Genetic algorithm-based form error evaluation

Abstract

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.