[en] Beam hopping (BH) is considered to provide a high level of flexibility to manage irregular and time-varying traffic requests in future multi-beam satellite systems. In BH optimization, adopting conventional iterative heuristics may have their own limitations in providing timely solutions, and directly using data-driven technique to approximate optimization variables may lead to constraint violation and degraded performance. In this paper, we explore a combined learning-and-optimization (L&O) approach to provide an efficient, feasible, and near-optimal solution. The investigations are from the following aspects: 1) Integration ofBH optimization and learning techniques; 2) Features to be learned in BH design; 3) How to address the feasibility issue incurred by machine learning. We provide numerical results and analysis to show that the learning component in L&O significantly accelerates the procedure of identifying promising BH patterns, resulting in reduced computing time from seconds/minutes to milliseconds level. The identified learning feature enables high accuracy in predictions. In addition, the optimization component in L&O guarantees the solution’s feasibility and improves the overall performance with around 5% gap to the optimum.