$T^2$ control charts are used to primarily monitor the mean vector of quality characteristics of a process. Recent studies have shown that using variable sampling interval (VSI) schemes results in charts with more statistical power for detecting small to moderate shifts in the process mean vector. In this study, we have presented a multiple-objective economic statistical design of VSI $T^2$ control chart when the in-control process mean vector and process covariance matrix are unknown. Then we exert to find the Pareto-optimal designs in which the two objectives are minimized simultaneously by using the Non-dominated sorting genetic algorithm. Through an illustrative example, the advantages of the proposed approach is shown by providing a list of viable optimal solutions and graphical representations, thereby bolding the advantage of flexibility and adaptability.