Surrogate-Based Reduced-Dimension Global Optimization in Process Systems Engineering

  • Chapter
  • First Online:
High-Dimensional Optimization and Probability

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 191))

Abstract

High dimensional global optimization problems arise frequently in process systems engineering. This is a result of the complex mechanistic relationships that describe process systems, and/or their large-scale nature. High dimensional optimization problems can often be more easily solved by instead solving a sequence of reduced-dimension subproblems. Surrogate models can allow the formulation of reduced-dimension subproblems by approximating the key features of the original model. Surrogate-based optimization (SBO) is to use surrogate modeling to solve a sequence of approximate reduced-dimension subproblems, in order to converge to a high quality solution to the original high dimensional problem. Here we review the key characteristics of SBO frameworks and their application to process systems optimization problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. L.T. Biegler, Recent advances in chemical process optimization. Chem. Ingenieur Tech. 86(7), 943–952 (2014)

    Article  Google Scholar 

  2. R. Horst, H. Tuy, Global Optimization: Deterministic Approaches (Springer, Berlin, 2013)

    MATH  Google Scholar 

  3. S.A. Vavasis, Complexity issues in global optimization: a survey, in Handbook of Global Optimization (Springer, Berlin, 1995), pp. 27–41

    Book  Google Scholar 

  4. I. Harjunkoski, C.T. Maravelias, P. Bongers, P.M. Castro, S. Engell, I.E. Grossmann, J. Hooker, C. Méndez, G. Sand, J. Wassick, Scope for industrial applications of production scheduling models and solution methods. Comput. Chem. Eng. 62, 161–193 (2014)

    Article  Google Scholar 

  5. Z. Li, M. Ierapetritou, Process scheduling under uncertainty: review and challenges. Comput. Chem. Eng. 32(4–5), 715–727 (2008)

    Article  Google Scholar 

  6. J.R. Birge, F. Louveaux, Introduction to Stochastic Programming (Springer, Berlin, 2011)

    Book  Google Scholar 

  7. R.K. Ahuja, T.L. Magnanti, J.B. Orlin, M.R. Reddy, Applications of network optimization, in Handbooks in Operations Research and Management Science, vol. 7 (1995), pp. 1–83

    Google Scholar 

  8. J. Li, S.E. Demirel, M.M. Faruque Hasan, Simultaneous process synthesis and process intensification using building blocks, in Computer Aided Chemical Engineering, vol. 40 (Elsevier, Amsterdam, 2017), pp. 1171–1176

    Google Scholar 

  9. C.A. Henao, C.T. Maravelias, Surrogate-based superstructure optimization framework. AIChE J. 57(5), 1216–1232 (2011)

    Article  Google Scholar 

  10. J.A. Caballero, I.E. Grossmann, An algorithm for the use of surrogate models in modular flowsheet optimization. AIChE J. 54(10), 2633–2650 (2008)

    Article  Google Scholar 

  11. B. Duarte, P.M. Saraiva, C.C. Pantelides, Combined mechanistic and empirical modelling. Int. J. Chem. Reactor Eng. 2(1) (2004). https://doi.org/10.2202/1542-6580.1128

  12. L. Leifsson, H. Sævarsdóttir, S. Sigurdsson, A. Vésteinsson, Grey-box modeling of an ocean vessel for operational optimization. Simul. Model. Pract. Theory 16(8), 923–932 (2008)

    Article  Google Scholar 

  13. H. Shi, F. You, A novel adaptive surrogate modeling-based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations. AIChE J. 61(12), 4191–4209 (2015)

    Article  Google Scholar 

  14. B. Beykal, F. Boukouvala, C.A. Floudas, E.N. Pistikopoulos, Optimal design of energy systems using constrained grey-box multi-objective optimization. Comput. Chem. Eng. 116, 488–502 (2018)

    Article  Google Scholar 

  15. Y. Oussar, G. Dreyfus, How to be a gray box: dynamic semi-physical modeling. Neural Netw. 14(9), 1161–1172 (2001)

    Article  Google Scholar 

  16. I. Goodfellow, Y. Bengio, A. Courville, Deep Learning (MIT Press, Cambridge, 2016)

    MATH  Google Scholar 

  17. J.H. Friedman, Multivariate adaptive regression splines. Ann. Stat. 19, 1–67 (1991)

    MathSciNet  MATH  Google Scholar 

  18. G. Matheron, Principles of geostatistics. Econ. Geol. 58(8), 1246–1266 (1963)

    Article  Google Scholar 

  19. S. Koziel, D.E. Ciaurri, L. Leifsson, Surrogate-based methods, in Computational Optimization, Methods and Algorithms (Springer, Berlin, 2011), pp. 33–59

    Book  Google Scholar 

  20. C. Audet, J. Denni, D. Moore, A. Booker, P. Frank, A surrogate-model-based method for constrained optimization, in 8th Symposium on Multidisciplinary Analysis and Optimization (2000), p. 4891

    Google Scholar 

  21. Z.-H. Han, K.-S. Zhang, et al., Surrogate-based optimization, in Real-World Applications of Genetic Algorithms, vol. 343 (2012)

    Google Scholar 

  22. A. Cozad, N.V. Sahinidis, D.C. Miller, A combined first-principles and data-driven approach to model building. Comput. Chem. Eng. 73, 116–127 (2015)

    Article  Google Scholar 

  23. A.I.J. Forrester, A.J. Keane, Recent advances in surrogate-based optimization. Progr. Aerospace Sci. 45(1–3), 50–79 (2009)

