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According to a new design paradigm called Converging Design, high-level optimization objectives such as resilience and sustainability can be pursued through iterative simulation and feedback. Unlike traditional design processes that prioritize desirable seismic performance at various seismic hazard levels, the Converging Design methodology also considers the long-term ecological impact of construction and functional recovery. This methodology requires navigating competing priorities, which can be pursued through multiobjective optimization (MOO). However, computational costs and incorporating uncertainty in seismic analysis also demand that optimization frameworks use algorithms and analysis resolutions that are appropriate to the decisions being made as the design is refined. While such a framework could be applied to any material, mass timber systems are increasingly attractive as a potential sustainable solution for buildings. In this study, using a Python-based object-oriented program, an automated structural design procedure is developed to evaluate the seismic and sustainability performance of parametrically definable mass timber building configurations. Different geometric classes with Cross-Laminated Timber Rocking Walls are modeled using OpenSees and are automatically designed. Their behavior is then studied to provide insights into the relationship between structural variables and the optimization objectives. The results show a clear trade-off between Seismic Safety (the inverse of risk) and Global Warming Potential due to the construction of different design options, although the nature of this trade-off depends on the desired seismic behavior limit states. The developed software thus enables designers to efficiently explore a range of early design options for mass timber lateral systems and to achieve optimal solutions that balance seismic and sustainability performance.