The deterioration in the bridges that cross the watercourses is a situation that must be resolved in a timely manner to avoid the collapse of its structure. Its repair can mean a high cost, road and environmental alteration. An effective solution, which minimizes this impact, is the installation of a superstructure in the form of an arch that covers the entire length of the bridge and which, by means of a hook anchored to the deck of the bridge, allows the arch to support the weight. This structure must try to maintain the original properties of the bridge, so the calculation of the magnitude of tension of the hangers and the order in which it is applied should not cause damage to the structure. In this document, we propose to optimize the process of calculating the hanger magnitudes and the order in which they must be applied using the moth search algorithm, in order to obtain one or several satisfactory solutions. Finally, we present the results obtained for an arch bridge and three hangers and, thus, evaluate the efficiency and effectiveness in the process of obtaining results in comparison with the Black Hole Algorithm.