In this paper, a square textured parallel slider is considered for a study to improve the hydrodynamic performance of moving parts. The numerical method is employed for the analysis of a square texture with different bottom profiles: flat, triangle T1, triangle T2, and curved. The governing Reynolds equation is solved using a finite difference numerical discretization technique with the Gauss-Seidel iterative scheme. To obtain optimized process parameters, the response surface methodology-based central composite design along with grey relational analysis multi-objective optimization is used. The multi-objective responses are the load capacity and friction coefficient. The triangle T2 bottom profile yields the highest load capacity and the lowest friction coefficient compared to flat, triangle T1, and curved bottom profiles, of which the triangle T1 bottom profile yields the worst results. For the triangle T2 bottom profile, the flow speed is found to be the most significant process parameter, followed by the aspect ratio. Texture density is found to be the least significant parameter based on increasing the load capacity and decreasing the friction coefficient.