Disruptions in urban road networks can quickly and significantly reduce the quality of the whole transportation network, and impact urban mobility for light vehicles, public transportation, etc. In this study, we consider both unidirectional and multidirectional road network problems with disruptions and connecting requirements. These problems aim at reconfiguring the urban network in terms of road direction in order to maintain a path among all points of the network (strong connectivity). The former is defined on simple graphs, mainly modeling part of a city such as historical centers, while the latter relies on multigraphs, modeling more general networks. Restoring the network (strong connectivity) after some disruptions may require the modification of the orientation of some streets, that is, arc reversals. Such actions can disturb users' driving habits. Thus, two objectives are considered separately: minimizing the total travel distance and minimizing the number of arc reversals. We define formally both problems and propose two metaheuristics, a biased random key genetic algorithm and an iterated local search. Numerical experiments have been performed on a set of generated instances and on the urban network of Troyes (France).