## 1 Introduction
A total of 104 chamber geometries and 23 injection strategies were evaluated to meet performance and emission targets. The optimized design significantly lowered NOx and soot emissions while maintaining engine power. [PERSON] and [PERSON] [14] investigated the effects of hydrogen injection strategies on engine performance and emissions. Their work concluded that optimizing parameters such as injection timing, pressure, and dual injection strategies can enhance mixture uniformity and tumble strength, ultimately reducing the mass fraction of fuel burned in regions exceeding 2500 K values and NOx emissions. [PERSON] et al. [15] performed a computational study to improve fuel-air mixing and combustion efficiency in a high-speed direct-injection hydrogen engine. They evaluated eight injector cap geometries under engine-like conditions (6000 rpm, stoichiometric mixture, IMEP > 25 bar) using 3D CFD simulations. Designs aligned with the cylinder axis or tumble vortex enhanced mixture uniformity by up to 5%, while upstream-directed jets reduced it by 15%. The best design increased output by 5% and reduced combustion duration by 30%, demonstrating the impact of optimized cap geometry on in-cylinder flow and combustion. Although [PERSON] et al. [15] achieved performance improvements through their injector cap optimization, their study was conducted with a relatively richer mixture (approximately lambda 1.3) and did not account for emission formation. In contrast, the present work was carried out under leaner combustion conditions with a global lambda of 2.1, which inherently favors lower NOx emissions. Due to this fundamental difference in operating regimes and evaluation focus, a direct one-to-one comparison between the two studies may not fully capture the emission-oriented contributions of the current methodology. [PERSON] [16], supported by BMW Group Research and Technology, conducted three-dimensional numerical simulations to investigate mixture formation and combustion processes in direct-injection hydrogen engines. His findings highlighted the importance of accurate turbulence and combustion modeling and provided burning velocity data for hydrogen-air mixtures under different injection strategies (homogeneous, stratified, and multi-injection modes). [PERSON] et al. [17] investigated the effects of fuel inlet configuration on fluid flow and thrust performance in aero-engine combustion chambers. Using CFD simulations performed in ANSYS CFX with geometries modeled in Creo 6.0, they compared single and double fuel inlet designs. The study found that the double inlet configuration significantly increased outlet pressure and thrust. These results suggest improved combustion efficiency and potential gains in turbine performance. [PERSON] et al. [18] conducted a CFD-based investigation to compare the combustion and flow characteristics of aero-engine chambers with single and double fuel inlets. Their results indicated that the double-inlet configuration enhanced fuel-air mixing, leading to a 49% increase in outlet pressure and a 48% improvement in thrust compared to the single-inlet design. These findings suggest that fuel inlet configuration plays a critical role in optimizing combustion chamber performance. Building upon this insight, further studies are needed to explore detailed flow structures, flame development, and the associated thermal effects under various operating conditions. In contrast to this case-specific numerical investigation, our study incorporates experimental validation through Particle Image Velocimetry (PIV) measurements to ensure the reliability of the CFD model under realistic flow conditions. Moreover, rather than evaluating a fixed set of injector configurations, a mathematical design framework was developed by coupling the validated model with a Kriging-based Multi-Objective Genetic Algorithm (MOGA).