Abstract <p>This paper presents a new method for accurately determining the crack length in damaged steel beam structures. The proposed method combines the geometric updating technique of the finite element model (FEM) with a new variant of atom search optimization (ASO) called Lévy–ASO. The key feature of the Lévy–ASO algorithm is that it generates random step lengths determined by the Lévy distribution. Based on these step lengths, Lévy–ASO can achieve wider movements to expand the search space or narrower movements to exploit the potential search spaces, which is close the global optimum. It leads to a new search strategy within the ASO algorithm, effectively improving its ability to find the global optimum solution and escape the local optimum. To compare the effectiveness of Lévy–ASO with the original ASO, 23 classical benchmark functions are used as the first example. The comparison results show the superiority of Lévy–ASO over the original ASO in both accuracy and convergence rate. Then, a series of experiments were conducted on damaged steel beams with the crack lengths of 2 mm, 4 mm, 8 mm, and 10 mm to demonstrate the effectiveness and reliability of Lévy–ASO in determining the crack length of steel beams. Based on the vibration frequencies measured in these experiments and obtained from the finite element (FE) model, an objective function is established. The process of finding the crack length is carried out using the Lévy–ASO algorithm to optimize the objective function, which is established based on the analysis of the FEM where the geometric coordinates of the crack length are adjusted. This study proves the effectiveness of the proposed method, and the Lévy–ASO algorithm is recognized as a promising optimization algorithm for solving various engineering optimization problems.</p>