Abstract
The rigorous and efficient determination of the global solution of a nonconvex MINLP problem arising from product portfolio optimization introduced by Kallrath (2003) is addressed. The objective of the optimization problem is to determine the optimal number and capacity of reactors satisfying the demand and leading to a minimal total cost. Based on the model developed by Kallrath (2003), an improved formulation is proposed, which consists of a concave objective function and linear constraints with binary and continuous variables. A variety of techniques are developed to tighten the model and accelerate the convergence to the optimal solution. A customized branch and bound approach that exploits the special mathematical structure is proposed to solve the model to global optimality. Computational results for two case studies are presented. In both case studies, the global solutions are obtained and proved optimal very efficiently in contrast to available commercial MINLP solvers.
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References
C.S. Adjiman I.P. Androulakis C.A. Floudas (2000) ArticleTitleGlobal Optimization of Mixed-Integer Nonlinear Problems AICHE Journal 46 1769–1797 Occurrence Handle10.1002/aic.690460908
C.S. Adjiman S. Dallwig C.A. Floudas A. Neumaier (1998) ArticleTitleA Global Optimization Method, αBB, for General Twice-differentiable Constrained NLPs – I Theoretical Advances. Computers and Chemical Engineering 22 1137–1158 Occurrence Handle10.1016/S0098-1354(98)00027-1
Brooke, A., Kendrick, D. and Meeraus, A. (1988). GAMS: A User’s Guide, The Scientific Press.
Floudas, C.A. (1995). Nonlinear and Mixed-Integer Optimization, Oxford University Press.
C.A. Floudas (2000) