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Hybrid Algorithm for Risk Conscious Chemical Batch Planning Under Uncertainty

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Modeling, Simulation and Optimization of Complex Processes

Abstract

We consider planning problems of flexible chemical batch processes paying special attention to uncertainties in problem data. The optimization problems are formulated as two-stage stochastic mixed-integer models in which some of the decisions (first-stage) have to be made under uncertainty and the remaining decisions (second-stage) can be made after the realization of the uncertain parameters. The uncertain model parameters are represented by a finite set of scenarios. The risk conscious planning problem under uncertainty is solved by a stage decomposition approach using a multi-objective evolutionary algorithm which optimizes the expected scenario costs and the risk criterion with respect to the first-stage decisions. The second-stage scenario decisions are handled by mathematical programming. Results from numerical experiments for a multi-product batch plant are presented.

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References

  1. T. Bäck. Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York, 1996.

    MATH  Google Scholar 

  2. A. Bonfill, M. Bagajewicz, A. Espuna, and L. Puigjaner. Risk management in the scheduling of batch plants under uncertain market demand. Industrial and Engineering Chemistry Research, 43:741–750, 2004.

    Article  Google Scholar 

  3. J. F. Birge and F. Louveaux. Introduction to Stochastic Programming. Springer, New York, 1997.

    MATH  Google Scholar 

  4. K. Deb. Multi-Objective Optimization using Evolutionary Algorithms. Wiley-Interscience Series in Systems and Optimization. John Wiley & Sons, Chichester, 2001.

    MATH  Google Scholar 

  5. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2):182–197, 2002.

    Article  Google Scholar 

  6. M. Emmerich, M. Schütz, B. Gross, and M. Grötzner. Mixed-integer evolution strategy for chemical plant optimization. In I. C. Parmee, editor, ”Evolutionary Design and Manufacture” (ACDM 2000), pages 55–67. Springer, 2000.

    Google Scholar 

  7. J. Knowles, D. Corne, and K. Deb. Multiobjective Problem Solving from Nature: From Concepts to Applications. Natural Computing Series, 2008.

    Google Scholar 

  8. Z. Li and M. Ierapetritou. Process scheduling under uncertainty: Review and challenges. Comp. and Chem. Eng., 32:715–727, 2008.

    Article  Google Scholar 

  9. A. Ruszczynski and A. Shapiro, editors. Stochastic Programming. Handbooks in Operations Research and Management Science. Elsevier, Amsterdam, The Netherlands, 2003.

    MATH  Google Scholar 

  10. G. Rudolph. An evolutionary algorithm for integer programming. In Y. Davidor, H.-P. Schwefel, and R. Männer, editors, PPSN III, volume 866 of LNCS, pages 193–197. Springer, Berlin, 1994.

    Google Scholar 

  11. G. Sand and S. Engell. Modelling and solving real-time scheduling problems by stochastic integer programming. Comp. and Chem. Eng., 28:1087–1103, 2004.

    Article  Google Scholar 

  12. M. Suh and T. Lee. Robust optimization method for the economic term in chemical process design and planning. Ind. Eng. Chem. Res., 40:5950–5959, 2001.

    Article  Google Scholar 

  13. N. J. Samsatli, L. G. Papageorgiou, and N. Shah. Robustness metrics for dynamic optimization models under parameter uncercainty. AIChE J., 44:1993–2006, 1998.

    Article  Google Scholar 

  14. J. Till, G. Sand, S. Engell, M. Emmerich, and Schönemann L. A hybrid algorithm for solving two-stage stochastic integer problems by combining evolutionary algorithms and mathematical programming methods. In Proc. European Symposium on Computer Aided Process Engineering (ESCAPE-15), pages 187–192, 2005.

    Google Scholar 

  15. J. Till, G. Sand, M. Urselmann, and S. Engell. Hybrid evolutionary algorithms for solving two-stage stochastic integer programs in chemical batch scheduling. Comp. and Chem. Eng., 31:630–647, 2007.

    Article  Google Scholar 

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Correspondence to Thomas Tometzki .

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Tometzki, T., Engell, S. (2012). Hybrid Algorithm for Risk Conscious Chemical Batch Planning Under Uncertainty. In: Bock, H., Hoang, X., Rannacher, R., Schlöder, J. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25707-0_24

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