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 operators need 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 to solve 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：多目标进化算法是解决多目标优化问题的主要方法。过去几十年间涌现了大量多目标进化算法，其算子需要基于领域知识进行精心的人工设计。近年来，已有研究尝试用基于学习的算子（如神经网络模型）替代多目标进化算法中的人工设计算子。然而，这类模型的设计与训练仍需大量投入，且学习得到的算子可能难以泛化至新问题的求解。针对上述挑战，本研究探索了一种利用强大大语言模型设计多目标进化算法算子的新方法。通过恰当的提示工程，我们成功使通用大语言模型以零样本方式充当基于分解的多目标进化算法（MOEA/D）的黑箱搜索算子。此外，通过从大语言模型行为中学习，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多目标进化算法新版本——MOEA/D-LO。在不同测试基准上的实验表明，所提方法能取得与广泛使用的多目标进化算法相媲美的竞争力。尤其值得关注的是，仅从少数实例学习得到的算子，在面对模式与设定迥异的新问题时仍展现出稳健的泛化性能。研究结果揭示了预训练大语言模型在多目标进化算法设计中的潜在应用价值。