Many polycrystalline materials exhibit anisotropy in their thermal, electrical, optical and mechanical properties owing to preferred orientations in crystallite packing. A knowledge of the directions and degree of preferred orientation is essential in understanding and predicting the physical properties of these materials. The directions of preferred orientation in a specimen are a function of crystallite shape and the process used to form the body. In extruded or rolled materials it is common to find two types of orientation, one normal to the surface of the body, the second within the surface in the rolling or extrusion directioni ' 2 Fabrication techniques based on casting, deposition or pressing, however, will introduce preferred orientations normal to the surface only, with crystallite directions within the surface at random.The most common method of representing preferred orientation is to construct a stereographic projection of the normals to a crystallographic plane, called a pole figure 3 , 4 Other techniques such as representing the angular distribution of a particular direction in a crystallographic reference frame (inverse pole figure) 5 -8 or analytical methods 9 , 10 have been developed. The data required by these techniques for displaying preferred orientation is obtained by measuring the orientation of a large number of crystallites. This may be
We set out to demonstrate the effectiveness of distributed genetic algorithms using multivariate crossover in optimizing a function of a sizable number of independent variables. Our results show that this afgorithm has unique potential in optimizing such functions. The muhivariate crossover mets-strategy, however, did not result in a singularly better performance of the algorithm than did simplier crossover s~ategies.
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