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Much attention has been paid to the methodology for measuring the performance of EDM (Electric Discharge Machining). In this paper, an optimization methodology, based on a combination of multivariate linear regression and the Particle swarm optimization method, is constructed to obtain optimum process parameters for EDM machining. The machining tests presented in this study are performed on an ONA NX4 die-sinking machine under different machining parameters such as discharge current (I), voltage (V) and pulse time (Ton ). The optimization strategy developed aims to maximize the material removal rate MRR, extend the lifetime of the TWR electrode and minimize the surface roughness Ra of AISI 1095 steel. Mathematical optimization models are developed by linear regression using multiple explanatory variables to predict the outcome of MRR, TWR and Ra responses. The models developed have a useful and significant precession compared to the experimental values: 97% for MRR, 94% for TWR and 82% for Ra. [ABSTRACT FROM AUTHOR]