## 4 Conclusions  
The application of differential evolution (DE) optimization for minimizing the forming responses, such as effective stress, strain, and punch force, while maximizing the strain rate has been presented in this paper. The geometrical attributes such as billet size, reduction ratio, punch angle, and land height that significantly affect cold forging backward extrusion of different steels, namely AISI 1010, 1018, and 1045, have been optimized. The fitness function was designed by mapping the forming responses for DE optimization. The forming responses were recorded through FE simulations and the models required for DE optimization were developed using artificial neural network (ANN), which were strategically planned according to full factorial experimental design (FFD). The error back propagation training algorithm (EBPTA) has been employed for ANN modeling. Following are the observations made through our investigation. * The forming responses are observed to be majorly affected by the reduction ratio, whereas, the marginal influence of the punch angle and land height is witnessed. However, punch angle and land height are major concerns in deciding the service life of the punches in cold forging backward extrusion. The effect of the billet size ratio is seen in the range from 0.3 to 0.6, and a further increase in the volume merely increases the values of forming responses. The deformation is also largely affected by the carbon content of the steel, as evidenced by AISI 1010, 1018, and 1045 steel materials. * The optimal punch angle for a reduction ratio of 0.3 is at 170\({}^{\circ}\) irrespective of the billet size ratio and type of AISI grade chosen steels tested. However, the punch angle is highly susceptible to the carbon content of the steel, reduction, and billet size ratio. Similarly, optimal land height is found to be closer to around 4 mm for AISI 1010 and 1018, whereas minimal (about 2 mm) for AISI 1045 for the increased reduction and billet size ratios. Hence, it is clear that steel's formability is majorly affected by the steel's carbon content, while land height and punch angle are decided based on the internal profile of the component and has a bearing upon punch service life. * Effective stress and strain optimal values obtained from optimization were observed to be of a similar trend and increased with reduction and billet size ratios. However, effective strain and punch force optimal values were reported to increase with decreased reduction ratios and remain marginally affected by billet size ratios. For the estimation of effective stress experimentally, the deformation or the strain is determined during cold forging and an analytical model comprising of the slab and power analysis has been implemented to arrive at the effective stress. The effective stress and strain values from experiments and those from the FE simulation and DE method are in good agreement. Figure 25: Comparison of micro-hardness values for AISI steels. * The cold forging backward extruded components have also been examined for better mechanical soundness, which eventually confirms the appropriateness of the identified variables. The microstructural observations for forged parts split in transverse sections revealed directionally oriented grain refinement. The micro-hardness along the transverse section for the cold forging backward extruded AISI grade steels were analyzed and it was observed that the average micro-hardness value of AISI 1018 was 267 Hv when comparatively higher than AISI 1010 and AISI 1045 steels. However, the cold forging backward extrusion resulted in an overall increase in average hardness and might be attributed to the fact that cold forging backward extrusion complies with the production of superior parts with good strength. Conceptualization, P.M.P. and V.N.G. ; methodology, P.M.P. and V.N.G. ; software, R.S.K. and P.M.P. ; validation, V.N.K. and J.P.D. ; formal analysis, P.M.P. and R.S.K. ; investigation, P.M.P. ; resources, V.N.K. and V.N.G. ; data curation, P.M.P., R.S.K. and V.N.G.