In real applications, typically, there is a lack of information about the uncertainty/dynamismassociated with them. An effort has been done in the literature for finding robust solutions for their associated Constraint Satisfaction Problems (CSPs). Here, we analyze a previous exact/complete approach from the state-of-the-art that focuses on CSPs with ordered domains and dynamic bounds. However, this approach has low performance in large-scale CSPs. For this reason, in this paper, we present an inexact/incomplete approach that is faster at finding robust solutions for large-scale CSPs. This is specially handy when the computation time available for finding a solution is limited and/or a new solution must be re-computed on-line (because the original one is lost due to the dynamism). Specifically, we present a Large Neighbourhood Search (LNS) algorithm combined with Constraint Programming(CP) and Branch-and-bound (B&B) that searches for robust solutions. Furthermore, we also present a robust-value selection heuristic that guides the search towards more promising branches. We evaluate our approach with large-scale CSPs instances. Including the case study of scheduling problems. The evaluation shows a considerable improvement in the robustness of the solutions achieved by our algorithm for large-scale CSPs.