The Statistical Filter Approach to Constrained Optimization

• Published in: Technometrics Vol. 62; no. 3; pp. 303 - 312
• Main Authors: Pourmohamad, Tony, Lee, Herbert K. H.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02.07.2020; American Society for Quality
• Subjects: Algorithms; Black box function; Computer experiment; Computer simulator; Constraints; Design optimization; Hybridization; Multivariate Gaussian process; Nonlinear programming; Numerical methods; Optimization; Optimization algorithms; Response surface methodology; Statistical analysis; Statistical models
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1080/00401706.2019.1638304

Expensive black box systems arise in many engineering applications but can be difficult to optimize because their output functions may be complex, multi-modal, and difficult to understand. The task becomes even more challenging when the optimization is subject to multiple constraints and no derivative information is available. In this article, we combine response surface modeling and filter methods in order to solve problems of this nature. In employing a filter algorithm for solving constrained optimization problems, we establish a novel probabilistic metric for guiding the filter. Overall, this hybridization of statistical modeling and nonlinear programming efficiently utilizes both global and local search in order to quickly converge to a global solution to the constrained optimization problem. To demonstrate the effectiveness of the proposed methods, we perform numerical tests on a synthetic test problem, a problem from the literature, and a real-world hydrology computer experiment optimization problem.