Wind energy turns out to be the most influential alternative source of energy to deal with the demand-supply and environmental crisis of fossil fuels. However, the very uncertain nature of wind is generally ignored while designing a wind farm. Depending on the decently long life span of wind turbines, wind farms can face long term variations in the wind flow, affecting the power production capability severely. In this study, a flexible robust optimization methodology has been proposed to design wind farm layouts under varying wind state conditions. The proposed methodology assumes different realizations of wind state uncertainty distributions in terms of different frequencies of occurrences for wind speeds and directions and provides solutions for the worst case and the best case scenarios by solving two-stage robust counterpart formulations. Using the idea of index representation of grids, a novel technique utilizing the concept of variable resolution grid on need has been proposed to provide Pareto solutions for the multi-objective cost-power trade-off problem. The pros and cons of these competitive solutions and the benefits of adopting the worst case over the deterministic solutions (for each scenario considering no uncertainty) have been thoroughly analyzed to provide an idea of the minimum guaranteed power production that can be achieved under uncertainty. © 2019 IEEE.