Controlled longitudinal emittance blow-up in the CERN SPS is necessary to stabilize high-intensity beams for the High-Luminosity LHC (HL-LHC) by increasing the synchrotron frequency spread. The process consists of injecting bandwidth-limited noise into the main RF phase loop to diffuse particles in the core of the bunch. The setting up of the noise parameters, such as frequency band and amplitude, is a non-trivial and time-consuming procedure that has been performed manually so far. In this preliminary study, several optimization methods are investigated to set up the noise parameters automatically. We apply the CERN Common Optimization Interfaces as a generic framework for the optimization algorithm. Single-bunch profiles generated with the BLonD simulation code have been used to investigate the optimization algorithms offline. Furthermore, analysis has been carried out on measured bunch profiles in the SPS to define the problem constraints and properly formulate the objective function