Wire electrical discharge machining is a thermal energy-based non-conventional machining process which can machine conductive materials with high precision. In this present work, machining of Inconel-825 was performed using wire electrical discharge machining. Multi-objective parametric optimization was performed for maximum cutting rate and minimum surface roughness using teaching–learning-based optimization, grey relational analysis, and genetic algorithm. Four wire electrical discharge machining parameters, namely spark off time (SOFF), spark on time (SON), peak current (IP), and angle of cutting (A) were considered. Comparison of optimum wire electrical discharge machining parameters through teaching–learning-based optimization, grey relational analysis, and genetic algorithm was performed. The better optimum solution for wire electrical discharge machining parameters was obtained using teaching–learning-based optimization and optimum values were at IP (1 A), SON (30 µs), SOFF (12.5 µs), and A (44.8°) with cutting rate as 19.744 mm/min and surface roughness as 1.331 µm. The optimum results obtained using optimization techniques were validated with the experimental results and error was observed to be within 5%. Moreover, response surface models were developed to predict the cutting rate and surface roughness in terms of wire electrical discharge machining parameters using analysis of variance.