Solving NP-hard problems traditionally relies on heuristics, yet manually designing effective heuristics for complex problems remains a significant challenge. While recent advancements like FunSearch have shown that large language models (LLMs) can be integrated into evolutionary algorithms (EAs) for heuristic design, their potential is hindered by limitations in balancing exploitation and exploration. We introduce Quality-Uncertainty Balanced Evolution (QUBE), a novel approach that enhances LLM+EA methods by redefining the priority criterion within the FunSearch framework. QUBE employs the Quality-Uncertainty Trade-off Criterion (QUTC), based on our proposed Uncertainty-Inclusive Quality metric, to evaluate and guide the evolutionary process. Through extensive experiments on challenging NP-complete problems, QUBE demonstrates significant performance improvements over FunSearch and baseline methods. Our code are available at https://github.com/zzjchen/QUBE\_code.

翻译：解决NP难问题传统上依赖于启发式方法，然而为复杂问题手动设计有效的启发式方法仍然是一个重大挑战。尽管FunSearch等最新进展表明，大语言模型（LLMs）可以集成到演化算法（EAs）中用于启发式设计，但其潜力受到平衡利用与探索方面局限性的制约。我们提出了质量-不确定性平衡演化（QUBE），这是一种通过在FunSearch框架内重新定义优先级准则来增强LLM+EA方法的新颖方法。QUBE采用基于我们提出的不确定性包容质量度量的质量-不确定性权衡准则（QUTC），来评估和指导演化过程。通过对具有挑战性的NP完全问题进行的广泛实验，QUBE相较于FunSearch和基线方法展现出显著的性能提升。我们的代码可在 https://github.com/zzjchen/QUBE\_code 获取。