A Global Optimization Algorithm Based on $C^{1}$ Piecewise Response Surface Patches

A new surrogate objective function is suggested for the global optimization of electromagnetic devices. The surrogate objective function is constructed using a C¹ piecewise response surface incorporated with the design sensitivities computed by using the finite-element method. The sampling data points used for constructing the response surface are adaptively inserted during the optimization process. After the surrogate objective function is constructed, the global optimum point is obtained by using a genetic algorithm. Applications to benchmark problems and the optimum design of a permanent magnet system show the effectiveness of the proposed algorithm