Display omitted •A high-power-density design method via adaptive NSGA-III and surrogate sub-models for polymer gear systems is outlined.•The key factors affecting the operating performance of polymer accessory gearbox are explained.•Compared with metallic design scheme, the polymer scheme achieves a 49 % weight reduction and power density with 22.5 kW/kg. There is a growing and prevalent trend in the power transmission field of high-performance polymers replacing metallic materials given the strict light-weight requirement. Polymer gears exhibit a low elasticity modulus, high-temperature sensitivity, and increased geometric design flexibility, presenting technical challenges to the straightforward application of metallic design methods to polymer gear systems. This study is centred on the development of a high-power-density polymer gear transmission system for the accessory unit of a gas turbine engine, utilising an adaptive NSGA-III algorithm and surrogate sub-models. A comprehensive assessment indicator for the operating performance of the transmission system is suggested, encompassing gear strength, bearing temperature, and shaft torsional stiffness. The model made it possible to simultaneously optimise forty-six structural parameters, including gear tooth module, web thickness, and bearing clearance. In contrast to the original steel design scheme, the optimised polymer gear transmission system indicated a 49% reduction in weight and a 1.96-fold increase in power density. This presents a method for substituting steel with polymers for effective power transmission.