During the design of complex systems, software architects have to deal with a tangle of abstract artefacts, measures and ideas to discover the most fitting underlying architecture. A common way to structure these systems is in terms of their interacting software components, whose composition and connections need to be properly adjusted. Its abstract and highly combinatorial nature increases the complexity of the problem. In this scenario, Search-based Software Engineering (SBSE) may serve to support this decision making process from initial analysis models, since the discovery of component-based architectures can be formulated as a challenging multiple optimisation problem, where different metrics and configurations can be applied depending on the design requirements and its specific domain. Many-objective optimisation evolutionary algorithms can provide an interesting alternative to classical multi-objective approaches. This paper presents a comparative study of five different algorithms, including an empirical analysis of their behaviour in terms of quality and variety of the returned solutions. Results are also discussed considering those aspects of concern to the expert in the decision making process, like the number and type of architectures found. The analysis of many-objectives algorithms constitutes an important challenge, since some of them have never been explored before in SBSE.