Induction motor design requires making numerous tradeoffs, especially when including electromagnetic noise criterion besides usual criteria like efficiency and cost. Moreover, adding the noise objective significantly increases computational time as it must be evaluated at variable speed in order to take into account resonance effects. In that case, the application of multiobjective optimization algorithms can be hard for their computational cost as for the difficulty to interpret multidimensional results in both design variables and objectives spaces. This paper first describes a fast analytical model of a variable-speed induction machine which calculates both motor performances and sound power level of electromagnetic origin. This model is then coupled to Nondominating Sorting Genetic Algorithm (NSGA-II) in order to perform global constrained optimizations with respect to several objectives (e.g., noise level, efficiency and material cost). As induction machine design involves both continuous and discrete variables, a modified NSGA-II algorithm handling mixed variables is detailed. Finally, some optimization results are presented and analyzed by the aid of several visualization tools.