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Efficient parallel solution of large-scale nonlinear dynamic optimization problems

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Abstract

This paper presents a decomposition strategy applicable to DAE constrained optimization problems. A common solution method for such problems is to apply a direct transcription method and solve the resulting nonlinear program using an interior-point algorithm. For this approach, the time to solve the linearized KKT system at each iteration typically dominates the total solution time. In our proposed method, we exploit the structure of the KKT system resulting from a direct collocation scheme for approximating the DAE constraints in order to compute the necessary linear algebra operations on multiple processors. This approach is applied to find the optimal control profile of a combined cycle power plant with promising results on both distributed memory and shared memory computing architectures with speedups of over 50 times possible.

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Acknowledgments

The authors thank Francesco Casella for providing the combined cycle power plant model used in this work and Joel Andersson for his assistance with interfacing our software with CasADi. The authors gratefully acknowledge partial financial support for Daniel Word provided by Sandia National Laboratories and the Office of Advanced Scientific Computing Research within the DOE Office of Science as part of the Applied Mathematics program. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U. S. Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000. Thanks is also extended for financial support for Jia Kang provided by the National Science Foundation Cyber-Enabled Discovery and Innovation (CDI)-Type II. The authors gratefully acknowledge partial financial support for Carl Laird and Daniel Word from the National Science Foundation (CAREER Grant CBET# 0955205). The authors gratefully acknowledges financial support for Johan Akesson from the Swedish Science Foundation through the grant Lund Center for Control of Complex Engineering Systems (LCCC).

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Authors and Affiliations

  1. Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX, USA

    Daniel P. Word & Jia Kang

  2. School of Chemical Engineering, Purdue University West Lafayette, IN, USA

    Carl D. Laird

  3. Department of Automatic Control, Lund University, Lund, Sweden

    Johan Akesson

  4. Modelon AB, Lund, Sweden

    Johan Akesson

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  1. Daniel P. Word
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Correspondence to Carl D. Laird.

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Word, D.P., Kang, J., Akesson, J. et al. Efficient parallel solution of large-scale nonlinear dynamic optimization problems. Comput Optim Appl 59, 667–688 (2014). https://doi.org/10.1007/s10589-014-9651-2

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