The search for the optimal pair of active and protection paths in a network with Shared Risk Link Groups (SRLG) is a challenging but high-value problem in the industry that is inevitable in ensuring reliable connections on the modern Internet. We propose a new approach to solving this problem, with a novel use of statistical analysis of the distribution of paths with respect to their cost, which is an integral part of our innovation. The key idea in our algorithm is to employ iterative updates of cost bounds, allowing efficient pruning of suboptimal paths. This idea drives an efficacious exploration of the search space. We benchmark our algorithms against the state-of-the-art algorithms that exploit the alternative strategy of conflicting links exclusion, showing that our approach has the advantage of finding more feasible connections within a set time limit.