In this study, the appropriate input parameters for achieving minimum surface roughness and high material removal rate are selected for wire electrical discharge machining of cold-work steel 2601. Mathematical modeling acquired by experimental result analysis is used to find the relation between input parameters including electrical current, gap voltage, open-circuit voltage and pulse-off time and output parameters. Subsequently, with exploitation of variance analysis, importance and effective percentages of each parameter are studied. The combination of optimum machining parameters is acquired using the analysis of ratios of signal-to-noise. Finally, according to multiple-objective optimization, outputs acquired from Non-dominated Sorting Genetic Algorithm led in achieving appropriate models. The optimization results showed suggested method has a high performance in problem solving.