This paper suggests a unified and automated design methodology for synthesizing designs for multi-domain systems, such as mechatronic systems. A multi-domain dynamic system includes a mixture of electrical, mechanical, hydraulic, pneumatic, and/or thermal components, making it difficult use a single design tool to design a system to meet specified performance goals. The multi-domain design approach is not only efficient for mixed-domain problems, but is also useful for addressing separate single-domain design problems with a single tool. Bond graphs (BGs) are domain independent, allow free composition, and are efficient for classification and analysis of models, allowing rapid determination of various types of acceptability or feasibility of candidate designs. This can sharply reduce the time needed for analysis of designs that are infeasible or otherwise unattractive. Genetic programming is well recognized as a powerful tool for open-ended search. The combination of these two powerful methods is therefore an appropriate target for a better system for synthesis of complex multi-domain systems. The approach described here will evolve new designs (represented as BGs) with ever-improving performance, in an iterative loop of synthesis, analysis, and feedback to the synthesis process. The suggested design methodology has been applied here to three design examples. The first is a domain-independent eigenvalue placement design problem that is tested for some sample target sets of eigenvalues. The second is in the electrical domain––design of analog filters to achieve specified performance over a given frequency range. The third is in the electromechanical domain––redesign of a printer drive system to obtain desirable steady-state position of a rotational load.