This thesis examines how Particle Swarm Optimization (PSO) can be improved and applied to the shape optimization of an automotive rubber bumper. The work begins with a review of engineering optimization methods and shows why PSO is suitable for the problems with several design variables. A complete PSO algorithm was implemented in MATLAB and tested on well-known benchmark functions, helping to understand how different parameters influence the algorithm’s behavior. These parameters were then tuned through multiple repeated runs to achieve a more reliable and stable version of PSO. After tuning, the algorithm was used to optimize the bumper geometry, supported by a detailed finite element model describing the rubber’s compression behavior. Because running many FE simulations is time-consuming, a surrogate model based on Support Vector Regression (SVR) was created to provide fast predictions during optimization. The combined surrogate-based PSO method successfully identified a design whose force–displacement curve was very close to the target data. Overall, the study shows that integrating PSO with surrogate modeling is an efficient and practical solution for engineering problems that rely on expensive simulations.