The Comparison A-Optimal and I-Optimal Design in Non-Linear Models to Increase Purity Levels Silicon Dioxide

Muftih Alwi Aliu; Utami Dyah Syafitri; Anwar Fitrianto; Irzaman Irzaman

doi:10.37905/jjom.v6i2.26253

The Comparison A-Optimal and I-Optimal Design in Non-Linear Models to Increase Purity Levels Silicon Dioxide

Muftih Alwi Aliu, Utami Dyah Syafitri, Anwar Fitrianto, Irzaman Irzaman

Abstract

One of the obstacles that arise in optimal design is the non-linear model. The relationship between temperature factors and the temperature increase rates with the purity of silicon dioxide (SiO₂) forms a non-linear pattern. Determining the optimal design for a non-linear model is relatively more complex than a linear model because it requires additional information in its information matrix. Therefore, this issue necessitates further research on optimal design in non-linear models. This study uses the polynomial Taylor approach to approximate the non-linear equation through a linear equation using the appropriate optimal design methods, namely A-Optimal and I-Optimal criterion. The point search algorithm used was variable neighborhood search, this algorithm searches for design points by exploring several different neighborhood structures. These two methods were chosen to compare the characteristics and performance of the designs produced, aiming to obtain an optimal design to improve SiO₂ purity (non-linear case) using the same algorithm, VNS. The research results showed that the design pattern produced by the A-Optimal design formed three temperature groups, namely the minimum temperature of 800°C - 820°C, the middle temperature of 850°C, 860°C, and the maximum temperature of 900°C, with varying temperature increase rates in the design area. The design pattern produced by the I-Optimal design formed a full quadratic pattern, namely the minimum temperature of 800°C and the maximum temperature of 900°C, with varying temperature increase rates in the design area. The I-Optimal design demonstrated the best performance (most optimal) in the aspect of prediction variance compared to the A-Optimal design across all alternative points in this study to improve SiO₂ purity.

Keywords

Non-linear Model; Optimal Design; Silicon Dioxide; Variable Neighborhood Search

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DOI: https://doi.org/10.37905/jjom.v6i2.26253