A branch-and-bound algorithm with growing datasets for large-scale parameter estimation

European Journal of Operational Research, vol. 316, pp. 36–45

Abstract

The solution of nonconvex parameter estimation problems with deterministic global optimization methods is desirable but challenging, especially if large measurement datasets are considered. We propose to exploit the structure of this class of optimization problems to enable their solution with the spatial branch-and-bound algorithm. In detail, we start with a reduced dataset in the root node and progressively augment it, converging to the full dataset. We show for nonlinear programs (NLPs) that our algorithm converges to the global solution of the original problem considering the full dataset. The implementation of the algorithm extends our open-source solver MAiNGO. A numerical case study with a mixed-integer nonlinear program (MINLP) from chemical engineering and a dynamic optimization problem from biochemistry both using noise-free measurement data emphasizes the potential for savings of computational effort with our proposed approach.

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, 52074, Germany

2. Alexander Mitsos Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   Institute of Energy and Climate Research: Energy Systems Engineering (IEK-10), Forschungszentrum Jülich GmbH, Jülich, 52425, Germany

   JARA-CSD, Aachen, 52056, Germany

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, 52074, Germany

3. Dominik Bongartz

   KU Leuven

   Affiliation as printed

   Department of Chemical Engineering, KU Leuven, Leuven, 3001, Belgium

4. Ian H. Bell

   National Institute of Standards and Technology

   Affiliation as printed

   Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, 80305, CO, United States

5. Nikolay Ivanov Nikolov Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Aachen, 52056, Germany

6. Angelos Tsoukalas corresponding

   Erasmus University Rotterdam

   Affiliation as printed

   Department of Technology and Operations Management, Rotterdam School of Management (RSM), Erasmus University Rotterdam, Rotterdam, 3062 PA, Netherlands