(696e) Integrated Scheduling and Dynamic Optimization of Complex Batch Processes Using a Generalized Benders Decomposition Approach

To improve the performance of the entire process, the scheduling problem and the dynamic optimization problem should be solved in an integrated way such that the recipe data can be optimized in terms of the economic criteria [1-6]. However, solving the integrated problem is much more challenging than solving the subproblems sequentially. The complexity of the integrated problem arises from the coupling of binary variables in the scheduling problem with differential equations characterizing the dynamic models. The integration results in a complicated mixed-integer dynamic optimization (MIDO) [7, 8].

Though there are previous studies on integrated problems of a batch process with general network structures [9, 10], they did not provide an effective method to solve the integrated problem. A consequence is that the returned solution could be only suboptimal after a reasonable amount of time. These studies solved complicated MIDO problems using the simultaneous method which reformulated an MIDO problem into an MINLP problem by discretizing the differential equations [11]. Then a general-purpose MINLP solver was invoked to solve the reformulated MINLP problems. However, the MINLPs were large-scale and challenging to solve. Except for very simple examples, the simultaneous method encountered difficulties in solving the MINLP problems to optimality within limited computational resources [9, 10]. After a long computational time, the optimality gap could be still unsatisfactorily large.

To reduce the computational complexity, we develop a tailored and efficient decomposition method based on the framework of generalized Benders decomposition (GBD) by exploiting the special structure of the integrated problem. The decomposed master problem is a scheduling problem with variable processing times and processing costs, as well as the Benders cuts. The primal problem comprises a set of separable dynamic optimization problems for the processing units. By collaboratively optimizing the process scheduling and the process dynamics, the proposed method substantially improve the overall economic performance of the batch production compared with the conventional sequential method which solves the scheduling problem and the dynamic optimization problems separately.

The decomposition method enables us to solve a complex integrated problem to optimality within a short computational time while the direct solution methods fail. Three case studies with different complexities demonstrate advantages of the proposed method. In the simple case, the proposed method returns the same optimal solution as the simultaneous method. The computational time of the proposed method is, however, reduced by two orders of magnitude. In the two complex cases, the proposed method still finds the optimal solution while the simultaneous method only finds an suboptimal one within 24 or 50 hours.

References

[1]        I. Grossmann, "Enterprise-wide optimization: A new frontier in process systems engineering," AIChE Journal, vol. 51, pp. 1846-1857, Jul 2005.

[2]        J. M. Wassick, A. Agarwal, N. Akiya, J. Ferrio, S. Bury, and F. You, "Addressing the operational challenges in the development, manufacture, and supply of advanced materials and performance products," Computers & Chemical Engineering, vol. 47, pp. 157-169, 2012.

[3]        Y. Chu and F. You, "Integration of scheduling and control with online closed-loop implementation: Fast computational strategy and large-scale global optimization algorithm," Computers & Chemical Engineering, vol. 47, pp. 248-268, Dec 20 2012.

[4]        Y. Chu and F. You, "Integration of cyclic scheduling and dynamic optimization using generalized Benders decomposition methods coupled with global mixed-integer fractional programming approaches," Computers & Chemical Engineering,  Submitted, 2013.

[5]        Y. Chu and F. You, "Integrated scheduling and dynamic optimization of sequential batch processes with online implementation," AIChE Journal,  Accepted, DOI: 10.1002/aic.14022, 2013.

[6]        Y. Chu and F. You, "Integrated scheduling and dynamic optimization of complex batch processes with general network structure using a generalized Benders decomposition," Industrial & Engineering Chemistry Research, Submitted, 2013.

[7]        V. Bansal, V. Sakizlis, R. Ross, J. D. Perkins, and E. N. Pistikopoulos, "New algorithms for mixed-integer dynamic optimization," Computers & Chemical Engineering, vol. 27, pp. 647-668, May 15 2003.

[8]        P. I. Barton, R. J. Allgor, W. F. Feehery, and S. Galan, "Dynamic optimization in a discontinuous world," Industrial & Engineering Chemistry Research, vol. 37, pp. 966-981, Mar 1998.

[9]        B. V. Mishra, E. Mayer, J. Raisch, and A. Kienle, "Short-term scheduling of batch processes. A comparative study of different approaches," Industrial & Engineering Chemistry Research, vol. 44, pp. 4022-4034, May 2005.

[10]      Y. S. Nie, L. T. Biegler, and J. M. Wassick, "Integrated scheduling and dynamic optimization of batch processes using state equipment networks," AIChE Journal, vol. 58, pp. 3416-3432, Nov 2012.

[11]      J. E. Cuthrell and L. T. Biegler, "On the optimization of differential-algebraic process systems," AIChE Journal, vol. 33, pp. 1257-1270, Aug 1987.