In this study, we provide two approximate methods for solving both Unidirectional and Multidirectional Road Network problems with Disruptions and connecting requirements. These problems aim at defining alternative paths to deviate traffic flows, allowing the arc orientation to be reversed, such that the network remains strongly connected. The objectives are set to minimize the total travel cost and the number of reversed arcs. Two methods, a Biased Random Key Genetic Algorithm and an Iterated Local Search, are proposed. Numerical experiments with single objective and bi-objective versions are performed and results are hence compared to the exact method studied in previous works.