<abstract> <p>In the production and processing of precision shaft-hole class parts, the wear of cutting tools, machine chatter, and insufficient lubrication can lead to changes in their roundness, which in turn affects the overall performance of the relevant products. To improve the accuracy of roundness error assessments, Bat algorithm (BA) is applied to roundness error assessments. An improved bat algorithm (IBA) is proposed to counteract the original lack of variational mechanisms, which can easily lead BA to fall into local extremes and induce premature convergence. First, logistic chaos initialisation is applied to the initial solution generation to enhance the variation mechanism of the population and improve the solution quality; second, a sinusoidal control factor is added to BA to control the nonlinear inertia weights during the iterative process, and the balance between the global search and local search of the algorithm is dynamically adjusted to improve the optimization-seeking accuracy and stability of the algorithm. Finally, the sparrow search algorithm (SSA) is integrated into BA, exploiting the ability of explorer bats to perform a large range search, so that the algorithm can jump out of local extremes and the convergence speed of the algorithm can be improved. The performance of IBA was tested against the classical metaheuristic algorithm on eight benchmark functions, and the results showed that IBA significantly outperformed the other algorithms in terms of solution accuracy, convergence speed, and stability. Simulation and example verification show that IBA can quickly find the centre of a minimum inclusion region when there are many or few sampling points, and the obtained roundness error value is more accurate than that of other algorithms, which verifies the feasibility and effectiveness of IBA in evaluating roundness errors.</p> </abstract>