Annals of Operations Research

, Volume 132, Issue 1–4, pp 135–155 | Cite as

Model Independent Parametric Decision Making

  • Ipsita Banerjee
  • Marianthi G. Ierapetritou
Article

Abstract

Accurate knowledge of the effect of parameter uncertainty on process design and operation is essential for optimal and feasible operation of a process plant. Existing approaches dealing with uncertainty in the design and process operations level assume the existence of a well defined model to represent process behavior and in almost all cases convexity of the involved equations. However, most of the realistic case studies cannot be described by well characterised models. Thus, a new approach is presented in this paper based on the idea of High Dimensional Model Reduction technique which utilize a reduced number of model runs to build an uncertainty propagation model that expresses process feasibility. Building on this idea a systematic iterative procedure is developed for design under uncertainty with a unique characteristic of providing parametric expression of the optimal objective with respect to uncertain parameters. The proposed approach treats the system as a black box since it does not rely on the nature of the mathematical model of the process, as is illustrated through a number of examples.

uncertainty parametric analysis HDMR 

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References

  1. Banerjee, I. and M.G. Ierapetritou. (2003). "Parametric Process Synthesis for General Nonlinear Models." Computers and Chemical Engineering 27, 1499.CrossRefGoogle Scholar
  2. Birge, J.R. and F. Louveaux. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. Berlin: Springer.Google Scholar
  3. Box, G.E.P. and N.R. Draper. (1987). Empirical Model Building and Response Surfaces.New York: Wiley.Google Scholar
  4. Diwekar, U. (2002). "Optimization under Uncertainty: An Overview." SIAG/OPT Views-and-News 13, 1–8.Google Scholar
  5. Gal, T. (1984). "Linear Parametric Programming-A Brief Survey." Mathematical Programming Study 21, 43.Google Scholar
  6. Ganesh, N. and L.T. Biegler. (1987). "A Reduced Hessian Strategy for Sensitivity Analysis of Optimal Flowsheets." AIChE Journal 33, 282–296.CrossRefGoogle Scholar
  7. Goyal, V. and M.G. Ierapetritou. (2002). "Determination of Operability Limits Using Simplicial Approximation." AIChE Journal 48, 2902–2909.CrossRefGoogle Scholar
  8. Goyal, V. and M.G. Ierapetritou. (2003). "A Novel Framework for Evaluating the Feasibility/Operability of Non-Convex Processes." AIChE Journal 49, 1233–1240.CrossRefGoogle Scholar
  9. Grossmann, I.E. and R.W.H. Sargent. (1978). "Optimum Design of Chemical Plants with Uncertain Parameters." AIChE Journal 24, 1021–1028.CrossRefGoogle Scholar
  10. Grossmann, I.E. and K.P. Halernane. (1982). "A Decomposition Strategy for Designing Flexible Chemical Plants." AIChE Journal 28, 686–694.CrossRefGoogle Scholar
  11. Halemane, K.P. and I.E. Grossmann. (1983). "Optimal Process Design under Uncertainty." AIChE Journal 29, 425–433.CrossRefGoogle Scholar
  12. Hene, T.S., V. Dua, and E.N. Pistikopoulos. (2002). "A Hybrid Parametric/Stochastic Programming Ap-proach for Mixed-Integer Nonlinear Problems under Uncertainty." Industrial and Engineering Chemistry Research 41, 67–77.CrossRefGoogle Scholar
  13. Ierapetritou, M.G., J. Acevedo, and E.N. Pistikopoulos. (1996). "An Optimization Approach for Process Engineering Problems under Uncertainty." Computers and Chemical Engineering 20, 703–709.Google Scholar
  14. Ierapetritou, M.G. (2001). "A New Approach for Quantifying Process Feasibility: Convex and 1-D Quasi-Convex Regions." AIChE Journal 47, 1407–1417.CrossRefGoogle Scholar
  15. Jenkins, L. (1982). "Parametric Mixed-Integer Programming: An Application to Solid Waste Management." Management Science 28, 1270–1284.Google Scholar
  16. Jenkins, L. (1990). "Parametric Methods in Integer Linear Programming." Annals of Operation Research 27, 77–96.Google Scholar