    Article  Google Scholar 

  24. B. Shahriari, K. Swersky, Z. Wang, R.P. Adams, N. De Freitas, Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104(1), 148–175 (2015)

    Article  Google Scholar 

  25. M.D. McKay, R.J. Beckman, W.J. Conover, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1), 55–61 (2000)

    Article  Google Scholar 

  26. N.V. Queipo, R.T. Haftka, W. Shyy, T. Goel, R. Vaidyanathan, P. Kevin Tucker, Surrogate-based analysis and optimization. Progr. Aerospace Sci. 41(1), 1–28 (2005)

    Article  Google Scholar 

  27. K. Kazda, X. Li, Nonconvex multivariate piecewise-linear fitting using the difference-of-convex representation. Comput. Chem. Eng. 150, 107310 (2021)

    Article  Google Scholar 

  28. B. Geißler, A. Martin, A. Morsi, L. Schewe, Using piecewise linear functions for solving MINLPs, in Mixed Integer Nonlinear Programming (Springer, Berlin, 2012), pp. 287–314

    Book  Google Scholar 

  29. R. Burlacu, B. Geißler, L. Schewe, Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes. Optim. Methods Softw. 35(1), 37–64 (2020)

    Article  MathSciNet  Google Scholar 

  30. A. Cozad, N.V. Sahinidis, D.C. Miller, Learning surrogate models for simulation-based optimization. AIChE J. 60(6), 2211–2227 (2014)

    Article  Google Scholar 

  31. A. Bhosekar, M. Ierapetritou, Advances in surrogate based modeling, feasibility analysis, and optimization: a review. Comput. Chem. Eng. 108, 250–267 (2018)

    Article  Google Scholar 

  32. K. McBride, K. Sundmacher, Overview of surrogate modeling in chemical process engineering. Chem. Ingenieur Tech. 91(3), 228–239 (2019)

    Article  Google Scholar 

  33. L. Jia, R. Alizadeh, J. Hao, G. Wang, J.K. Allen, F. Mistree, A rule-based method for automated surrogate model selection. Adv. Eng. Inform. 45, 101123 (2020)

    Article  Google Scholar 

  34. M. Ben Salem, O. Roustant, F. Gamboa, L. Tomaso, Universal prediction distribution for surrogate models. SIAM/ASA J. Uncertainty Quantif. 5(1), 1086–1109 (2017)

    Article  MathSciNet  Google Scholar 

  35. M. Mistry, D. Letsios, G. Krennrich, R.M. Lee, R. Misener, Mixed-integer convex nonlinear optimization with gradient-boosted trees embedded. INFORMS J. Comput. 33(3), 1103–1119 (2021)

    Article  MathSciNet  Google Scholar 

  36. A. Thebelt, J. Kronqvist, M. Mistry, R. M. Lee, N. Sudermann-Merx, R. Misener, Entmoot: a framework for optimization over ensemble tree models (2020). ar**v preprint ar**v:2003.04774

    Google Scholar 

  37. X.Y. Sun, D. Gong, S. Li, Classification and regression-based surrogate model-assisted interactive genetic algorithm with individual’s fuzzy fitness, in Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation (2009), pp. 907–914

    Google Scholar 

  38. A. Mehmani, S. Chowdhury, C. Meinrenken, A. Messac, Concurrent surrogate model selection (cosmos): optimizing model type, kernel function, and hyper-parameters. Struct. Multidiscip. Optim. 57(3), 1093–1114 (2018)

    Article  MathSciNet  Google Scholar 

  39. I. Fahmi, S. Cremaschi, Process synthesis of biodiesel production plant using artificial neural networks as the surrogate models. Comput. Chem. Eng. 46, 105–123 (2012)

    Article  Google Scholar 

  40. N. Quirante, J. Javaloyes, J.A. Caballero, Rigorous design of distillation columns using surrogate models based on k riging interpolation. AIChE J. 61(7), 2169–2187 (2015)

    Article  Google Scholar 

  41. M. Tawarmalani, N.V. Sahinidis, A polyhedral branch-and-cut approach to global optimization. Math. Program. 103, 225–249 (2005)

    Article  MathSciNet  Google Scholar 

  42. N.V. Sahinidis, BARON 21.1.13: Global Optimization of Mixed-Integer Nonlinear Programs, User’s Manual (2017)

    Google Scholar 

  43. A. Golzari, M.H. Sefat, S. Jamshidi, Development of an adaptive surrogate model for production optimization. J. Pet. Sci. Eng. 133, 677–688 (2015)

    Article  Google Scholar 

  44. H. Shi, F. You, Adaptive surrogate-based algorithm for integrated scheduling and dynamic optimization of sequential batch processes, in 2015 54th IEEE Conference on Decision and Control (CDC) (IEEE, Piscataway, 2015), pp. 7304–7309

    Google Scholar 

Download references

Acknowledgements

This research was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) through the Discovery Grant (RGPIN-2019-05217).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to **ang Li .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kazda, K., Li, X. (2022). Surrogate-Based Reduced-Dimension Global Optimization in Process Systems Engineering. In: Nikeghbali, A., Pardalos, P.M., Raigorodskii, A.M., Rassias, M.T. (eds) High-Dimensional Optimization and Probability. Springer Optimization and Its Applications, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-031-00832-0_10

Download citation

Publish with us

Policies and ethics

Navigation