This paper presents a Particle Swarm Optimization-based topology optimization method for the design of negative permeability dielectric metamaterials. As the electromagnetic metamaterials have some physical properties not available in nature, they have attracted a huge scientific research interest for decades. In fact, electromagnetic metamaterials can exhibit simultaneously negative permeability and negative permittivity. The aim of this work is to find an optimal topology of a dielectric metamaterial that achieves negative permeability at a given frequency. A binary Particle Swarm Optimization is developed and applied to a negative permeability dielectric metamaterial topology design problem. The optimization process is achieved using a developed numerical model of the studied metamaterial, which is solved by the Finite Element Method. First, the governing equations and the weak formulation of the electromagnetic problem are presented. Then, the optimization problem to be solved is formulated. The developed binary Particle Swarm Optimization method, and the developed interfacing method are explained. Some numerical examples are presented to demonstrate that the binary Particle Swarm Optimization is adapted to the topology optimization of negative permeability dielectric metamaterials, at given frequencies, to demonstrate the utility and validity of the presented method. 
Optimum topological design of negative permeability dielectric metamaterial using a new binary particle swarm algorithm