## 1 Introduction  
The cold forging process can manufacture parts with near-net shapes for greater strength and accuracy with less waste compared to hot forging [1; 2; 3]. The cold forging manufacturing process is mainly employed to produce the metal parts featured as less mass-enabled stronger ones. The present trend in manufacturing by the metal forming process seeks three critical aspects to be embedded in the product; better accuracy/precision, surface quality, and mechanical properties [4]. The cold forging process has been proven to be a favorable contender among other manufacturing processes for the production of such parts featured with precision, strength, and lightweight [5]. Moreover, the automotive and aerospace domain will be significantly affected by environmental aspects in the coming decade, with new norms affecting majorly on power-train [6; 7]. Cold forging qualifies these capabilities, and the parts produced out of cold forging are classified for superior mechanical properties induced by the process. Such typical parts are being employed where the strength becomes pivotal, for example, components of engines, power transmission, and housings, etc., [8; 9; 10]. In order to improve the mechanical stiffness of a component, cold forging was employed instead of the fine blanking process in an automotive part [11]. Despite offering distinct advantages over hot forging or other manufacturing processes, cold forging technology is still a challenge to the industry. Higher process force requirements and frequent die failures due to wear and fatigue can cause trouble when working out a cold forging cycle [12; 13]. The cold forging process comprises forward extrusion, backward extrusion, and combined forward-backward extrusion, and various axi-symmetrical configurations are possible depending on the final geometry to be achieved. The cold forging backward extrusion is employed for producing cup-shaped axi-symmetrical parts used in automobile and aerospace applications [14]. Since the huge amount of forces required to deform the metal in cold forging backward extrusion, the die elements are often subjected to severe stresses and are prone to failures [15; 16; 17]. Therefore, the industry must pay close attention to economic viability to produce the components. The cold forging backward extrusion is a relatively complex process as the material's flow pattern depends on several factors, such as the frictional conditions at the work-piece/tooling interface, the geometry of the bullet (pre-form), die elements, the material type, and the percentage reductions [18]. Due to the complexity of the analysis and many process variables, it is not easy to estimate the forming aspects of a given component [19]. Recent advances in process design and optimization show the extensive use of finite element method (FEM) simulation tools that reduced process development lead time [20]. The finite element technique was used to investigate the complex process design of the cold forging with a floating die to obtain a suitable die velocity, which depends on the contact stress between die and workpiece [21]. Investigations of thermal effects on workpiece optimization for complex geometries like propeller hubs were carried out using FE simulation technique [22]. The effect of mechanical and thermal loads on the components' accuracy produced through the cold forging process with due consideration on spring-back was studied by [PERSON] et al. [23] using FEM. Since many process variables are included in the cold forging process, researchers have contributed in developing predictive models by optimizing process variables in the cold forging domain using meta-heuristic techniques along with FEM. Further, the geometry of the work part (pre-form) influences the metal fill pattern in the die cavity to achieve the final configuration. [PERSON] et al. [24] illustrated the pre-form optimization using a neural network and genetic algorithm that resulted in a 50% reduction of the forging force.