Abstract: With the continuous promotion of the "Carbon peak and carbon neutrality", the regional energy internet based on energy router has received widespread attention. This article aims to study an energy routing strategy, which enables the system to operate in a low-carbon and economically efficient manner by selecting the optimal energy routing path. It should be emphasized that in the graph structured regional energy internet, the energy routing path with the least power loss may not necessarily lead to the lowest carbon emissions, and vice versa. In order to simultaneously reduce the power losses and carbon emissions in the system, this paper proposes an energy routing strategy to achieve Pareto optimality between power losses and carbon emissions by controlling the output of each microgrid and selecting the energy supply path. First, this article proposes a congestion free path search method based on depth-first search to obtain energy routing path. Afterwards, adaptive geometry estimation based multi-objective evolutionary algorithm (AGE-MOEA) is used to quickly obtain the Pareto optimal set. Then, the optimal compromise solution can be selected through the comprehensive weight-technique for order preference by similarity to an ideal solution (TOPSIS). Finally, simulation analysis is conducted in the regional energy internet scenario, and the results show that compared with the existing energy routing algorithm, the energy routing strategy proposed in this paper can reduce carbon emissions by 58.24% with only a 4.73% increase in power losses. Moreover, the AGE-MOEA used in this paper reduces the solution time by 5.8% compared to the existing algorithm while guaranteeing the effectiveness of the solution.