Inconel 625 is a super alloy that has excellent thermal and mechanical properties but is arduous to machine with conventional machining processes due to high melting point and hardness. Wire Electro Discharge machining, that have been an avowed unconventional process of machining that is mainly applied for the machining of tough and hard materials such as Inconel 625. An attempt, in this article, have been made to optimize the WEDM process parameters like servo voltage, peak current, spark-on time, spark-off time while machining on Inconel 625. The study considers Material Removal Rate (MRR) and Surface Roughness (SR) as performance parameters of machining process. L16 orthogonal array is implemented to design the experiments. Mathematical relations between the response parameters and the input variables are computed using of Response Surface Methodology (RSM). The mathematical models are then employed as a fitness function in the Multi-objective Grasshopper Optimization Algorithm (MOGOA) for determining optimal process parameters. Later, a comparison of MOGOA has been done with Non-dominated Sorting Genetic Algorithm II (NSGA- II) and Multiple Objective Particle Swarm Optimization (MOPSO) and found superior to both. Also, for responses like surface roughness (SR) and material removal rate (MRR), the predicted values in the present study are found to be in good proximity to the experimented values.