Conventional machining of titanium matrix composite (TMC) is very intricate for its superior strength-to-weight ratio and resistance to fatigue and corrosion. The novelty lies in the analysis of multi-objective genetic algorithm (MOGA) coupled with desirability, forming desirable multi-objective genetic algorithm (DMOGA) of wire electro-discharge machining (WEDM) machining characteristics of performance measures varying power (P), peak current (IP) and time-off (Toff). In this paper, investigation is carried on design of experiments (DOE) on performance measures like material removal rate (MRR), surface roughness (SR), kerf width (KW) and over cut (OC) and reasonable results are attained and authenticated by confirmatory test. Optimality is attained when P is 7.37 W, Toff is 27.87 µs, IP is 9.71 A, MRR is 3.61 mm3/min, SR is 1.39 µm, KW is 0.35 mm, OC is 0.09 mm and combined desirability is 0.72.