This paper aims to propose an adaptive nonmonotone line search for direction-based multiobjective optimization (MO) algorithms. All direction-based MO algorithms can be equipped with this line search, especially the BFGS quasi-Newton algorithm is applied in this study. To validate the proposed line search some well-known line searches, including Armijo, maximum nonmonotone and average nonmonotone line searches, were considered. In order to make a comprehensive comparison between the proposed line sereach and the aforementioned line searches two criteria are considered: the computational effort and quality of the approximated nondominated frontier. The results confirm the remarkable superiority of the proposed line search over the mentioned line searches. In addition, this line search preserves the quality of the obtained nondominated frontier. It should be noted that we established the convergency of BFGS quasi-Newton algorithm equipped with the proposed line search under some mild conditions.

本文旨在为基于方向的多目标优化 (MO) 算法提出一种自适应非单调线搜索。所有基于方向的MO算法都可以配备这种线搜索，特别是BFGS拟牛顿算法在本研究中得到应用。为了验证提议的线搜索，考虑了一些众所周知的线搜索，包括 Armijo、最大非单调和平均非单调线搜索。为了对提议的线路搜索和上述线路搜索进行全面比较，需要考虑两个标准：近似非支配边界的计算工作量和质量。结果证实了所提出的线搜索相对于所提到的线搜索的显着优势。此外，这种线搜索保留了获得的非支配边界的质量。