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Extra info for Advanced Computational and Design Techniques in Applied Electromagnetic Systems
Desired and optimized flux densities 5. Conclusion A new technique for the design optimization of electromagnetic devices is presented. It uses GAs as the search method. GAs provide a high level of robustness by Figure 5. Field solution simulating nature's capability of adapting to many different environments. Through the application of the proposed technique to the design optimization of the pole face of an electric motor, the performance characteristics of the GAs have been proved powerful in solving optimization problems that have high dimensional objective functions with many local minima.
C O N C L U S I O N S We have applied the GA for the ground state configurations of the Coulomb gas with fractional charges Q = n — / , / = p/q. A square crossover operator was introduced to generate child configurations from parent configurations. The size of square crossover region was quite important in generating optimal configurations. With a larger square operator the minimum energy randomly fluctuates, while with a smaller one, it converges quickly to the local minima, a premature convergence.
For numerical calculations, we have applied the genetic optimization algorithm to get the minimum energy charge configurations for rational values of / = p/q, where the integers q and p are relative primes. The results for the ground state configurations are presented for 2 < q < 16. 1.  in the presence of external magnetic fields. To understand the static and dynamical behavior of the vortex, it is essential to know the ground state configurations of the vortices. Therefore, there is a surge of interest in the static and dynamic phase transitions of the two-dimensional Coulomb gas model[2-3], which describes the motion of vortex.