Accurate Design of Array Coils for Transcranial Magnetic Stimulation by means of Continuous FSO

The closed forms of the Continuous Flock-of-Starling Optimization (CFSO) are applied to the optimization of the array coils usually used for TranscranialMagnetic Stimulation. The CFSO is the continuous equivalent model of the FSO algorithm, and it is expressed in terms of a state space representation. The trajectories of the CFSO particles, which explore the space solutions of the optimization problem, are obtained by solving a differential equations system within suitable Time-Windows (TWs). Thanks to the representation in terms of differential equations, it is possible to drive the trajectory by passing from convergence to divergence or vice-versa, and then from exploration to exploitation. Moreover, it is possible to refine the solution by reducing the amplitude of the TWs, during the optimization procedure, enhancing the performance of numerical FSO algorithm. The use of closed forms makes the CFSO easy to be implemented and accurate in quality of solution. Validation results are presented and the performances of different optimal array coils configurations have been compared.