When it comes to the construction of hydraulic structures, the hydraulic performance and acoustic performance of centrifugal pumps are connected and conflicting. In order to find a solution to this issue, a technique for optimising the design of a volute that is based on a radial basis function (RBF) neural network and a genetic algorithm (GA) has been developed. The effectiveness of the centrifugal pump as well as the total amount of sound pressure level are employed as the targets for optimisation. The factors that are used for optimisation purposes are the installation angle of the volute tongue, the height of the volute diffuser tube, the installation angle of the volute tongue, and the diameter of the base circle. The Latin hyper-cube sampling (LHS) method is used to construct the sample space. The RBF neural network method is used to develop the agent model between the optimisation variables and goals. Finally, the GA method is utilised to do multi-objective optimisation. In order to do a comparative investigation of the hydraulic and acoustic performance of the persons in the Pareto solution set under a variety of different working situations, the initial individuals and two individuals from the set's extremes are chosen. The findings indicate that under the rated working conditions, the efficiency of the optimal individual of efficiency increases by 3.79%, while the internal noise of the optimal individual of sound pressure level decreases by 5.5% and the external noise decreases by 2.3%. The results also show that the initial individual had a lower level of efficiency than the optimal individual.