In this paper the genetic algorithm (GA) method is applied to the optimization problem of a linear one-degree-of-freedom (1-DOF) vibration isolator mount and the method is extended to the optimization of a linear quarter car suspension model. A novel criterion for selecting optimal suspension parameters is presented. An optimal relationship between the root mean square (RMS) of the absolute acceleration and the RMS of the relative displacement is found. Although the systems are linear, it is difficult to find such optimal relation analytically. The optimum solution is obtained numerically by utilizing GA and employing a cost function that seeks minimizing absolute acceleration RMS sensitivity to changes in relative displacement RMS. The combination of RMS and absolute acceleration sensitivity minimization produces optimal suspension that is robust to broadband frequency excitation. The GA method increases the probability of finding the global optimum solution and avoids convergence to a local minimum which is a drawback of gradient-based methods. Given allowable mount relative displacement (working space), designers can use the results to specify the optimal mount and suspension. The cost function employed can be extended to optimize multi-DOF (MDOF) and non-linear vibrating mechanical systems in frequency domain. Applying the method to a linear quarter car model illustrates the applicability of the method to MDOF systems. An example is given to demonstrate the optimality of the solution obtained by the GA technique.