###### Abstract  
This paper introduces a multi-objective optimization problem (MPO) for the forming process parameters of disc forgings using grey relational analysis (GRA) and the response surface methodology (RSM). Firstly, an experimental design based on the Box-Behnken design (BBD) principle was established, and simulations were performed in Deform to obtain response data. Secondly, GRA was used to transform the MPO into a grey relational degree (GRD) problem, and the entropic weight method was integrated to ascertain the influence weights of each variable on GRD. Then, a quadratic polynomial prediction model based on the RSM was constructed, and its accuracy was ensured through model validation. Finally, the optimal process parameter combination was determined through the particle swarm optimization algorithm, which included a friction coefficient of 0.3, an initial temperature of 1250 \({}^{\circ}\)C, and a downward pressing speed of 7.5 mm/s. The results of the experimental investigation indicate that optimized process parameters significantly reduce the forming load, equivalent stress, and damage value, effectively enhancing the overall quality of forged parts. disc forging; process parameter optimization; grey relational analysis; response surface methodology; particle swarm optimization +
Footnote †: journal: Applied  
the non-uniformity in equivalent strain distribution and improve the precision of forgings during the upsetting process. However, numerical simulation technology also has some limitations. The default process parameters in the simulation process are often not optimal, and reliance on mathematical models and optimization techniques is needed to quickly and accurately acquire the best processing parameters. [PERSON] et al. [5] introduced an alternative model based on orthogonal decomposition, which was applied to the cold upsetting process in steel billets and developed a neural network-based control prediction model which integrated different process variables, parameterized fields, and shapes, laying the basis for creating digital twins in forging operations. [PERSON] et al. [6] simulated the extrusion process using Deform 10.1, collecting simulation data through the Taguchi method for the experimental design, and determined the best values for input process parameters through variance analysis to achieve the optimization of the minimum compression force. [PERSON] et al. [7] simulated the microstructure development of the alloy 30 Cr2 Ni4 MoV under multi-directional forging conditions and constructed a backpropagation neural network model of predicting the microstructure evolution of the alloy 30 Cr2 Ni4 MoV during multi-directional forging deformation, enhancing its microstructure prediction accuracy. [PERSON] et al. [8] conducted numerical simulations of the cycloidal ball rocker arm during its radial forging process, utilizing an optimization algorithm that combines neural networks and genetic algorithms to seek the best structural parameters. In conclusion, these research efforts focus on enhancing the performance of a single objective while the impact of other factors during the forming process is neglected. However, the combined effects of multiple factors in actual production should be considered. In recent years, MPO has provided a more comprehensive and effective solution for optimizing process parameters during the forming process. For example, [PERSON] et al. [9] used thin-walled plastic auto audio housing as a case study, implementing MPO of plastic injection molding process parameters utilizing entropy weight, random forest, and genetic algorithms. [PERSON] et al. [10] proposed a double-layer optimization method for hinge beam structure forging, conducting a secondary optimization on the hinge beam's intermediate billet structure, which enhanced the grain fineness in the final forged product and decreased the deformation force required for forging. Considering the complexity of MPO, many scholars have introduced the GRD to solve MPO. [PERSON] et al.