In this work, a method is developed for the component design of chassis bushings with contoured inner cores, aided by artificial neural networks (ANNs) and design optimization. First, a model of a physical chassis bushing is generated using the finite element method (FEM). To determine the material parameters of the material model, a material parameter optimization is conducted. Based on the bushing model, different samples for a design study are generated using the design of experiments method. Due to invalid areas of the geometrical model definitions, constraints are established and the design parameter space is cleaned up. From the cleaned design parameter space, a database of several design parameter samples and three associated quasi-static stiffnesses, calculated with FEM simulations, is generated. The database is subsequently used for the training and hyper-parameter optimization of the ANN. Subsequently, the feed-forward ANN is employed in a design study, where stiffnesses are prescribed and design parameters identified. The design process is inverted with the help of a constrained design parameter optimization (DO), based on particle swarm optimization (PSO). Two usecases are defined for the evaluation of the design accuracy of the entire method. The design parameters found are validated by corresponding FEM simulations.