Manifold mapping optimization with of without true gradients

This paper deals with the Space Mapping optimization algorithms in general and with the Manifold Mapping technique in particular. The idea of such algorithms is to optimize a model with a minimum number of each objective function evaluations using a less accurate but faster model. In this optimization procedure, fine and coarse models interact at each iteration in order to adjust themselves in order to converge to the real optimum. The Manifold Mapping technique guarantees mathematically this convergence but requires gradients of both fine and coarse model. Approximated gradients can be used for some cases but are subject to divergence. True gradients can be obtained for many numerical model using adjoint techniques, symbolic or automatic differentiation. In this context, we have tested several Manifold Mapping variants and compared their convergence in the case of real magnetic device optimization.Electrical Engineering, Mathematics and Computer Scienc