The acoustic and hydraulic performances of centrifugal pumps are related and incompatible when it comes to building hydraulic structures. A method for optimizing the design of a volute based on a genetic algorithm (GA) and radial basis function (RBF) neural network has been created in order to solve this problem. The targets for optimization are the total amount of sound pressure level and the centrifugal pump's effectiveness. The diameter of the base circle, the height of the volute diffuser tube, the installation angle of the volute tongue, and the installation angle of the volute tongue are the variables that are optimized. To build the sample space, the Latin hyper-cube sampling (LHS) method is employed. Using the RBF neural network technique, an agent model is created between the objectives and optimization variables. Finally, multi-objective optimization is done using the GA method. The first two people and two people from the set's extremes are selected in order to conduct a comparative analysis of the hydraulic and acoustic performance of the people in the Pareto solution set under a range of distinct operating conditions. The results show that the optimal individual of efficiency's efficiency grows by 3.79% under the rated working conditions, whereas the optimal individual of sound pressure level's internal noise falls by 5.5% and the external noise decreases by 2.3%. The outcomes additionally demonstrate that the initial person was less efficient than the ideal person.