Quality of Experience (QoE) measures a user's satisfaction with a service delivery. However QoE is a very subjective measure and is context dependent, making it difficult for a service provider to estimate and optimize user's QoE. In this paper, we look at how the provider can maximize QoE by optimizing wireless bandwidth allocation, especially for mobile cloud applications. The multi-stimuli version of the “IQX” hypothesis is used to model the QoE of a user, and this model is used in formulation of a nonlinear optimization problem, which is solved using NSGA-II. Simulations using realistic parameters based on 802.11n demonstrate a reduction in the required bandwidth by as much as 33% (i.e., more users can be accommodated by the system), while maintaining the same level of QoE. Our evolutionary-algorithm-based approach is able to discover the optimal bandwidth allocation. The problem of equalizing user QoE is explored and a tradeoff between QoE and fairness is studied, while being characterized using a Pareto front.