Directed quick search guided evolutionary framework for large-scale multi-objective optimization problems

Abstract

For large-scale multi-objective evolutionary algorithms (LSMOEAs), obtaining efficient evolutionary directions in an ultrahigh-dimensional decision space to produce high-quality offspring is a major challenge. This study proposes a novel framework called the directed quick search-guided large-scale evolutionary framework (QSLMOF) to address multi-objective optimization problems on a large scale. The framework contains two innovative strategies: the bidirectional vector-based sampling strategy (BDVS) and the quick search-guided directed reproduction strategy (QS-DRS). BDVS is introduced as an approach to swiftly discern promising solutions that can steer the exploration in the large-scale decision space. This is achieved by formulating two distinct types of sampling directions to rapidly reduce the search space and strike a delicate balance between convergence and diversity. In QS-DRS, we introduced the concept of the potential convergence gradient (PCG), incorporating directional information from historical searches and convergence directions indicated byelite solutions in the current population. With this property, inferior solutions can obtain excellent search directions to explore the decision space, which can improve the convergence rate and prevent the search from falling into a local optimum. The proposed large-scale evolutionary framework incorporates an existing environmental selection mechanism. Comprehensive experiments show that the two novel strategies improve the search efficiency and evolutionary quality of LSMOEAs in ultrahigh-dimensional decision spaces. Moreover, the proposed framework outperformed seven state-of-the-art LSMOEAs for nine large-scale multi-objective benchmark problems LSMOP1-LSMOP9 with up to three objectives and 10000 decision variables.