Titanium alloys are known to have some excellent properties, such as good biocompatibility, good fatigue resistance and high strength to weight ratio. Due to these properties, Ti6Al4V alloy is widely used in the biomedical field, aerospace and automobile industries. In this article, pulse on-time (TON), pulse off time (TOFF), and servo voltage (SV) were selected as process parameters for wire electric discharge machining (WEDM) on Ti6Al4V alloy. The material removal rate (MRR) and surface roughness (SR) were determined as responses. MRR and SR have been equated by a central composite design (CCD: a response surface method technique). Then multi-objective Artificial Bee Colony optimization (MO-ABC) with Gray relational analysis (GRA) was selected as a priori approach for multi-objective optimization. Also, a multi-objective grasshopper optimization algorithm (MO-GOA) has been chosen as a posterior approach for optimization. These two algorithms have been tested on various iterations and populations. Based on the elapsed time, it has been found that the priori approach of multi-objective optimization is better than the posterior approach of multi-objective optimization. When comparing these algorithms based on the results, it is obtained that the posterior approach gives a better combination of multiple results. The major outcome of the research is that the priori method is quick, while the posterior approach produces many promising solutions.