With the increasing scale of the power system, the existing distributed optimization dispatching method has the defects of slow calculation speed and poor optimization effect. To address this issue, a hierarchical distributed acceleration optimization method is proposed. Firstly, considering the objective function and constraints of economic dispatch in the power system, a hierarchical distributed optimization model is constructed. Then, based on the multi-objective optimization algorithm, a self-attention mechanism deep neural network (SADNN) is introduced and combined with a hierarchical distributed optimization model to propose a hierarchical distributed multi-objective mantis accelerated search algorithm based on SADNN (SADNN-HDMOMASA). This algorithm is used to improve the efficiency of economic dispatch in the power system and accelerate the calculation process of the entire system. Finally, the proposed algorithm is analyzed in simulation examples. The results show that: in the IEEE 118-bus system, the method proposed in this paper reduces carbon emissions by 1.13%, cost by 3.97%, and total system running time by 34.29 s compared to the hierarchical distributed optimization method. In the IEEE 2208-bus system, compared with the hierarchical distributed optimization method, the method proposed in this paper saves 1.13% of costs and 10.14% of carbon emissions, and improves computing speed by 23%. The proposed algorithm can effectively save the system power generation cost and carbon emissions while improving computing speed.