Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the search operators need a carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and the learned operators might not generalize well on new problems. To tackle the above challenges, this work investigates a novel approach that leverages the powerful large language model (LLM) to design MOEA operators. With proper prompt engineering, we successfully let a general LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D) in a zero-shot manner. In addition, by learning from the LLM behavior, we further design an explicit white-box operator with randomness and propose a new version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on different test benchmarks show that our proposed method can achieve competitive performance with widely used MOEAs. It is also promising to see the operator only learned from a few instances can have robust generalization performance on unseen problems with quite different patterns and settings. The results reveal the potential benefits of using pre-trained LLMs in the design of MOEAs.To foster reproducibility and accessibility, the source code is https://github.com/FeiLiu36/LLM4MOEA.

翻译：多目标进化算法（MOEAs）是解决多目标优化问题（MOPs）的主要方法。过去几十年间提出了众多MOEAs，其搜索算子需要结合领域知识进行精心手工设计。近年来，研究者尝试用基于学习的算子（如神经网络模型）替代MOEAs中手工设计的算子。然而，设计与训练此类模型仍需大量投入，且习得算子在新问题上的泛化能力可能不足。为应对上述挑战，本研究探索了一种利用强大大语言模型（LLM）设计MOEA算子的新方法。通过恰当的提示工程，我们成功使通用LLM以零样本方式充当基于分解的MOEA（MOEA/D）的黑箱搜索算子。此外，通过从LLM行为中学习，我们进一步设计了具有随机性的显式白箱算子，并提出了基于分解的MOEA新版本——MOEA/D-LO。在不同测试基准上的实验表明，所提方法能够取得与广泛使用的MOEAs相当的竞争性能。值得注意的是，仅从少量实例习得的算子，在模式与设置迥异的新问题上展现出稳健的泛化能力。该结果揭示了将预训练LLM应用于MOEA设计的潜在价值。为促进可复现性与可访问性，相关源代码已发布于https://github.com/FeiLiu36/LLM4MOEA。