Due to the increase in environmental awareness, activities aimed at increasing the efficiency of internal combustion engines and reducing harmful emissions are also growing. In spark-ignited engines, this can be achieved by burning lean mixtures whose excess air ratio λ exceeds the values of 1.4, so the problem of mixture flammability is encountered by using conventional SI engine ignition system. Conventional SI engines operate with a stoichiometric mixture (λ = 1) or a slightly rich mixture at full load (λ ≈ 0.9) ignited by an external ignition source by the appearance of an electric spark between the spark plug electrodes. By applying the classic ignition system of SI engines, it is possible to achieve ignition of lean mixtures and stable combustion up to the value of excess air ratio λ of 1.4, and to initiate combustion of additionally lean mixtures (λ > 1.4) it is necessary to apply ignition systems with higher energy levels. The flammability limit of lean mixtures can be increased by using an active combustion pre-chamber containing an injector and a spark plug for the mixture ignition. In SI engines with a pre-chamber, this mode of combustion is most commonly called Turbulent Jet Ignition (TJI) where the ignition of a lean mixture in the main combustion chamber is achieved by the penetration of multiple turbulent jets of combustion products from the pre-chamber. Since the penetration of turbulent jets into the main combustion chamber depends on the geometry of the pre-chamber, the diameter and number of nozzles, it is necessary to analyze which parameter values are most favorable for SI engine operation, and to achieve minimum fuel consumption. On the other hand, the application of very lean mixtures in comparison with the conventional mode of operation of SI engines at partial loads (intake restriction) reduces the peak temperatures during combustion, which reduces the emission of nitrogen oxides. In this paper, the combustion model for the SI engine with a pre-chamber is upgraded, and the upgrade of the combustion model includes the influence of the propagation of multiple flame cores and the modification of the equation to calculate the heat release rate in the main combustion chamber. In order to perform the calibration and verification of the upgraded combustion model, a 3D simulation based on the finite volume method (AVL Fire™) was performed for one engine operating point. The results of 3D flow and combustion calculations were used to determine the values of the calibration constants of the upgraded combustion model in AVL BOOST™ version 2013.2. Sensitivity analysis for the parameters of the turbulence and combustion model was performed, which determined the most important parameters in the model calibration process. In addition to the adopted calibration values of the turbulence and combustion model, the most favorable geometric and operating parameters were determined in order to achieve the minimum indicated specific fuel consumption. The determination of the most favorable geometric and operating parameters of the engine was performed using the Nelder-Mead optimization algorithm available within AVL BOOST™. In the first step, simultaneous optimization of geometric and operating parameters was performed at 6 operating points (2 engine speeds and 3 levels of air excess ratio), where the occurrence of knock during combustion was controlled at full engine loads. After that, the mean values for the pre-chamber volume and the nozzle diameter were adopted, and the values of the operating parameters for the expected operating range of the pre-chamber SI engine were optimized.