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.

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。过去几十年中，研究者提出了许多MOEAs，其搜索算子需要依赖领域知识进行精心手工设计。近年来，已有一些尝试用基于学习的算子（如神经网络模型）替代MOEAs中的人工设计算子。然而，这类模型的设计与训练仍需大量投入，且学习到的算子可能难以在新问题上良好泛化。为应对上述挑战，本研究探索了一种新方法，即利用强大的大语言模型（LLM）来设计MOEA算子。通过恰当的提示工程，我们成功让一个通用LLM以零样本方式充当基于分解的MOEA（MOEA/D）的黑盒搜索算子。此外，通过从LLM行为中学习，我们进一步设计了一个显式白盒算子（包含随机性），并提出了一种新的基于分解的MOEA版本，称为MOEA/D-LO。在不同测试基准上的实验表明，所提方法能够与广泛使用的MOEAs取得竞争性性能。尤其令人鼓舞的是，仅从少量实例中学习到的算子，在模式与设置差异显著的全新问题上展现出稳健的泛化性能。这些结果揭示了将预训练LLM应用于MOEA设计的潜在优势。