This paper presents a new approach to the analysis of the transient overvoltage (TOV) generated duringswitching of vacuum circuit breaker (VCB). The new technique overlaps the merits of both Fast FourierTransform (FFT) and Wavelet Transform (WT). The new approach was applied on a real case study of apumping station of a wastewater treatment plant located at Abu Rawash, Egypt. The pumping station isdriven by induction motors. Alternative transients program (ATP) is used to simulate the selected casestudy. The Referential Integrity between FFT and WT analyses (RI-FFT/WT) is employed to choose the RCsnubber circuit parameters (R and C). The optimal snubber circuit parameters design was determinedfrom the hybridization between genetic algorithm (GA) and RI-FFT/WT. It is evident from the simulationresults that the new hybrid GA-FFT/WT approach succeeded in the selection of the most optimal RC-snubber circuits required for the mitigation of the TOV.