Large Language Model Aided Multi-objective Evolutionary Algorithm: A Low-cost Adaptive Approach

Multi-objective optimization is a common problem in practical applications, and multi-objective evolutionary algorithms (MOEAs) are considered one of the effective methods to solve these problems. However, their randomness sometimes prevents algorithms from rapidly converging to the global optimum, and the design of their genetic operators often requires complicated manual tuning. To overcome this challenge, this study proposes a new framework that combines a large language model (LLM) with traditional MOEAs to enhance the algorithm's search capability and generalization performance. In our framework, we employ adaptive and hybrid mechanisms to integrate the LLM with the MOEA, thereby accelerating algorithmic convergence. Specifically, we leverage an augmented evaluation function and automated prompt construction within the adaptive mechanism to flexibly adjust the utilization of the LLM, generating high-quality solutions that are further refined and optimized through genetic operators. Concurrently, the hybrid mechanism aims to minimize prompt costs as much as possible. By adopting this approach, we maximize the benefits of the LLM's language understanding and generative capabilities, providing the MOEA with more intelligent and efficient search strategies. We conducted experiments on multiple multi-objective optimization benchmark problems. The results demonstrate that this framework reduces the average Inverted Generational Distance(IGD) by 21.5% and improves hypervolume (HV) by 15.3% compared to NSGA-II, while reducing token costs by 21.5% through adaptive mechanisms. These experimental findings reveal the potential advantages of LLMs in the design of MOEAs. For the specific implementation code, please refer to https://github.com/Luna888666/NSGAIILLM.