The automatic transmission system is very crucial for the high-speed vehicles, where the planetary or epicyclic gearbox is a standard feature. With the increase in design intricacies of planetary gearbox, mathematical modelling has become complex in nature and therefore there is a need for modelling of multistage planetary gearbox including the shifting scheme. A random search-based synthesis of three degrees of freedom (DOF) high-speed planetary gearbox has been presented in this paper, which derives an efficient gear shifting mechanism through designing the transmission schematic of eight speed gearboxes compounded with four planetary gear sets. Furthermore, with the help of lever analogy, the transmission power flow and relative power efficiency have been determined to analyse the gearbox design. A simulation-based testing and validation have been performed which show the proposed model is efficient and produces satisfactory shift quality through better torque characteristics while shifting the gears. A new heuristic method to determine suitable compounding arrangement, based on mechanism enumeration, for designing a gearbox layout is proposed here. An important finding on automotive gear shift quality due to closer gear ratio is also reported in this work.