MANIFOLD MAPPING OPTIMIZATION WITH OR WITHOUT TRUE GRADIENTS

Benoît Delinchant (1) , D. Lahaye (2) , Frédéric Wurtz (1) , Jean-Louis Coulomb (1)

1 G2ELab - Laboratoire de Génie Electrique de Grenoble
2 Numerical Analysis Unit Delft University of Technology

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 calls 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.

Mots clés: Space Mapping; Manifold Mapping; Optimization; Surrogate model; Gradients; Symbolic derivation; Automatic differentiation

Domaines: Energie électrique

Benoît Delinchant, D. Lahaye, Frédéric Wurtz, Jean-Louis Coulomb. MANIFOLD MAPPING OPTIMIZATION WITH OR WITHOUT TRUE GRADIENTS. Electrimacs 2011, Jun 2011, Cergy-Pontoise, France. ⟨hal-00600301⟩