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Towards Global Parameter Estimation Exploiting Reduced Data Sets

Published

Author(s)

Susanne Sass, Angelos Tsoukalas, Ian Bell, Dominik Bongartz, Jaromil Najman, Alexander Mitsos

Abstract

We focus on deterministic global optimization (DGO) methods for solving nonconvex parameter estimation problems. In estimation problems, realistic and accurate solutions require a fitting against huge measurement data sets often. However, many of the resulting large scale models are intractable for current DGO solvers. Thus, we aim at accelerating a DGO methods, more precisely, the branch-and-bound algorithm, by using reduced data sets for constructing valid bounds for the full large-scale model. To that end, we compare how the lower and upper bounds change when replacing the full data set with different reduced data sets. We consider both the results for the whole feasible region and 100 smaller subregions which can be interpreted as different nodes of a possible branch-and-bound tree. In this preliminary study, we focus on fitting the equation of state for propane. On the one hand, this model is of high interest for chemical industries and engineering. On the other hand, the resulting estimation problem is a sophisticated nonconvex mixed-integer nonlinear optimization problem. Our results indicate that both regions containing solution candidates and regions containing only low-quality fits can be identified based on reduced data sets. Based on this particular case study, we can not derive a general conjecture concerning the actual time gain, while still the majority of the reduced data sets results in faster convergence.
Citation
Optimization Methods and Software

Keywords

global optimization, branch and bound

Citation

Sass, S. , Tsoukalas, A. , Bell, I. , Bongartz, D. , Najman, J. and Mitsos, A. (2023), Towards Global Parameter Estimation Exploiting Reduced Data Sets, Optimization Methods and Software, [online], https://doi.org/10.1080/10556788.2023.2205645, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=933653 (Accessed April 18, 2024)
Created April 5, 2023, Updated May 9, 2023