In systems engineering, practitioners shall explore numerous architectural alternatives until choosing the most adequate variant. The decision-making process is most of the time a manual, time-consuming, and error-prone activity. The exploration and justification of architectural solutions is ad-hoc and mainly consists in a series of tries and errors on the mod-eling assets. In this paper, we report on an industrial case study in which we apply variability modeling techniques to automate the assessment and comparison of several candidate architectures (variants). We first describe how we can use a model-based approach such as the Common Variability Language (CVL) to specify the architectural variability. We show that the selection of an architectural variant is a multi-criteria decision problem in which there are numerous interactions (veto, favor, complementary) between criteria. We present a tooled process for exploring architectural variants integrating both CVL and the MYRIAD method for assessing and comparing variants based on an explicit preference model coming from the elicitation of stakeholders' concerns. This solution allows understanding differences among variants and their satisfactions with respect to criteria. Beyond variant selection automation improvement, this experiment results highlight that the approach improves rationality in the assessment and provides decision arguments when selecting the preferred variants.