This study proposes a novel approach to optimize the structure of the hinge beam in cubic presses, aiming to enhance the safety and reduce costs. The finite element method is used to analyze the stress distribution of the hinge beam under operating conditions, revealing a significant stress concentration at the oil inlet edge. To optimize the structure, the Taguchi method, the NSGA-II multi-objective optimization algorithm, and the entropy-TOPSIS method are combined to consider both the maximum stress and total weight. The results demonstrate a reduction of 199.121 kg and 11.97 MPa in the total weight and maximum stress of the hinge beam, respectively, representing a decrease of 4.12% and 1.72%. Furthermore, the simulation results of the optimal structure demonstrate a high degree of accuracy, with only 0.27% difference between the algorithm-optimized and simulation values. The proposed optimization method not only improves the efficiency of the optimization, but also avoids the mutual exclusion between the maximum stress and total weight. It significantly improves the reliability of the hinge beam and reduces its manufacturing costs, thereby shortening the development cycle of the new hinge beam.