Runoff is greatly influenced by changes in climate conditions. Predicting runoff and analyzing its variations under future climates are crucial for ensuring water security, managing water resources effectively, and promoting sustainable development within the catchment area. As the key step in runoff modeling, the calibration of hydrological model parameters plays an important role in models’ performance. Identifying an efficient and reliable optimization algorithm and objective function continues to be a significant challenge in applying hydrological models. This study selected new algorithms, including the strategic random search (SRS) and sparrow search algorithm (SSA) used in hydrology, gold rush optimizer (GRO) and snow ablation optimizer (SAO) not used in hydrology, and classical algorithms, i.e., shuffling complex evolution (SCE-UA) and particle swarm optimization (PSO), to calibrate the two-parameter monthly water balance model (TWBM), abcd, and HYMOD model under the four objective functions of the Kling–Gupta efficiency (KGE) variant based on knowable moments (KMoments) and considering the high and low flows (HiLo) for monthly runoff simulation and future runoff prediction in Tunxi basin, China. Furthermore, the identified algorithm and objective function scenario with the best performance were applied for runoff prediction under climate change projections. The results show that the abcd model has the best performance, followed by the HYMOD and TWBM models, and the rank of model stability is abcd > TWBM > HYMOD with the change of algorithms, objective functions, and contributing calibration years in the history period. The KMoments based on KGE can play a positive role in the model calibration, while the effect of adding the HiLo is unstable. The SRS algorithm exhibits a faster, more stable, and more efficient search than the others in hydrological model calibration. The runoff obtained from the optimal model showed a decrease in the future monthly runoff compared to the reference period under all SSP scenarios. In addition, the distribution of monthly runoff changed, with the monthly maximum runoff changing from June to May. Decreases in the monthly simulated runoff mainly occurred from February to July (10.9–56.1%). These findings may be helpful for the determination of model parameter calibration strategies, thus improving the accuracy and efficiency of hydrological modeling for runoff prediction.