  17. Jenkins, L. and D. Peters. (1987). "A Computational Comparison of Gomory and Knapsack Cuts." Computers and Operation Research 14, 449–456.Google Scholar
  18. Jongen, H.T. and G.W. Weber. (1990). "On Parametric Nonlinear Programming." Annals of Operation Research 27, 253–259.Google Scholar
  19. Kubic, W.L. and F.P. Stein. (1988). "A Theory of Design Reliability Using Probability and Fuzzy Sets." AIChE Journal 34, 583–601.Google Scholar
  20. Loh, W.L. (1996). "On Latin Hypercube Sampling." Annals of Statistics 24, 2058–2080.Google Scholar
  21. Lu, R., Y. Luo, and J.P. Conte. (1994). "Reliability Evaluation of Reinforced Concrete Beam." Structural Safety 14, 277–298.CrossRefGoogle Scholar
  22. McRae, G.J., J.W. Tilden, and J.H. Seinfeld. (1982). "Global Sensitivity Analysis-A Computational Im-plementation of the Fourier Amplitude Sensitivity Analysis (FAST)." Computers and Chemical Engineering 6, 15–25.CrossRefGoogle Scholar
  23. Ohtake, Y. and N. Nishida. (1985). "A Branch and Bound Algorithm for 0-1 Parametric Mixed-Integer Programming." Operations Research Letters 4, 41–45.Google Scholar
  24. Paules, G.E. and C.A. Floudas. (1992). "Stochastic Programming in Process Synthesis: A Two-Stage Model with MINLP Recourse for Multiperiod Heat-Integrated Distillation Sequences." Computers and Chemical Engineering 16, 189–210.CrossRefGoogle Scholar
  25. Pistikopoulos, E.N. and T.A. Mazzuchi. (1990). "A Novel Flexibility Analysis Approach for Processes with Stochastic Parameters." Computers and Chemical Engineering 14, 991–1000.CrossRefGoogle Scholar
  26. Rabitz, H. and O. Alis. (1999). "General Foundations of High Dimensional Model Representations." Journal of Mathematical Chemistry 25, 197–233.CrossRefGoogle Scholar
  27. Rabitz, H., O. Alis, J. Shorter, and K. Shim. (1998). "Efficient Input-Output Model Representations." Computer Physics Communications 117(1), 11–20.Google Scholar
  28. Reinhart, H.J., D.W.T. Rippin. (1986). "The Design of Flexible Batch Chemical Plants." In Annual AIChE Meeting, New Orleans, Paper No. 50e.Google Scholar
  29. Saboo, A.K., M. Morari, and D.C. Woodcock. (1983). "Design of Resilient Processing Plants-VIII. A Resilience Index for Heat Exchanger Networks." Chemical Engineering Science 40, 1553–1565.Google Scholar
  30. Sahinidis, N.V., I.E. Grossmann, R.E. Fornari, and M. Chathrathi. (1989). "Optimization Model for Long-Range Planning in Chemical Industry." Computers and Chemcal Engineering 13, 1049–1063.Google Scholar
  31. Shorter, J., P.C. Ip, and H. Rabitz. (1999). "An Efficient Chemical Kinetics Solver Using High Dimensional Model Representations." Journal of Physical Chemistry A 103, 7192–7198.CrossRefGoogle Scholar
  32. Sobol, I.M. (1994). A Primer for Monte Carlo Method. CRC Press.Google Scholar
  33. Straub, D.A. and I.E. Grossmann. (1993). "Design Optimization of Stochastic Flexibility." Computers and Chemical Engineering 17, 339.CrossRefGoogle Scholar
  34. Swaney, R.E. and I.E. Grossmann. (1985). "An Index of Operational Flexibility in Chemical Process Design-Part I: Formulation and Theory." AIChE Journal 31, 621–630.Google Scholar
  35. Takamatsu, T., I. Hashimoto, and H. Ohno. (1970). "Optimal Design of a Large Complex System from the Viewpoint of Sensitivity Analysis." Industrial Engineering Chemistry Process Design and Development 9, 368–379.Google Scholar
  36. Wang, S.W., H. Levy II, G. Li, and H. Rabitz. (1999). "Fully Equivalent Operational Models for At-mospheric Chemical Kinetics within Global Chemistry-Transport Models." Journal of Geophysical Research 104(D23), 30417–30426.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Ipsita Banerjee
    • 1
  • Marianthi G. Ierapetritou
    • 1
  1. 1.Department of Chemical and Biochemical EngineeringRutgers UniversityPiscatawayUSA

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