Optimization by Zooms Without and with Second-Order Polynomial Models Applied to a 2-D Simulation

In this paper, the optimization method by zooms based on the design of experiments concept is presented, in two variants. The first variant only requires access to the values of the objective function at different points in the feasible domain, grouped in designs of successive experiments, oriented towards the most convenient values. The second variant additionally calculates second-order polynomial models that approximate the objective function on each design, facilitating the increase of the convergence speed of the algorithm. The two variants fit very well with the numerical simulations by the finite element method. Therefore a comparative study of their application on a bi-dimensional numerical model of an electromagnetic device is presented. The results highlight the simplicity of the first variant but also the high convergence speed of the second one.