Drilling of cooling holes in turbine blades on difficult to machine materials like Inconel 718 has been one of the significant applications of micro-EDM. Owing to the difficulties in the contact measurement techniques, the actual side wall characteristics of micro-holes were not explored in detail. In this study, optical non-contact 3D profilometry is used to characterize the side wall surface. The 3D roughness parameter, Sa, has been introduced to measure the side wall surface quality of the holes drilled using micro-EDM. Along with side wall roughness, all the significant responses in the micro-hole manufacturing like material removal rate, overcut, and taper angle were also taken as the responses. The voltage, feed rate, and electrode rotation speed were chosen as the factors. The Box–Behnken design for three factors was used as the experimental design to conduct the study. The analysis showed that voltage was the most significant factor influencing all the responses within the design space. Multi-objective optimization of the process parameters was carried out by the method of sum of weighted objectives using genetic algorithm. A machining strategy was proposed combining both response surface methodology and genetic algorithm to formulate an optimum cutting condition which was able to reduce the inner side wall surface roughness to 1.3587 $$\upmu $$ m. The predicted responses were validated experimentally and the maximum relative error obtained was less than 10%.