As a new type of controllable flexible power distribution equipment

flexible multi-state switch（FMSS） can be adopted to effectively optimize the operation of the distribution network.Consequently

to minimize the voltage deviation and minimum network loss

a multi-objective optimization model for distribution network with multi-port FMSS is constructed. The NSGA-II algorithm is used to solve the model to obtain the Pareto optimal solution set. Furthermore

it is proposed to use the multi-objective comprehensive promotion ratio as a standard to get the optimal solution. Finally

the IEEE 33-node system is taken as an example to compare and analyze the optimization ability of different port numbers FMSS. The results show that the proposed model and algorithm can be adopted to effectively improve the voltage level and network loss of the system. The optimization ability of FMSS with different port numbers increases with the increase of the number of power channels

but the improvement effect gradually becomes saturated.