In this paper, control of the stationary response of a half-car model with a magnetorheological (MR) damper moving over a random road is considered. The MR damper is characterized using Bingham and modified Bouc-Wen models whose parameters are determined optimally using a multi-objective optimization technique and nondominated sorting genetic algorithm II. The multi-objective optimization problem is solved by minimizing the difference between the root mean square sprung mass acceleration, the sum of the front and rear suspension strokes and the sum of the front and rear road holding response of the half-car model with the MR damper, and those of an active suspension system based on linear quadratic regulator (LQR) control. The control force of the MR damper suspension is constrained to lie within ±5% of the control force corresponding to the active suspension system based on LQR control. It is observed that the MR damper suspension systems with optimal parameters perform an order of magnitude better than the passive suspension and perform as well as active suspensions with limited state feedback, and closer to the performance of fully active suspensions. In the case of MR damper suspensions, the vehicle response statistics are obtained using the equivalent linearization method and verified by Monte Carlo simulation. © The Author(s) 2014.