著的未见过数据加速比；（ii）保留多样化上下文的策略优于仅保留最近或最快尝试的策略；（iii）基于验证的选择提升了所有策略的未见过数据加速比。
英文摘要：
Combinatorial problems appear in numerous industrial applications. A common approach is to formulate these problems as declarative constraint models that can subsequently be compiled to and solved by a range of back-end solvers. Recent work shows that Large Language Models (LLMs) can produce correct models from natural language, but even a correct model can be expensive to solve because performance remains sensitive to modelling choices. In this work, we investigate whether LLMs can automate performance-oriented model reformulation. Inspired by Automatic Heuristic Design (AHD), we use an evolutionary framework in which an LLM proposes candidate reformulations that are verified and benchmarked against the user-defined baseline model. We compare AHD-adapted search strategies that control which prior attempts, instructions, and measured feedback enter each prompt. Existing retention strategies prioritize recency or performance, but do not explicitly diversify the context. To cover this gap, we introduce Profile-Diverse Retention (PDR), which applies Maximal Marginal Relevance (MMR) to instance-level runtime vectors to retain behaviourally diverse attempts. We systematically evaluate the strategies on eight CSPLib problems using validation-based final model selection. The results show that: (i) iterative reformulation can produce substantial held-out speedups; (ii) strategies that keep the retained context diverse outperform those that retain only recent or the fastest attempts; and (iii) validation-based selection improves the held-out speedup of every strategy.
