The design of system architectures is a complex task which involves major stakes. During this activity, system designers must create design alternatives and compare them in order to select the most relevant system architecture given a set of criteria. In order to investigate different alternatives, designers must generally limit their trade studies to a small portion of the design-space which can be composed of a huge amount of solutions. Traditionally, the architecture design process is mainly driven by engineering judgment and designers' experiences and the selected alternatives are often adapted versions of known solutions. The risk is then to select a pertinent but yet under optimal solution. In order to increase the confidence in the optimality of the selected solution, the coverage of the design-space must be increased. The use of computational design synthesis methods proved to be an efficient way to support designers in the design of engineering artifacts (structures, electrical circuits...). In order to assist system designers during the architecture design process, a computational method for complex systems is defined. This method uses an evolutionary approach (genetic algorithms) to guide the design-space exploration process toward optimal zones. The initial population of the genetic algorithm is created thanks to a computational design synthesis technique which permits to create different physical architectures and allocation mappings for a given functional architecture. The method permits to obtain the optimal solutions of the stated design problem. These solutions can be then used by designers for more detailed trade studies or for technical negotiations with system suppliers.