Adaptive Geodesic Flow Kernel Transfer for Many-Task Optimization

Many-task optimization problems (MaTOP) involve more than three tasks, which can be solved simultaneously via knowledge transfer by utilizing complementary information of different tasks. Due to the biases between tasks, relevant tasks are usually selected for knowledge transfer to avoid negative effects. There are two challenging issues, i.e., source task selection and inter-task knowledge transfer. To address these issues, this paper proposes an adaptive geodesic flow kernel transfer method (AGFKTM) for MaTOP. In AGFKTM, multiple source tasks are selected based on both the similarity between tasks and the performance of tasks. In this way, similar and well-performed tasks are selected with a high priority. In addition, an adaptive geodesic flow kernel is constructed to implement knowledge transfer, in which the adopted subspaces along the geodesic flow path are adaptively controlled. Particularly, the transferred solutions are used to generate new ones using mutation operators. Integrating the AGFKTM into differential evolution, a new algorithm named AGFKT-DE is put forward. Experimental results on GECCO20MaTOP benchmark show that the new algorithm outperforms state-of-the-art algorithms.