To address the issues of low computational efficiency and blind parameter searching in the optimization of water hammer protection schemes

a collaborative optimization method for protection parameters based on theoretical formulas is proposed. This study aims to construct a precise optimization space through theoretical formulas so that an intelligent and rapid design of the parameters can be achieved. First

a limiting valve-closing time formula for water hammer that accounts for pipe-valve coupling is derived to determine the initial closing time and establish the search domain. Using this formula

the Method of Characteristics (MOC) is employed to generate sample data for training a Multi-Layer Perceptron (MLP) surrogate model

with valve-closing time and surge tank diameter as input variables. The NSGA-III algorithm is then applied for multi-objective iterative optimization

and the optimal scheme is selected using Grey Relational Analysis (GRA). The results indicate that the derived valve-closing time formula has high accuracy

with a relative deviation of less than 2% between the theoretically assumed piezometric head and the MOC simulation results. The MLP surrogate model demonstrates excellent predictive performance

achieving an average R2 exceeding 0.94 and an average RMSE of less than 0.3 m in 5-fold cross-validation. Furthermore

the optimized surge tank volume is reduced by 20.5% compared to the initial design

significantly improving both the cost-effectiveness and safety of the water hammer protection scheme.