Evaluation of minimum zone sphericity by combining single-space contraction strategy with multi-directional adaptive search algorithm

Abstract With the aim of achieving faster and more accurate assessments of the minimum zone sphericity, this paper describes a method that combines a single-space contraction strategy (SSCS) with a multi-directional adaptive search (MDAS) algorithm. SSCS is designed to generate highly targeted initial candidate points for the minimum zone sphere center in the established contraction space, and then the MDAS algorithm constructs new solutions with some offset value. These new solutions are located across a diverse area of the search space to ensure that the global optimum is not missed. The diversity of the search direction and the adaptability of the search step size are guaranteed by rearranging the matrix of candidate points. Experimental examples and comparison results indicate that the proposed method achieves excellent convergence behavior, reaching the global optimum faster than conventional heuristic methods. Across six different datasets, the average calculation time required to achieve a solution accuracy of δ  = 10 nm is less than 0.0273 s, and a solution accuracy of δ  = 0.01 nm can be attained in less than 0.0494 s. The proposed method is also suitable for rapid, high-precision evaluation of minimum zone roundness, cylindricity, or straightness.