In this paper, the control of the stationary response of a quarter car model to random road excitation with a Magnetorheological (MR) damper as a semi-active suspension device is considered. The MR damper is a hypothetical analytical damper whose parameters are determined optimally using a multi-objective optimization technique Non-dominated Sorting Genetic Algorithm II (NSGA II). The hysteretic behaviour of the MR damper is characterized using Bingham and modified Bouc-Wen models. The multi-objective optimization problem is solved by minimizing the difference between the root mean square (rms) sprung mass acceleration, suspension stroke and the road holding responses of the quarter car model with the MR damper and those of the active suspension system based on linear quadratic regulator (LQR) control with the constraint that the MR damper control force lies between ±5 percent of the LQR control force. 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. © 2012 Elsevier Ltd. All rights reserved.