Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

Wanyonyi, Samson W.; Okango, Ayubu Anapapa; Koech, Julius

doi:10.9734/ajpas/2021/v12i430292

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…D-optimality is a criterion for optimal experimental design that aims to minimize the determinant of the variance-covariance matrix of the estimated parameters. It focuses on good model parameter estimation [12] and furthermore makes both the variance and the covariance among the model parameter estimates very small. This criterion ensures that the estimated parameters are as precise as possible and that the design provides the most information about the parameters by minimizing the determinant of the |X T • X| −1 (D from determinant).…”

Section: D-optimalitymentioning

confidence: 99%

A Genetic Algorithm-Enhanced Sensor Marks Selection Algorithm for Wavefront Aberration Modeling in Extreme-UV (EUV) Photolithography

Magklaras,

Alefragis,

Gogos

et al. 2023

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In photolithographic processes, nanometer-level-precision wavefront-aberration models enable the machine to be able to meet the overlay (OVL) drift and critical dimension (CD) specifications. Software control algorithms take as input these models and correct any expected wavefront imperfections before reaching the wafer. In such way, a near-optimal image is exposed on the wafer surface. Optimizing the parameters of these models, however, involves several time costly sensor measurements which reduce the throughput performance of the machine in terms of exposed wafers per hour. In that case, photolithography machines come across the trade-off between throughput and quality. Therefore, one of the most common optimal experimental design (OED) problems in photolithography machines (and not only) is how to choose the minimum amount of sensor measurements that will provide the maximum amount of information. Additionally, each sensor measurement corresponds to a point on the wafer surface and therefore we must measure uniformly around the wafer surface as well. In order to solve this problem, we propose a sensor mark selection algorithm which exploits genetic algorithms. The proposed solution first selects a pool of points that qualify as candidates to be selected in order to meet the uniformity constraint. Then, the point that provides the maximum amount of information, quantified by the Fisher-based criteria of G-, D-, and A-optimality, is selected and added to the measurement scheme. This process, however, is considered “greedy”, and for this reason, genetic algorithms (GA) are exploited to further improve the solution. By repeating in parallel the “greedy” part several times, we obtain an initial population that will be the input to our GA. This meta-heuristic approach outperforms the “greedy” approach significantly. The proposed solution is applied in a real life semiconductors industry use case and achieves interesting industry as well as academical results.

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Section: D-optimalitymentioning

confidence: 99%

A Genetic Algorithm-Enhanced Sensor Marks Selection Algorithm for Wavefront Aberration Modeling in Extreme-UV (EUV) Photolithography

Magklaras,

Alefragis,

Gogos

et al. 2023

Information

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“…Calculate and determine the estimated variance of the predicted value (SPV(x)). SPV can be calculated by [14]:…”

Section: Steps Of the Variable Neighborhood Search (Vns) Algorithmmentioning

confidence: 99%

G-Optimal Design of Non-Linear Model to Increase Purity Levels of Silicon Dioxide

Wulandari

Erfiani

Irzaman

et al. 2023

BAREKENG: J. Math. & App.

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Silicon Dioxide (SiO2) is one of the most abundant minerals found on earth. SiO2 is widely used in various fields, so its availability as a finite natural resource diminishes. A purity procedure can raise the purity of low-quality silica by altering the temperature and rate of temperature rise. This study aims to obtain the best design for increasing SiO2 levels—the G-optimal design on a non-linear model using the Variable Neighborhood Search (VNS) algorithm. The VNS algorithm employs two types of neighborhoods, one acquired by replacing one design point with a candidate set and the other by replacing two design points with two points in the candidate set. The model used to increase silicon dioxide's purity is a non-linear model that follows the exponential decay distribution. The best design points obtained from the G-optimal design on the relationship between temperature (oC) and the rate of temperature increase (oC/min) 800 oC to 900 oC is a pair of points 800 oC and 1,67 oC /min, 800 oC and 2,17 oC/min, 815 oC and 2,50 oC/min, 825 oC and 2,00 oC/min, 845 oC and 2,34 oC/min, 895 oC and 3,34 oC/min 900 oC and 3,50 oC/min with a G-efficiency of 96,41%.

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Compositional Optimization for Miticidal Activity, Ecotoxicity, and Phytotoxicity of Rosmarinus officinalis Essential Oils as Biorational Pesticides

Yoon,

Tak

2024

J. Agric. Food Chem.

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Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

Cited by 4 publications

References 25 publications

A Genetic Algorithm-Enhanced Sensor Marks Selection Algorithm for Wavefront Aberration Modeling in Extreme-UV (EUV) Photolithography

A Genetic Algorithm-Enhanced Sensor Marks Selection Algorithm for Wavefront Aberration Modeling in Extreme-UV (EUV) Photolithography

G-Optimal Design of Non-Linear Model to Increase Purity Levels of Silicon Dioxide

Compositional Optimization for Miticidal Activity, Ecotoxicity, and Phytotoxicity of Rosmarinus officinalis Essential Oils as Biorational Pesticides

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