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Processes 2015, 3(3), 541-567; doi:10.3390/pr3030541

Multi-Period Dynamic Optimization for Large-Scale Differential-Algebraic Process Models under Uncertainty

Department of Chemical Engineering, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4L7, Canada
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Author to whom correspondence should be addressed.
Academic Editor: Carl D. Laird
Received: 29 May 2015 / Revised: 6 July 2015 / Accepted: 6 July 2015 / Published: 14 July 2015
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
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Abstract

A technique for optimizing large-scale differential-algebraic process models under uncertainty using a parallel embedded model approach is developed in this article. A combined multi-period multiple-shooting discretization scheme is proposed, which creates a significant number of independent numerical integration tasks for each shooting interval over all scenario/period realizations. Each independent integration task is able to be solved in parallel as part of the function evaluations within a gradient-based non-linear programming solver. The focus of this paper is on demonstrating potential computation performance improvement when the embedded differential-algebraic equation model solution of the multi-period discretization is implemented in parallel. We assess our parallel dynamic optimization approach on two case studies; the first is a benchmark literature problem, while the second is a large-scale air separation problem that considers a robust set-point transition under parametric uncertainty. Results indicate that focusing on the speed-up of the embedded model evaluation can significantly decrease the overall computation time; however, as the multi-period formulation grows with increased realizations, the computational burden quickly shifts to the internal computation performed within the non-linear programming algorithm. This highlights the need for further decomposition, structure exploitation and parallelization within the non-linear programming algorithm and is the subject for further investigation. View Full-Text
Keywords: multi-period dynamic optimization; differential-algebraic equations; applied non-linear programming; multiple-shooting; parallel computing multi-period dynamic optimization; differential-algebraic equations; applied non-linear programming; multiple-shooting; parallel computing
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Washington, I.D.; Swartz, C.L. Multi-Period Dynamic Optimization for Large-Scale Differential-Algebraic Process Models under Uncertainty. Processes 2015, 3, 541-567.

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