(340e) Parallel Computing Strategies for Large-Scale Dynamic Optimization Under Uncertainty

Dynamic optimization is important for solving many practical problems in process engineering such as model predictive control, moving horizon state estimation, optimal control, and parameter estimation. A particularly important application within this domain is the integration of design and control, which offers a systematic approach for inclusion of dynamic performance considerations in plant design calculations.  In order to construct a realistic design formulation, uncertainty must be taken into account.  One approach to incorporating uncertainty into such formulations is using a multiperiod (or multi-scenario) discretization of the infinite dimensional uncertainty space [1]. However, when applied to differential-algebriac equation (DAE) systems, such discretizations often yield large and potentially unwieldy systems of equations, which must be solved in an efficient manner to yield tractable solutions. Fortunately, the resulting uncertainty realizations at the DAE level are independent within the state space, which allows for the DAE solution to be implemented in a highly parallel manner. Our approach to solving this large multiperiod dynamic optimization formulation is to use a parallel multiple-shooting algorithm [2].  The algorithm decomposes the differential equations within the optimization formulation by partitioning both the number of periods (scenarios) and shooting intervals and off-loading each of these independent integration tasks to a parallel computing cluster, thus significantly speeding up each iteration of the nonlinear programming algorithm.

Our focus of this talk will be on describing strategies for efficiently decomposing and solving such large-scale multi-period DAE representations. More specifically, we will  hightlight the following aspects: (1) the multi-period dynamic optimization formulation and how uncertainty is introduced within the model; (2) a review of possible approaches for sampling the uncertainty space [3,4]; (3) our approach for decomposing and parallelizing embedded DAE model representations over each independent shooting interval and scenario realization; (4) an assessment of the potential computation improvements of the parallel algorithm for solving embedded DAEs utilizing an adaptive DAE solver with simultaneous forward sensitivity generation. Our implementation makes use of readily available (off-the-shelf) NLP and DAE solvers combined with the Matlab computing environment and associated parallel toolbox.

Case studies involving integrated design and control will be presented and numerical results investigated, which aim to demonstrate the potential computing speedup and efficiency of the parallelized multi-period algorithm with increasing processors and load. Additionally, avenues for future research will be identified and some prespective provided on the application of the proposed techniques to industrial large-scale DAE models.

Keywords: parallel computing, large-scale DAEs, multiperiod nonlinear optimization

[1] M.J. Mohideen, J.D. Perkins, and E.N. Pistikopoulos, Optimal design of dynamic systems under uncertainty, AIChE Journal 42, 8, pp. 2251-2272 (1996).

[2] D.B. Leineweber, A. Schafer, H.G. Bock and J.P. Schloder, An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 2: Software aspects and applications, Computers and Chemical Engineering 27, pp. 167-174 (2003).

[3] U. Diwekar, Introduction to Applied Optimization. Kluwer Academic Publishers, 2003.

[4] G. Paramasivan and A. Kienle, Decentralized control system design under uncertainty using mixed-integer optimization, Chem. Eng. Technol. 35, pp. 261-271 (2012).