Silicon based integrated optical devices have the outstanding advantages of small footprint and high integration level. They have broad application prospects in the fields of optical communication, data center optical interconnection and so on. However, the size of silicon-based waveguide coupler is relatively large, and the working bandwidth and process tolerance are limited. The design of silicon-based multimode routing photonic devices still faces big challenges. In this paper, two advanced design methods are introduced for silicon-based integrated optical devices developed in recent years: shortcuts to adiabaticity method and transformation optics method, their physical principles are briefly expounded, and typical applications in the design of silicon-based integrated optical devices are presented.