## 1 Introduction
Artificial intelligence (AI) techniques have been utilized and compared in the design of the predictive tool for forging operations that comprise of input-output relationships, where the focus was on minimizing operational loads, material consumption, and energy without affecting the quality of the part being forged [25]. The present paper proposes to integrate two natural computing algorithms, the artificial neural network (ANN) and differential evolution (DE) algorithm, to model and optimize the cold forging process of AISI steel grades such as AISI 1010, 1018, and 1045. The ability to capture highly non-linear relations between several process parameters and responses of ANN makes it suitable to model the cold forging process. Once properly trained with experimental input-output data set, known as training patterns, ANN can further generalize the process behavior for any new data points. DE is a new branch of natural computing optimization algorithms. DE is real-coded population-based search algorithm and has proven to be highly efficient in providing global optimal solutions. The DE algorithm is based on the creation of new offspring chromosome generation through reproduction involving crossover, mutation, and natural selection. The crossover using the best-fit chromosome improves the DE convergence speed. On the other hand, randomly selected chromosome pairs are employed in the mutation process helps to maintain the population diversity and overcome the destructive crossover. DE exhibits self-tuning property and hence uses few control parameters which are easy to determine for a given problem. The overall DE algorithm is very simple and, hence, easy to develop the program. The adoption of the cold forging process is limited in industry, mainly because of higher force requirements leading to frequent die failures; particularly, in cold forging backward extrusion, where the punches are more prone to breakages when working out steel as a billet material. Hence, there is a need to adopt a systematic approach to achieve a deeper understanding of the cold forging backward extrusion. Process modeling, along with advanced finite element simulation tools, have relatively more benefits over traditional trial and error methods to analyze the feasibility of the process. Moreover, the study would benefit small and medium-scale industries that cannot afford design and simulation tools to understand the forming behavior of different steels and also to decide upon the optimal parameters for the economic viability of the process. Cold forging is a quite complex process; however, conventional process modeling and optimization methods lack in capturing the non-linearity involved in the process. Therefore, the intent of the work is to build predictive models and optimize the cold forging process using AI techniques. In addition, a comparative study on forming behavior of different AISI steel grades will definitely assist in arriving at the best combinations, which will increase the punch performance. The investigations on the forming aspects will help industries to reduce development time as well as cost. In the current investigation, a comparative study has been carried out on the forming behavior of different AISI grade steels that emphasizes the role of finite element simulation coupled with differential evolution optimization technique for analyzing the effect of critical geometrical factors: namely, billet size, reduction, punch angle, and land height. As part of experimental validation, an attempt has been made to capture the forming responses, such as forging force, effective strain, strain rate, and stress. Micro-structural observations including micro-hardness studies have also been performed on the cold forged samples to verify the quality of the forgings, confirming the appropriateness of the identified variables and their levels.