A turbulent jet ignition engine enables operation with lean mixtures, decreasing nitrogen oxide (NOX) emissions up to 92%, while the engine efficiency can be increased compared to conventional spark-ignition engines. The geometry of the pre-chamber and engine operating parameters play the most important role in the performance of turbulent jet ignition engines and, therefore, must be optimized. The initial experimental and 3D CFD results of a single-cylinder engine fueled by gasoline were used for the calibration of a 0D/1D simulation model. The 0D/1D simulation model was upgraded to capture the effects of multiple flame propagations, and the evolution of the turbulence level was described by the new K-k-ε turbulence model, which considers the strong turbulent jets occurring in the main chamber. The optimization of the pre-chamber volume, the orifice diameter, the injected fuel mass in the pre-chamber and the spark timing was made over 9 different operating points covering the variation in engine speed and load with the objective of minimizing the fuel consumption while avoiding knock. Two optimization methods using 0D/1D simulations were presented: an individual optimization method for each operating point and a simultaneous optimization method over 9 operating points. It was found that the optimal pre-chamber volume at each operating point was around 5% of the clearance volume, while the favorable orifice diameters depended on engine load, with optimal values around 2.5 mm and 1.2 mm at stoichiometric mixtures and lean mixtures, respectively. Simultaneous optimization of the pre-chamber geometry for all considered operating points resulted in a pre-chamber volume equal to 5.14% of the clearance volume and an orifice diameter of 1.1 mm.