An adaptive nonmonotone line search for multiobjective optimization problems

摘要

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 wellknown 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.