The general radial flow (GRF) could successfully analyze the groundwater flow in a fractured medium which has generally a more complex mechanism due to the scale-dependent heterogeneity and dynamic processes for both individual fracture and fracture networks. A new optimization scheme, referred to as the automatic shifting method (ASM), was established in order to eradicate the subjectivity and some definite difficulties in classical graphical curve matching (GCM) for the determination flow parameters of GRF from in-situ pumping test data. The logic behind the ASM is similar to GCM but it simplifies and enhances the estimation process by optimizing newly introduced parameters (the horizontal and vertical shifts) together with the flow dimension parameter via Water Cycle Algorithm (WCA). The proposed ASM was tested with several hypothetical pumping test scenarios as well as a number of real field data. In addition, the capability of WCA was thoroughly compared with other competitive derivative-free, nature inspired population-based optimization algorithms by implementing a multi decision criteria analysis. The proposed ASM with WCA could achieve the outstanding estimation performance for the implemented analyses. In conclusion, ASM has a great potential to be modified for interpreting test data obtained from different groundwater models.