This paper presents a detailed study of the construction and cable-stressing process for the strengthening of bridges by the conversion of the structural typology from continuous beams to tied-arch bridges. The basic stages of the construction method and the basic assumptions of the study and applications of stress method, based on automated optimization using genetic algorithms, are described. Additionally, a criterion of design variables, constraints and objective functions are defined. Finally, an example of application to the San Luis Bridge in Chile is presented and illustrates the use of the algorithm.