Performance Analysis of a Differential Evolution Algorithm in Modeling Parameter Extraction of Optical Material

Saber, Md. Ghulam; Ahmed, Ashik; Sagor, Rakibul Hasan

doi:10.1007/s12633-016-9422-z

Cited by 6 publications

(7 citation statements)

References 37 publications

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“…Particle-swarm optimization has been employed for optimizing diffraction grating filters, photonic-crystal waveguides, or the duality symmetry of core–shell particles . Differential evolution strategies have been investigated in the context of light focusing photonic crystals and for parameter extraction of optical materials Model-based optimization methods construct a model of the objective function in order to find promising sampling parameters.…”

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confidence: 99%

“…31 Differential evolution strategies have been investigated in the context of light focusing photonic crystals 32 and for parameter extraction of optical materials. 33 • Model-based optimization methods construct a model of the objective function in order to find promising sampling parameters. One important representative is Bayesian optimization, which constructs a statistical model of the objective function.…”

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confidence: 99%

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Benchmarking Five Global Optimization Approaches for Nano-optical Shape Optimization and Parameter Reconstruction

Schneider¹,

Santiago²,

Soltwisch

et al. 2019

ACS Photonics

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Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays nano-fabrication technologies for which a rational design is no longer feasible. Also, numerical resources are available to enable the computational photonic material design and to identify structures that meet predefined optical properties for specific applications. However, the optimization objective function is in general non-convex and its computation remains resource demanding such that the right choice for the optimization method is crucial to obtain excellent results. Here, we benchmark five global optimization methods for three typical nano-optical optimization problems: downhill simplex optimization, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, particle swarm optimization, differential evolution, and Bayesian optimization. In the shown examples from the field of shape optimization and parameter reconstruction, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods. AbstractThis document provides supporting information to "Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction" regarding the implementation and numerical setting of the optimization methods as well as a visualization of the different optimization strategies.

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confidence: 99%

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confidence: 99%

Benchmarking Five Global Optimization Approaches for Nano-optical Shape Optimization and Parameter Reconstruction

Schneider¹,

Santiago²,

Soltwisch

et al. 2019

ACS Photonics

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“…Developed by Storn and Price (1997), DE has shown good performance and quality compared with other EAs in parameter adjustment problems involving real-type variables analogous to the system considered in this work (Trejo-Zúñiga et al, 2013;Peng et al, 2009;Chong et al, 2012). In recent years, DE has been widely used to deal with a wide range of reference tests and real-world application problems (Cai et al, 2008;Neri and Tirronen, 2010;Das and Suganthan, 2011;Rocca et al, 2011;Liu and Qiao, 2015;Saber et al, 2017). Yet, it was observed that the performance of the DE search process needed to be improved due to the increasing complexity of modern optimization problems (Fan and Zhang, 2016).…”

Section: Introductionmentioning

confidence: 91%

Fitting procedure based on Differential Evolution to evaluate impedance parameters of metal–coating systems

González

Greiner

Mena

et al. 2019

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Purpose Impedance data obtained by electrochemical impedance spectroscopy (EIS) are fitted to a relevant electrical equivalent circuit to evaluate parameters directly related to the resistance and the durability of metal–coating systems. The purpose of this study is to present a novel and more efficient computational strategy for the modelling of EIS measurements using the Differential Evolution paradigm. Design/methodology/approach An alternative method to non-linear regression algorithms for the analysis of measured data in terms of equivalent circuit parameters is provided by evolutionary algorithms, particularly the Differential Evolution (DE) algorithms (standard DE and a representative of the self-adaptive DE paradigm were used). Findings The results obtained with DE algorithms were compared with those yielding from commercial fitting software, achieving a more accurate solution, and a better parameter identification, in all the cases treated. Further, an enhanced fitting power for the modelling of metal–coating systems was obtained. Originality/value The great potential of the developed tool has been demonstrated in the analysis of the evolution of EIS spectra due to progressive degradation of metal–coating systems. Open codes of the different differential algorithms used are included, and also, examples tackled in the document are open. It allows the complete use, or improvement, of the developed tool by researchers.

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“…Minimizing Equation (1) can be done, e.g., using local methods such as the Gauß-Newton scheme or the Levenberg-Marquardt algorithm [17], or using global heuristic methods, for example particle swarm optimization [21,22] or differential evolution [23,24], or by maximizing the appropriate likelihood function using Markov chain Monte Carlo (MCMC) sampling methods [25].…”

Section: Established Approaches For Parameter Reconstructionmentioning

confidence: 99%

Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction

Plock,

Andrle,

Burger

et al. 2022

Preprint

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Parameter reconstructions are indispensable in metrology. Here, on wants to explain K experimental measurements by fitting to them a parameterized model of the measurement process. The model parameters are regularly determined by least-square methods, i.e., by minimizing the sum of the squared residuals between the K model predictions and the K experimental observations, χ 2 . The model functions often involve computationally demanding numerical simulations. Bayesian optimization methods are specifically suited for minimizing expensive model functions. However, in contrast to least-square methods such as the Levenberg-Marquardt algorithm, they only take the value of χ 2 into account, and neglect the K individual model outputs. We introduce a Bayesian targetvector optimization scheme that considers all K contributions of the model function and that is specifically suited for parameter reconstruction problems which are often based on hundreds of observations. Its performance is compared to established methods for an optical metrology reconstruction problem and two synthetic least-squares problems. The proposed method outperforms established optimization methods. It also enables to determine accurate uncertainty estimates with very few observations of the actual model function by using Markov chain Monte Carlo sampling on a trained surrogate model.

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Performance Analysis of a Differential Evolution Algorithm in Modeling Parameter Extraction of Optical Material

Cited by 6 publications

References 37 publications

Benchmarking Five Global Optimization Approaches for Nano-optical Shape Optimization and Parameter Reconstruction

Benchmarking Five Global Optimization Approaches for Nano-optical Shape Optimization and Parameter Reconstruction

Fitting procedure based on Differential Evolution to evaluate impedance parameters of metal–coating systems

Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction

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