Manifold mapping: a two-level optimization technique

Echeverria, David; Hemker, Piet

doi:10.1007/s00791-008-0096-y

Cited by 62 publications

(30 citation statements)

References 34 publications

(46 reference statements)

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“…For least-squares optimization problems, manifold mapping is supported by mathematically sound convergence theory [46]. We can identify four factors relevant for the convergence of the scheme above to the fine model optimizer x * f : 1) the model responses being smooth; 2) the coarse model optimization in (2) being well-posed; 3) the discrepancy of the optimal model response R f (x * f ) with respect to the design specification being small enough; 4) and the coarse model response being a sufficiently good approximation of the fine model response.…”

Section: Manifold-mapping Optimization Algorithmmentioning

confidence: 99%

“…The results in [46] rely mainly on the smoothness of the model responses involved. Therefore, we can expect convergence of the manifold-mapping algorithm for a cost function U smooth enough.…”

Section: Manifold-mapping Optimization Algorithmmentioning

confidence: 99%

“…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].…”

Section: Manifold-mapping Optimization Algorithmmentioning

confidence: 99%

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Reliable Simulation-Driven Design Optimization of Microwave Structures Using Manifold Mapping

Koziel¹,

Ciaurri²

2010

PIER B

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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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Section: Manifold-mapping Optimization Algorithmmentioning

confidence: 99%

Section: Manifold-mapping Optimization Algorithmmentioning

confidence: 99%

Section: Manifold-mapping Optimization Algorithmmentioning

confidence: 99%

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Reliable Simulation-Driven Design Optimization of Microwave Structures Using Manifold Mapping

Koziel¹,

Ciaurri²

2010

PIER B

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“…Linear convergence of the MM-algorithm is proved in [6] under the conditions that: (i) c(p(X)) and f (X) are C 2 -manifolds, (ii) the models c(p(x)) and f (x) show a sufficiently similar behaviour in the neighbourhood of the solution, and (iii) the matrices ∆C and ∆F are sufficiently well-conditioned. A precise formulation of these conditions is found in [6].…”

Section: A Trust-region Strategymentioning

confidence: 99%

“…This and the fact that S k (c(p(x k ))) = f (x k ), makes that, under convergence to x, the fixed point is a (local) optimum of the fine model minimization and as a consequence S = S [6]. The improved space-mapping scheme…”

mentioning

confidence: 99%

A trust-region strategy for manifold-mapping optimization

Hemker

Echeverria

2007

Journal of Computational Physics

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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 simpler, easier to optimize models. We observe the difference between the solution of the optimization problem and the computed space-mapping solutions. We repair this discrepancy by exploiting the correspondence with defect-correction iteration and we construct the manifold-mapping algorithm, which is as efficient as the space-mapping algorithm but converges to the exact solution. To increase the robustness of the algorithm we also introduce a trust-region strategy that is based on the generalized singular value decomposition of the linearized fine and coarse manifold representations. The effect of the strategy is shown by the solution of a variety of small non-linear least squares problems. simpler, easier to optimize models. We observe the difference between the solution of the optimization problem and the computed space-mapping solutions. We repair this discrepancy by exploiting the correspondence with defect-correction iteration and we construct the manifold-mapping algorithm, which is as efficient as the space-mapping algorithm but converges to the exact solution. REPORT MAS-E0618 AUGUST 2006To increase the robustness of the algorithm we also introduce a trust-region strategy that is based on the generalized singular value decomposition of the linearized fine and coarse manifold representations. The effect of the strategy is shown by the solution of a variety of small non-linear least squares problems.2000 Mathematics Subject Classification: 90C30, 65K05, 49M99, 49Q99

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Rapid redesign of multiband antennas with respect to operating conditions and material parameters of substrate

Koziel

Bekasiewicz

2020

Int J Numerical Modelling

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This work addresses geometry parameter scaling of multiband antennas for Internet of Things applications. The presented approach is comprehensive and permits redesign of the structure with respect to both the operating frequencies and material parameters of the dielectric substrate. A two-step procedure is developed with the initial design obtained from an inverse surrogate model constructed using a set of appropriately prepared reference points and the final design identified through an iterative correction procedure. The latter is necessary in order to account for limited accuracy of the surrogate. The proposed approach is validated using a dual-band microstrip patch antenna scaled over wide ranges of operating frequencies (1.5-2.5 GHz for the lower band and 5.0-6.0 GHz for the upper band), substrate thickness (0.7-1.5 mm), and substrate permittivity (2.5-3.5). The redesign cost corresponds to only up to three electromagnetic simulations of the antenna at hand. Reliability of the process is confirmed through experimental validation of the fabricated antenna prototypes.

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Manifold mapping: a two-level optimization technique

Cited by 62 publications

References 34 publications

Reliable Simulation-Driven Design Optimization of Microwave Structures Using Manifold Mapping

Reliable Simulation-Driven Design Optimization of Microwave Structures Using Manifold Mapping

A trust-region strategy for manifold-mapping optimization

Rapid redesign of multiband antennas with respect to operating conditions and material parameters of substrate

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