The introduction of a physics-based zero-dimensional stochastic reactor model combined with tabulated chemistry enables the simulation-supported development of future compression-ignited engines. The stochastic reactor model mimics mixture and temperature inhomogeneities induced by turbulence, direct injection and heat transfer. Thus, it is possible to improve the prediction of NOx emissions compared to common mean-value models. To reduce the number of designs to be evaluated during the simulation-based multi-objective optimization, genetic algorithms are proven to be an effective tool. Based on an initial set of designs, the algorithm aims to evolve the designs to find the best parameters for the given constraints and objectives. The extension by response surface models improves the prediction of the best possible Pareto Front, while the time of optimization is kept low. This work presents a novel methodology to couple the stochastic reactor model and the Non-dominated Sorting Genetic Algorithm. First, the stochastic reactor model is calibrated for 10 low, medium and high load operating points at various engine speeds. Second, each operating point is optimized to find the lowest fuel consumption and specific NOx emissions. The optimization input parameters are the temperature at intake valve closure, the compression ratio, the start of injection, the injection pressure and exhaust gas recirculation rate. Additionally, it is ensured that the maximum peak cylinder pressure and turbine inlet temperature are not exceeded. This enables a safe operation of the engine and exhaust aftertreatment system under the optimized conditions. Subsequently, a reliability analysis is performed to estimate the effect of off-nominal conditions on the objectives and constraints. The novel multi-objective optimization methodology has proven to deliver reasonable results. The zero-dimensional stochastic reactor model with tabulated chemistry is a fast running physics-based model that allow to run large optimization problems in a short amount of time. The combination with the reliability analysis also strengthens the confidence in the simulation-based optimized engine operation parameters.