Form error evaluation of geometrical products is a nonlinear optimization problem, for which a solution has been attempted by different methods with some complexity. A genetic algorithm (GA) was developed to deal with the problem, which was proved simple to understand and realize, and its key techniques have been investigated in detail. Firstly, the fitness function of GA was discussed emphatically as a bridge between GA and the concrete problems to be solved. Secondly, the real numbers-based representation of the desired solutions in the continual space optimization problem was discussed. Thirdly, many improved evolutionary strategies of GA were described on emphasis. These evolutionary strategies were the selection operation of ‘odd number selection plus roulette wheel selection’, the crossover operation of ‘arithmetic crossover between near relatives and far relatives’ and the mutation operation of ‘adaptive Gaussian’ mutation. After evolutions from generation to generation with the evolutionary strategies, the initial population produced stochastically around the least-squared solutions of the problem would be updated and improved iteratively till the best chromosome or individual of GA appeared. Finally, some examples were given to verify the evolutionary method. Experimental results show that the GA-based method can find desired solutions that are superior to the least-squared solutions except for a few examples in which the GA-based method can obtain similar results to those by the least-squared method. Compared with other optimization techniques, the GA-based method can obtain almost equal results but with less complicated models and computation time.

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An iterative neighborhood search approach (INSA) was proposed to precisely evaluate the circularity error under minimum zone conditions without directly solving nonlinear equations from coordinate measurement machine (CMM) data. The method starts with calculating the initial location and radius of an initial circular search scope. The location is the center of the circle based on an approximate least-squares method of all measurement data points uniformly sampled around the circle, and the radius is the circularity error value by using the approximate center as the datum center of two concentric circles enclosing all measurement data points. Then the circular search scope was divided according to some concentric circles and radials with some radius and angle step lengths. Intersections of the circles and radials were candidate centers for circularity evaluation under the minimum zone criteria. An optimal center with minimum circularity error value was picked out as a new location of the search scope. The distance from the old location was the radius of the new search scope. Further it was divided and the intersections were evaluated until the optimal solution was met. Some examples in the literature were used to verify the validity of this method. The results are the same as or better than those minimum zone solutions adopted from previous work, and computation time is no more than 0.07 s implementing on an IBM ThinkPad R40 laptop for all examples. The computation and comparison show that the proposed INSA is a precise, fast, convergent and simple approach which solved circularity evaluation problems effectively.

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