The New Approach for Dynamic Optimization with Variability Constraints

  • Paweł Dra̧gEmail author
  • Krystyn Styczeń
Part of the Studies in Computational Intelligence book series (SCI, volume 795)


In this work a new optimization approach for processes modeled by differential-algebraic equations with variability constraints was presented. The designed procedure was based on the modified direct shooting method, which can transform the dynamic optimization problem into a large-scale nonlinear optimization task (NLP). The first-order KKT optimality conditions with complementarity constraints were obtained. Finally, to solve the optimality conditions with the complementarity constraints, the solution procedure combining SQP algorithm with the filter approach as a globalization procedure was designed. The efficiency of the presented methodology was tested on a production process in chemical engineering.


Dynamic optimization Differential-algebraic equations Variability constraints Filter method Complementarity constraints 



One of the co-authors, Paweł Dra̧g, received financial support in the framework of “Młoda Kadra”- “Young Staff” 0402/0109/17 at Wrocław University of Science and Technology.


  1. 1.
    Augspurger, M., Choi, K.K., Udaykumar, H.S.: Optimizing fin design for a PCM-based thermal storage device using dynamic Kriging. Int. J. Heat Mass Transf. 121, 290–308 (2018). Scholar
  2. 2.
    Babaei N., Salamci M.U.: Controller design for personalized drugadministration in cancer therapy: successive approximation approach. Optimal Control Appl. Methods 138 (2017). Scholar
  3. 3.
    Baumrucker, B.T., Biegler, L.T.: MPEC strategies for cost optimization of pipeline operations. Comput. Chem. Eng. 34(6), 900–913 (2010). Scholar
  4. 4.
    Biegler L.T.: Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes. Society for Industrial and Applied Mathematics, Philadelphia (2010).
  5. 5.
    Biegler L.T.: Advanced optimization strategies for integrated dynamic process operations. Comput. Chem. Eng. (2017) (in press). Scholar
  6. 6.
    Biegler L.T., Campbell S.L, Mehrmann V.: Control and Optimization with Differential-Algebraic Constraints. Society for Industrial and Applied Mathematics, Philadelphia (2012).
  7. 7.
    Bloss, K.F., Biegler, L.T., Schiesser, W.E.: Dynamic process optimization through adjoint formulations and constraint aggregation. Ind. Eng. Chem. Res. 38(2), 421–432 (1999). Scholar
  8. 8.
    Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM J. Sci. Comput. 24(3), 1076–1089 (2003). Scholar
  9. 9.
    Dowling, A.W., Balwani, C., Gao, Q., Biegler, L.T.: Optimization of sub-ambient separation systems with embedded cubic equation of state thermodynamic models and complementarity constraints. Comput. Chem. Eng. 81, 323–343 (2015). Scholar
  10. 10.
    Dra̧g, P.: Algorytmy sterowania wielostadialnymi procesami deskryptorowymi. Akademicka Oficyna Wydawnicza EXIT, Warsaw (2016)Google Scholar
  11. 11.
    Dra̧g P., Styczeń K.: A general optimization-based approach for thermal processes modeling. In: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems: September 3–6, 2017, pp. 1347–1352. Prague, Czech Republic (2017).
  12. 12.
    Dra̧g P., Styczeń K.: A new optimization-based approach for aircraft landing in the presence of windshear. In: Communication Papers of the 2017 Federated Conference on Computer Science and Information Systems: September 3–6, 2017, pp. 83–88. Prague, Czech Republic (2017).
  13. 13.
    Dra̧g P., Styczeń K.: Process Control with the Variability Constraints. In: Fidanova S. (ed.) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol. 717, pp. 41–51. Springer (2018). Scholar
  14. 14.
    Dra̧g P., Styczeń K.: The variability constraints in simulation of index-2 differential-algebraic processes. In: Nivitzka, V., Korecko, S., Szakal, A. (eds.) INFORMATICS 2017: 2017 IEEE 14th International Scientific Conference on Informatics, November 14–16, 2017, Proceedings, pp. 80–86. Poprad, Slovakia (2017)Google Scholar
  15. 15.
    Dra̧g P., Styczeń K., Kwiatkowska M., Szczurek, A.: A review on the direct and indirect methods for solving optimal control problems with differential-algebraic constraints. In: Recent Advances in Computational Optimization, vol. 2016, pp. 91–105. Springer (2016). Scholar
  16. 16.
    Echebest, N., Schuverdt, M.L., Vignau, R.P.: An inexact restoration derivative-free filter method for nonlinear programming. Comput. Appl. Math. 36, 693–718 (2017). Scholar
  17. 17.
    Ferreira, P.S., Karas, E.W., Sachine, M., Sobral, F.N.C.: Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming. Optimization 66, 271–292 (2017). Scholar
  18. 18.
    Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. Ser. B 91, 239–269 (2002). Scholar
  19. 19.
    Jamaludin, M.Z., Li, H., Swartz, C.L.E.: The utilization of closed-loop prediction for dynamic real-time optimization. Can. J. Chem. Eng. 95, 1968–1978 (2017). Scholar
  20. 20.
    Koller, R.W., Ricardez-Sandoval, L.A., Biegler, L.T.: Stochastic back-off algorithm for simultaneous design, control and scheduling of multi-product systems under uncertainty. AIChE J. (2018) (in press). Scholar
  21. 21.
    Kwiatkowska M., Szczurek A., Dra̧g P.: Zastosowanie równań różniczkowo-algebraicznych do predykcji zmian parametrw powietrza wewnȩtrznego. Przegla̧d Elektrotechniczny 92, 181–184 (2015).
  22. 22.
    Li, J., Yang, Z.: A QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization. Appl. Math. Comput. 316, 52–72 (2018). Scholar
  23. 23.
    Ma, J., Mahapatra, P., Zitney, S.E., Biegler, L.T., Miller, D.C.: D-RM builder: a software tool for generating fast and accurate nonlinear dynamic reduced models from high-fidelity models. Comput. Chem. Eng. 94, 60–74 (2016). Scholar
  24. 24.
    Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, Springer Series in Operation Research and Financial Engineering (2006)zbMATHGoogle Scholar
  25. 25.
    Pandelidis, D., Anisimov, S.: Numerical study and optimization of the cross-flow Maisotsenko cycle indirect evaporative air cooler. Int. J. Heat Mass Transf. 103, 1029–1041 (2016). Scholar
  26. 26.
    Unal, C., Salamci, M.U.: Drug administration in cancer treatment via optimal nonlinear state feedback gain matrix design. IFAC-PapersOnLine 50(1), 9979–9984 (2017). Scholar
  27. 27.
    Wan, W., Eason, J.P., Nicholson, B., Biegler, L.T.: Parallel cyclic reduction decomposition for dynamic optimization problems. Comput. Chem. Eng. (2017) (in press).
  28. 28.
    Wang, L., Liu, X., Zhang, Z.: An efficient interior-point algorithm with new non-monotone line search filter method for nonlinear constrained programming. Eng. Optim. 49, 290–310 (2017). Scholar
  29. 29.
    Xu, P.: Production of chemicals using dynamic control of metabolic fluxes. Curr. Opin. Biotechnol. 53, 12–19 (2018). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Control Systems and MechatronicsWrocław University of Science and TechnologyWrocławPoland

Personalised recommendations