Abstract:C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a
MAS
Modelling, Analysis and Simulation
Modelling, Analysis and SimulationA trust-region strategy for manifold mapping optimization P.W. Hemker, D. Echeverría A trust-region strategy for manifold mapping optimization ABSTRACT As a starting point we take the space-mapping iteration technique by Bandler et al. for the efficient solution of optimization problems. This technique achieves acceleration of accurate design processes with the help of simple… Show more
“…Moreover, combinations of input and output space mapping are also possible. In addition, recently [24] proposed a new variant called manifold mapping which can be seen as a generalization to output space mapping. Actually, the co-kriging surrogate model [25,26] is inherently a multifidelity surrogate model that essentially applies a correction to the output of the low-fidelity model.…”
The increasing use of expensive computer simulations in engineering places a serious computational burden on associated optimization problems. Surrogate-based optimization becomes standard practice in analyzing such expensive black-box problems. This article discusses several approaches that use surrogate models for optimization and highlights one sequential design approach in particular, namely, expected improvement. The expected improvement approach is demonstrated on two electromagnetic problems, namely, a microwave filter and a textile antenna.
“…Moreover, combinations of input and output space mapping are also possible. In addition, recently [24] proposed a new variant called manifold mapping which can be seen as a generalization to output space mapping. Actually, the co-kriging surrogate model [25,26] is inherently a multifidelity surrogate model that essentially applies a correction to the output of the low-fidelity model.…”
The increasing use of expensive computer simulations in engineering places a serious computational burden on associated optimization problems. Surrogate-based optimization becomes standard practice in analyzing such expensive black-box problems. This article discusses several approaches that use surrogate models for optimization and highlights one sequential design approach in particular, namely, expected improvement. The expected improvement approach is demonstrated on two electromagnetic problems, namely, a microwave filter and a textile antenna.
“…The performance of the different methods is discussed in Example 2. Other approaches, for example, trust‐region‐type schemes, have also been introduced within the space mapping framework, see 26.…”
Section: Optimization Proceduresmentioning
confidence: 99%
“…Bandler et al . 22, 24 proposed the use of Broyden's method to construct linear approximations for the space mapping and also trust‐region approaches have been introduced to globalize the minimization process 25–27. These and other approaches are reviewed in 28, 29.…”
The goal of this paper is to present an efficient approach for dynamic compressor optimization in gas networks based on a space mapping approach. For the fine space a non-linear isothermal gas flow model is employed, whereas for the coarse-space model an algebraic model is applied. To solve an optimization problem with the nonlinear model is expensive. Nevertheless we desire to bring as much nonlinear effects into the optimization process as possible. The mathematical formulation and algorithmic aspects of a space mapping technique are developed. A framework in which such can be achieved for compressible isothermal gas flow is presented. Computational results and comparison between different approaches are presented. The results demonstrate that such a multi-level approach provides more accurate results efficiently.We observe less iterates for the Broyden-like method compared with the steepest descent or the nonlinear CG method. The poor performance of the nonlinear CG method might be due to the fact
“…The incorporation of a LevenbergMarquardt strategy in manifold mapping [30,47] can be seen as a convergence safeguard analogous to trust-region methods [48]. Manifold mapping can also be extended to designs where the constraints are determined by time-consuming functions, and where these constraints can be dealt with in a multi-level approach [46].…”
“…In this paper, a manifold-mapping (MM) technique [29,30] is applied to simulation-driven design of microwave structures. Manifold mapping can be considered as a response correction method that utilizes available fine model data to align the coarse and fine model responses not only at the current design but also at a number of points previously considered in the optimization.…”
Abstract-A computationally efficient surrogate-based framework for reliable simulation-driven design optimization of microwave structures is described. The key component of our algorithm is manifold mapping, a response correction technique that aligns the coarse model (computationally cheap representation of the structure under consideration) with the accurate but CPU-intensive (fine) model of the optimized device. The parameters of the manifold mapping surrogate are explicitly calculated based on the fine model data accumulated during the optimization process. Also, manifold mapping does not use any extractable parameters, which makes it easy to implement. Robustness and excellent convergence properties of the proposed algorithm are demonstrated through the design of several microwave devices including microstrip filters and a planar antenna.
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