Systematic cutting process design and optimization problems are studied for surface roughness minimization by stochastic algorithms. As the experimental background of the study, n-type single crystalline silicon (Si) ingot are cut into Si wafer with a thickness of 375 mu m using a wire saw machine. In order to optimize the cutting parameters successfully, a two-step study has been organized as (i) a detailed study on multiple nonlinear regression analysis of the process parameters for predicting the feed rate and wire speed effects, (ii) design and optimization steps. Regression models include linear, quadratic, trigonometric, logarithmic and their rational forms for the same surface roughness problem. In design and optimization section, four distinct stochastic optimization algorithms (Differential Evaluation, Nelder-Mead, Random Search and Simulated Annealing) have been performed systematically to avoid inherent scattering of the stochastic processes. To investigate the advantages and disadvantages of the introduced mathematical processes for the similar cutting process problems, a review list are also given for the optimization on volumetric metal removal rate (VMRR), wear ratio (WR), material removal rate (MRR) and surface roughness (SR) by distinguishing the modeling methodology, model types, and optimization algorithms. It is also shown that different rational regression models can be utilized with the collaboration of stochastic optimization methods successfully to minimize the surface roughness of Si wafers.