Application of Genetic Algorithms in Texture Analysis and Optimization

Abstract

The genetic algorithms method (GAM) is a modern computer technique based on some ideas taken from biological evolution theory. The GAM is especially useful in a study of problems being not completely determined. They are, e.g., problems having a few but not very different solutions or problems without a strict (exact) solution. The last situation may occur if it is enough to find a good enough solution but not necessarily the best one. In GAM approach, it is not necessary to know a priori a general scheme of problem solution; however, it is important to have a procedure estimating the quality of a solution. This procedure is necessary to eliminate some solutions and to accept another ones. In the last years, GAM was applied with success in different areas of science (e.g., sociology, construction engineering, artificial intelligence and many others). The present authors have applied GAM in crystallographic texture analysis: the orientation distribution function (ODF) was calculated from a set of measured pole figures. The quality of obtained results was very good; however, the calculation time and memory space were relatively high. The main reason of this situation was the use of spherical harmonic function series for the ODF representation. An important simplification of the calculation scheme (and of calculation time and memory space) can be obtained if ODF is represented by a sum of a few Gauss-type functions. The quality of solutions in this new approach is still very correct. The above-mentioned improved GAM scheme was also used to find an optimal crystallographic texture that optimizes the elastic properties of material. By using this approach the Young modulus can be maximised or minimised along a given sample direction.

Key Words:

• Genetic algorithms
• Crystal orientation
• Crystallographic texture
• Orientation distribution function
• Texture analysis
• Ideal orientation
• Series development
• Standard distributions
• Elastic constants
• Elastic anisotropy
• Optimization

Acknowledgments

The present work was supported by Joint Polish-French Research Project POLONIUM 2003 and by the Polish Committee of Scientific Research (K.B.N.).