Context: Modern society increasingly relies on complex and interconnected software systems. Systems-of-Systems (SoS) then enable interoperability among heterogeneous and independent systems, delivering capabilities that no individual system can provide. Their dynamic and evolving architectures demand systematic methods to analyze, verify, and optimize configurations before operating them. Problem: Such dynamic architectures pose challenges for ensuring performance, reliability, and other qualities in SoS, particularly in safety-critical domains. Existing studies often address isolated concerns or lack solutions that optimize architectures efficiently during design time. Objective: This paper presents SBOSoS, a framework (containing a structured process and an automated toolchain) that integrates modeling, simulation, and genetic algorithms (GAs) to explore near-optimal software architectures for SoS and can continuously refine architectures regarding a given quality attribute. A case study of a smart building SoS evaluates the framework’s feasibility. Results: The evaluation demonstrates the feasibility of SBO-SoS in effectively discovering quality-driven architectural configurations for SoS. Conclusion: By uniting simulation and optimization, SBO-SoS can support architects to design SoS that can assume at runtime near-optimal architectural configurations regarding given quality attributes.