Multimodal Genetic Algorithm with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis

In this contribution, a new genetic-algorithm-based method of finding roots and poles of a complex function of a complex variable is presented. The algorithm employs the phase analysis of the function to explore the complex plane with the use of the genetic algorithm. Hence, the candidate regions of root and pole occurrences are selected and verified with the use of discrete Cauchy’s argument principle. The algorithm is evaluated in an electromagnetic benchmark that successfully solves the eigenvalue problem determining the propagation of surface waves along a spatially dispersive graphene sheet. The numerical results show that the possibility to find all roots and poles of the function may be limited by the initial population size, especially when the search region is large and roots and poles are located close to each other.