Towards global parameter estimation exploiting reduced data sets

Optimization methods & software, vol. 38, pp. 1129–1141

Abstract

We focus on deterministic global optimization (DGO) for nonconvex parameter estimation problems. Realistic and accurate solutions often require a fitting against very large measurement data sets, resulting in intractable size for DGO. Thus, we aim at accelerating the branch-and-bound algorithm by using reduced data sets for constructing valid bounds. We focus on fitting the equation of state for propane, which is of high interest for the chemical industry. The resulting estimation problem is a challenging nonconvex mixed-integer nonlinear optimization problem. We investigate the validity of using reduced data sets by comparing how the lower and upper bounds change when replacing the full data set with different reduced data sets. We account for regions with high and low quality fits by considering the results for the whole feasible region and 100 different subregions. Our results indicate that both regions containing solution candidates and regions containing only low quality fits can be identified based on reduced data sets. Moreover, we observe that the average CPU time per branch-and-bound iteration typically decreases if reduced data sets are used.

Authors 6

1. Susanne Saß Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University

   Affiliation as printed

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany

2. Angelos Tsoukalas

   Erasmus University Rotterdam

   Affiliation as printed

   Department of Technology and Operations Management, RSM Erasmus University Rotterdam, Rotterdam, Netherlands

3. Ian H. Bell

   National Institute of Standards and Technology

   Affiliation as printed

   Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO, USA

4. Dominik Bongartz

   KU Leuven

   Affiliation as printed

   Department of Chemical Engineering, KU Leuven, Leuven, Belgium

5. Jaromił Najman Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University

   Affiliation as printed

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany

6. Alexander Mitsos corresponding Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Institute of Energy and Climate Research: Energy Systems Engineering (IEK-10), Forschungszentrum Jülich GmbH, Jülich, Germany

   JARA-CSD, Aachen, Germany

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany