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The advent of intelligent vehicles that can communicate with infrastructure as well as automate the movement provides a range of new options to address key urban traffic issues such as congestion and pollution, without the need for centralized traffic control. Furthermore, the advances in the information, communication, and sensing technologies have provided access to real-time traffic and emission data. Leveraging these advancements, a dynamic multi-objective eco-routing strategy for connected & automated vehicles (CAVs) is proposed and implemented in a distributed traffic management system. It is applied to the road network of downtown Toronto in an in-house agent-based traffic simulation platform. The performance of the proposed system is compared to various single-objective optimizations. Simulation results show the significance of incorporating real-time emission and traffic state into the dynamic routing, along with considering the expected delays at the downstream intersections. The proposed multi-objective eco-routing has the potential of reducing GHG and NOx emissions by 43% and 18.58%, respectively, while reducing average travel time by 40%.