Constraint reformulations for set point optimization problems using fuzzy cognitive map models

Garzón Casado, Alvaro; Cano Marchal, Pablo; Wagner, Christian; Gómez Ortega, Juan; Gámez García, Javier

Abstract

The selection of optimal set points is an important problem in modern process control. Fuzzy cognitive maps (FCMs) allow to construct models of complex processes using expert knowledge, which is particularly useful in situations where measuring the variables of interest online is problematic. These models can be used as constraints in optimization problems with the objective of determining optimal set points for those processes. This article presents a reformulation of the constraints imposed by the FCM models that reduces the complexity of the resulting optimization problem and enables the application of heuristic methods for its solution. Computational results show that the use of separable programming on the reformulated problem constitutes a very good alternative, both in terms of solution time and reliability in finding the optimum, enabling the application of FCM modeling to larger systems and easing the practical implementation of the approach.

Citation

Garzón Casado, A., Cano Marchal, P., Wagner, C., Gómez Ortega, J., & Gámez García, J. (2022). Constraint reformulations for set point optimization problems using fuzzy cognitive map models. Optimal Control Applications and Methods, 43(3), 711-721. https://doi.org/10.1002/oca.2846

• Journal Article Type: Article
• Acceptance Date: Dec 11, 2021
• Online Publication Date: Dec 23, 2021
• Publication Date: May 1, 2022
• Deposit Date: Dec 14, 2021
• Publicly Available Date: Dec 24, 2022
• Journal: Optimal Control Applications and Methods
• Print ISSN: 0143-2087
• Electronic ISSN: 1099-1514
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 43
• Issue: 3
• Pages: 711-721
• DOI: https://doi.org/10.1002/oca.2846
• Keywords: Fuzzy Cognitive Maps; Decision Support Systems; Optimization; Hierarchical Control 5
• Public URL: https://nottingham-repository.worktribe.com/output/7016947
• Publisher URL: https://onlinelibrary.wiley.com/doi/full/10.1002/oca.2846
• Additional Information: This is the peer reviewed version of the following article: Garzón Casado, A, Cano Marchal, P, Wagner, C, Gómez Ortega, J, Gámez García, J. Constraint reformulations for set point optimization problems using fuzzy cognitive map models. Optim Control Appl Meth. 2021; 1- 11, which has been published in final form at https://doi.org/10.1002/oca.2846. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.