A roadmap to modernize the architecture of an existing system must satisfy many strongly-positioned stakeholders and satisfy the constraints of continuing business operations as the plan is implemented. Our previous work reported on a method to engage with stakeholders to model architecture options for a modernization roadmap. These models have proven to be too large to analyze all options manually: Ad hoc approaches must be employed to prune the space of possible solutions, which risks dropping optimal solutions. We report here on a method that efficiently collects stakeholder preferences about architecture options and uses an automated search-based optimization approach over the full solution space to identify the most important architecture decisions, i.e., the decisions that have the most influence on stakeholder satisfaction.