The performance of an automatic optimization procedure may be significantly influenced by a priori choices concerning the methodology and training variables. As a result, the model's ability to accurately fit different observables may vary to some extent. In the case of OPC3, for example, it was considered crucial to impose constraints on the geometry of the molecules in order to ensure a quadrupole moment of zero. In the case of TIP3P-FB, a predominant emphasis was placed on a top-down approach, involving the simultaneous fitting to multiple thermodynamic observables across the liquid regime of water. To investigate the impact of these initial conditions and gain a comprehensive understanding of the optimization process, we conducted a series of six optimizations under identical constraints. Specifically, we minimized the discrepancy of radial distribution functions (RDFs), density, and static dielectric constant, at the standard conditions of 298 K and 1 bar. Since the results obtained with such optimization cycles vary to some extent, this setup did not produce a single solution (identical in all six runs) but rather a group of solutions. Noteworthy, the obtained solutions demonstrate a comparable score (as illustrated in Figure of the Supporting Information).