Mesh generation using genetic algorithms

Abstract

In this paper, a process of triangular meshes optimization employing genetic algorithms is proposed. From a given mesh, it is built a new one such that a fitness function is minimized taking into account the distribution of the error indicators which provides information about the density of the mesh, and some geometrical conditions that allow to keep the quality of the triangles. Obviously, here the main goal is to apply the genetic algorithms in those functions for which other techniques of optimization, is spite of being faster, do not allow to reach the best solution. The nodes control is got by binary codes, assuming that they are equivalent to chromosomes of a population. Then, the selection, crossover and mutation between parent chromosomes lead to a new population and so on, until the approximate solution of the global optimum is found. An analysis of the parameters values of reproduction, crossover and mutation probabilities and size of the population must be done to obtain a robust algorithm. Some test applications of adaptive meshes built by using the technique proposed here, are presented and discussed, referring numerical results with other meshes generators.