  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.
