In this work, the neural performance data sheets of the transistor are employed to determine the feasible design target space in the optimization of a microwave amplifier. In order to obtain these data sheets the ANN model of the active device is utilized to approximate the small-signal [S] and noise [N] parameter functions in the operation domain. Inputting of these characterization parameters into the performance characterization of the device results in the triplet of gain G(T), noise F, and input VSWR V-i and its source (Z(S)) and load (Z(L)) termination functions in the operation domain, from which the neural performance data sheets can be obtained. The genetic algorithms with the binary (BGA) and decimal (CPGA) numbers are utilized in the multi-objective optimization process for the global minimum of the objective function which is expressed as a function only gain of a matching circuit, in the negative exponential form to ensure the rapid convergence. Here optimization of a microwave amplifier with the Pi - type matching circuits is given as a worked example and its resulted performance ingredients are compared with the design targets.