A Novel Gaussian Process Surrogate Model with Expected Prediction Error for Optimization under Constraints

Hongri Cong, Bo Wang () and Zhe Wang
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Hongri Cong: School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK
Bo Wang: School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK
Zhe Wang: Covestro (Netherlands), 6167 RD Geleen, The Netherlands

Mathematics, 2024, vol. 12, issue 7, 1-21

Abstract: Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field.

Keywords: constrained optimization problems; Gaussian process regression; constrained expected improvement; constrained expected prediction error; Three-Bar Truss Design (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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