Method for spherical form error evaluation using cuckoo search algorithm

To obtain the accurate evaluation of minimum zone sphericity, this paper investigates a method in Cartesian coordinates using cuckoo search (CS) algorithm. In this method, an appropriate space is set as the search zone according to the solution obtained which is based on least square criteria. The aim of search is to find the best candidate position infinitely approximating the ideal reference center of minimum zone sphere. In order to improve the search efficiency, two essential parameters in CS, namely the control coefficient α of step size and the probability pa of discovering an invasive cuckoo's egg are set to 0.618 (value of golden ratio) and 0.05 (common value of statistical significance), respectively. The updating of the candidate points is carried out by Levy flights and biased/selective random walk mechanisms. Levy flights mechanism can ensure the real global optimum is not missed, biased/selective random walk mechanism guarantee the diversity of search direction and adaptability of search step size. During the updating, the new solution can be kept when it is better than the old one. In each search iteration, the position which corresponds to the smallest sphericity is regarded as the present optimum solution. When the iteration terminal condition is satisfied, the optimum position and corresponding sphericity are output as evaluation results. The validness of the proposed CS algorithm was tested by an application example, the results indicate that the proposed method has the advantage of excellent convergence and high efficiency, which is suitable for the hith-precision evaluation of minimum zone sphericity efficiently.