The demand of Advanced Machining Processes (AMP) is continuously increasing owing to the technological advancement. The problems based on AMP are complex in nature as it consisted of parameters which are interdependent. These problems also consisted of linear and nonlinear constraints. This makes the problem complex which may not be solved using traditional optimization techniques. The optimization of process parameters is indispensable to use AMP's at its aptness and to make it economical to use. This paper states the optimization of process parameters of Ultrasonic machining (USM) and Abrasive water jet machining (AWJM) processes to maximize the Material Removal Rate (MRR) using a socio inspired Cohort Intelligent (CI) algorithm. The constraints involved with these problems are handled using static penalty function approach. The solutions are compared with other contemporary techniques such as Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Modified Harmony Search (HS_M) and Genetic Algorithm (GA).