An effective genetic algorithm for circularity error unified evaluation

Abstract

There are four methods commonly used to evaluate the circularity error. They are: minimum zone circle (MZC) method, minimum circumscribed circle (MCC) method, maximum inscribed circle (MIC) method and least square circle (LSC) method. However, so far there is no a robust and effective approach to implement a unified evaluation of these four methods. In this paper, an effective genetic algorithm is presented for searching the above four circularity error evaluation methods simultaneously. The algorithm is implemented in real-code and only blend crossover operators are applied to two randomly selected individuals from the existing population. The algorithm does not require genetic parameters such as crossover and mutation probabilities to be set in advance as does a canonical GA; therefore it is very convenient to use in engineering metrology. The objective function calculation approaches of four circularity errors are developed and the initial population generation methods are given in order to save optimization time. Finally, the experimental results evaluated by different methods confirm that the proposed method can find the optimal solutions of these four methods. In comparison with existing evaluation methods, the algorithm is not only simple and robust, but also it unifies these four kinds of circularity evaluation. The algorithm can also be used for solving difficult form error minimization and profile evaluation problems of various geometric parts in engineering metrology.