This article presents a multi-objective design optimization study of a vehicle suspension system with passive variable stiffness and active damping. Design of suspension systems is particularly challenging when the effective mass of the vehicle is subject to considerable variation during service. Perfectly maintaining the suspension performance under the variable load typically requires a controlled actuator to emulate variable stiffness. This is typically done through a hydraulic or pneumatic system, which can be too costly for small/medium pick-up trucks. The system in this article employs two springs with an offset to the second spring so that it engages during large deformation only, thereby providing passive variable stiffness without expensive hydraulics. The system damping is assumed to be controlled via variable viscosity magnetizable fluid, which can be implemented in a compact, low-power set-up. Performance indices from the literature are evaluated at minimum and maximum weight, and regarded as objectives in a multi-objective problem. As the individual objectives are prone to having local optima, the multi-objective problem is prone to having a disjointed Pareto-space. To deal with this issue, a modification is proposed to a multi-objective genetic algorithm. The algorithm performance is investigated via analytical test functions as well as the design case of the suspension system.