A shortened time horizon approach for optimization with differential-algebraic constraints
Citation: Proceedings of the 16th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 25, pages 211–215 (2021)
Abstract. In this work a new numerical optimization scheme based on shortened time horizon approach was designed. The shortened time horizon strategy has never been presented or tested numerically. The new methodology was applied for single objective optimization task subject to a system of nonlinear differential-algebraic (DAEs) constraints. The new solution procedure is based on two main parts: i) designing of an alternative differential-algebraic constraints, ii) parametrization of a new constraints system by the multiple shooting approach and further simulation of the alternative system independently on small subintervals. The presented algorithm was used to solve optimization task of fed-batch reactor operation.
- J.T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, SIAM, Philadelphia, 2010, https://doi.org/10.1137/1.9780898718577.
- B. Beykal, M. Onel, O. Onel, E.N. Pistikopoulos, A data-driven optimization algorithm for differential algebraic equations with numerical infeasibilities, AIChE Journal, vol. 66, 2020, article no. e16657, https://doi.org/10.1002/aic.16657.
- B. Burnak, E.N. Pistikopoulos, Integrated process design, scheduling, and model predictive control of batch processes with closed-loop implementation, AIChE Journal, vol. 66, 2020, article no. e16981, https://doi.org/10.1002/aic.16981.
- A. Caspari, L. Lüken, P. Schäfer, Y. Vaupel, A. Mhamdi, L.T. Biegler, A. Mitsos, Dynamic optimization with complementarity constraints: Smoothing for direct shooting, Computers and Chemical Engineering, vol. 139, 2020, article no. 106891, https://doi.org/10.1016/j.compchemeng.2020.106891.
- P. Dra̧g, A Direct Optimization Algorithm for Problems with Differential-Algebraic Constraints: Application to Heat and Mass Transfer, Applied Sciences, vol. 10, 2020, art. no. 9027, pp. 1-19, https://doi.org/10.3390/app10249027.
- P. Dra̧g, K. Styczeń, The new approach for dynamic optimization with variability constraints. In: S. Fidanova (ed.), Recent advances in computational optimization : results of the Workshop on Computational Optimization WCO 2017. Cham, Springer, 2019. pp. 35-46, https://doi.org/10.1007/978-3-319-99648-6 3.
- M.T. Kelley, R. Baldick, M. Baldea, A direct transcription-based multiple shooting formulation for dynamic optimization, Computers and Chemical Engineering, vol. 140, 2020, art. no. 106846, https://doi.org/10.1016/j.compchemeng.2020.106846.
- R. Luus, O. Rosen, Application of dynamic programming to final state constrained optimal control problems, Industrial & Engineering Chemistry Research, vol. 30, 1991, pp. 1525-1530.
- D. Pandelidis, M. Dra̧g, P. Dra̧g, W. Worek, S. Cetin, Comparative analysis between traditional and M-Cycle based cooling tower, International Journal of Heat and Mass Transfer, vol. 159, 2020, art. no. 120124, pp. 1-13, https://doi.org/10.1016/j.ijheatmasstransfer.2020.120124.
- J. Nocedal, S. Wright, Numerical Optimization. Springer, New York, NY, 2006, https://doi.org/10.1007/978-0-387-40065-5.
- D.M. Yancy-Caballero, L.T. Biegler, R. Guirardello, Large-scale DAE-constrained optimization applied to a modified spouted bed reactor for ethylene production from methane, Computers and Chemical Engineering, vol. 113, 2018, pp 162-183, https://doi.org/10.1016/j.compchemeng.2018.03.017.