发表机构
LIACS, Leiden University, Leiden, Netherlands（LIACS，莱顿大学，莱顿，荷兰）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何设计多目标贝叶斯优化算法，核心方法是将LLaMEA框架扩展到MOBO，利用大语言模型生成算法并集成超参数优化。主要贡献是生成的算法在合成和实际工程问题上表现优异，能以低成本实现帕累托有效权衡。
AI 中文摘要
设计有效的多目标贝叶斯优化（MOBO）算法需要平衡许多相互依赖的设计选择，其最佳配置取决于问题，通常需要深厚的专业知识。我们将LLaMEA框架扩展到MOBO，在进化策略中使用大语言模型作为变异和交叉算子来生成完整的算法实现，并将SMAC超参数优化集成到进化循环中。在九次进化运行中，我们生成了约900种算法，并在十二个合成问题（ZDT、DTLZ、WFG）和三个实际工程问题（RE）上进行了基准测试，使用BoFire qParEGO实现作为最先进的贝叶斯优化基线。在合成套件上，最强的生成算法获得了最高的平均归一化超体积（0.971，而qParEGO为0.869），同时所需的挂钟时间减少了约６０倍；通过Friedman检验和事后分析，两者处于同一顶级性能组，每个问题的测试发现，生成的算法在12个问题中的7个上明显优于qParEGO，且从不差于qParEGO，以低一个数量级的成本匹配了最先进的精度。在三个未见的实际工程问题上，一个生成的算法获得了最佳的平均归一化超体积（0.985，而qParEGO为0.971），在三个问题中的两个上明显优于qParEGO，挂钟成本降低了约3.4倍，这证实了收益超出了合成范围。因此，基于大语言模型驱动的进化搜索可以发现通过手动设计难以实现的帕累托有效权衡的算法设计。
英文摘要
Designing effective multi-objective Bayesian optimization (MOBO) algorithms requires balancing many interdependent design choices whose optimal configuration is problem-dependent and typically demands deep expertise. We extend the LLaMEA framework to MOBO, using large language models as mutation and crossover operators within evolutionary strategies to generate complete algorithm implementations, with SMAC hyperparameter optimization integrated into the evolutionary loop. Across nine evolutionary runs we generated approximately 900 algorithms and benchmarked them on twelve synthetic problems (ZDT, DTLZ, WFG) and three real-world engineering problems (RE), using a BoFire qParEGO implementation as a state-of-the-art Bayesian-optimization baseline. On the synthetic suite the strongest generated algorithm attains the highest mean normalized hypervolume (0.971, vs. 0.869 for qParEGO) while requiring roughly 60x less wall-clock time; a Friedman test with post-hoc analysis places the two in a single top-performing group, and per-problem tests find the generated algorithm significantly better than qParEGO on 7 of the 12 problems and never worse, matching state-of-the-art accuracy at an order-of-magnitude lower cost. On the three unseen real-world engineering problems a generated algorithm attains the best mean normalized hypervolume (0.985, vs. 0.971 for qParEGO)--significantly better than qParEGO on two of the three problems--at roughly 3.4x lower wall-clock cost, confirming that the gains transfer beyond the synthetic regime. LLM-driven evolutionary search can thus discover algorithm designs that achieve Pareto-efficient trade-offs difficult to reach through manual design.
