We demonstrate a III-V-on-silicon-nitride mode-locked laser through the heterogeneous integration of a semiconductor optical amplifier on a passive silicon nitride cavity using the technique of micro-transfer printing. Specifically, we explore the impact of the gain voltage and saturable absorber current on the locking stability of a tunable mode-locked laser. By manipulating these parameters, we demonstrate the control of the optical spectrum across a wide range of wavelengths spanning from 1530 nm to 1580 nm. Furthermore, we implement an optimization approach based on a Monte Carlo analysis aimed at enhancing the mode overlap within the gain region. This adjustment enables the achievement of a laser emitting a 23 nm wide spectrum while maintaining a defined 10 dB bandwidth for a pulse repetition rate of 3 GHz.