eXtended Finite Element Method Connected with Multi-objective Optimization Algorithm Used in 3D Electromagnetic Problems

摘要

This paper describes a way to interconnect the independent mesh mode, eXtended Finite Element Method (XFEM), with multi-objective optimization mode based for the improvement process on the genetic evolution algorithms Non-Dominated Sorting Genetic Algorithm II (NSGA-II). XFEM is an approximation method and is mostly used in dealing with problems characterized by deformations, cracks, discontinuities, complex geometries and it doesn't require that the mesh must conform to the geometrical boundaries. NSGA-II is an evolutionary multi-objective optimization algorithm used on a large scale to generate solutions in different domains. The solution returned is on the form of the Pareto Front. This approach to couple XFEM method with NSGA-II optimization algorithm is of the interest from the perspective of using XFEM method which has the advantage of not being necessary to remesh the model at each step of the optimization process while the NSGA-II Algorithm is an iterative process who succeeds to generate optimal solutions for the studied objective functions. This developed system can be used in various three-dimensional (3D) optimization problems while maintaining the advantages of the XFEM method and meanwhile optimizing the model through the robust process used by the NSGA-II algorithm.