用模式识别降低难解优化问题的计算复杂度，实测提升79%求解质量
Bridging Pattern-Aware Complexity with NP-Hard Optimization: A Unifying Framework and Empirical Study
- 通过量化结构规律（如聚类、对称性）来识别可简化的问题模式
- 在22至2392城市规模的TSP测试中，求解质量最高提升79%
- 适合关注实际优化效率的研究者和工程应用开发者
NP难优化问题如旅行商问题（TSP）在最坏情况下无法高效求解，但现实实例常呈现可利用的模式。本文提出一种新型模式感知复杂度框架，通过量化并利用聚类、对称性等结构性规律，降低多个领域的有效计算复杂度，涵盖金融预测与大模型优化。基于严谨定义、定理及元学习驱动的求解流水线，引入模式利用效率（PUE）等指标，在TSP基准测试中实现最高达79%的解质量提升（城市数22至2392）。该方法不同于理论上的NP难性，提供统一且实用的模式驱动效率视角。
原文摘要 · Abstract (English)
NP hard optimization problems like the Traveling Salesman Problem (TSP) defy efficient solutions in the worst case, yet real-world instances often exhibit exploitable patterns. We propose a novel patternaware complexity framework that quantifies and leverages structural regularities e.g., clustering, symmetry to reduce effective computational complexity across domains, including financial forecasting and LLM optimization. With rigorous definitions, theorems, and a meta learning driven solver pipeline, we introduce metrics like Pattern Utilization Efficiency (PUE) and achieve up to 79 percent solution quality gains in TSP benchmarks (22 to 2392 cities). Distinct from theoretical NP hardness, our approach offers a unified, practical lens for pattern-driven efficiency.
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