Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming

Vassilis M. Charitopoulos; Lazaros G. Papageorgiou; Vivek Dua

doi:10.1016/J.ENG.2017.02.008

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Engineering ›› 2017, Vol. 3 ›› Issue (2) : 202-213. DOI: 10.1016/J.ENG.2017.02.008

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Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming

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Abstract

In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters.

Keywords

Parametric programming / Uncertainty / Process synthesis / Mixed-integer nonlinear programming / Symbolic manipulation

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Vassilis M. Charitopoulos, Lazaros G. Papageorgiou, Vivek Dua. Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming. Engineering, 2017, 3(2): 202‒213 https://doi.org/10.1016/J.ENG.2017.02.008

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Acknowledgements

The authors gratefully acknowledge financial support from EPSRC grants (EP/M027856/1, EP/M028240/1).

Compliance with ethics guidelines

Vassilis M. Charitopoulos, Lazaros G. Papageorgiou, and Vivek Dua declare that they have no conflict of interest or financial conflicts to disclose.

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2017 2017 THE AUTHORS. Published by Elsevier LTD on behalf of the Chinese Academy of Engineering and Higher Education Press Limited Company. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).