To help the reverse Brayton cycle cool the refrigerant from 100 K to 50 K, an auxiliary generator, with a housed stator, is studied and optimized, and the influences of weights in the cost- function on the results are discussed. The power demand and adiabatic characteristics of reverse Brayton cycle expansion are analyzed, after which the optimization indexes, including output rated power, efficiency, the air gap between rotor and stator, loss, and volume, are decided. The initial model of the auxiliary generator is then constructed and the parameters to be optimized are also determined. Taking the low loss and sinusoidal back-EMF as the evaluation indexes, the single parameter optimizations of the auxiliary generator are carried out. The co-simulation of the generator and its corresponding driving circuit is investigated, with which the power generation efficiency is calculated. The global optimizations of the generator parameters are carried out using a genetic algorithm. A suitable analytic hierarchy process (AHP) model is proposed, with which a three-order judgment matrix is constructed, and the effects of different weight combinations, in the cost-function, on generator performance are compared. The experimental results show that the output back-EMF amplitude is 28.2 V, which is about 10% smaller than the simulation results; the output power of the auxiliary generator under load is about 3.7 W, meeting the rated demand.