To improve the hydraulic performance of a new type of dishwasher pump and solve the multi-parameter optimization problem, a genetic algorithm was introduced to optimize the special design of the twin-volute structure. Six curvature radii of the twin-volute structure were defined as the optimization parameters, and 100 groups of design samples were generated based on the Latin hypercube sampling (LHS) method. The pump head and the efficiency were taken as the optimization objectives, i.e., to improve the efficiency as much as possible while ensuring that the head would not be lower than 2 m. The important parameters were identified via sensitivity analysis, and the optimization problem was solved in detail by using the multi-objective genetic algorithm (MOGA). The results showed that the external profile of the first to the fourth section of the twin-volute structure had the most significant effect on the pump head and efficiency. The response surface method (RSM) was used to select the intervals of optimization, and a comparative simulation of the pump schemes before and after optimization was performed. The head curve did not significantly change before and after optimization. By contrast, the efficiency of the dishwasher pump significantly increased, showing an increase of 2.7% under the design point. Compared with the original model, the impeller of the optimal model pump had a lower overall distribution of turbulent kinetic energy, reduced the vorticity in the twin-volute inlet area, and increased the pressure in the flow channel. Our research results confirm that the combination of RSM and MOGA can effectively solve the problem of optimization for new types of dishwashers and can provide a reference for the development of subsequent hydraulic models.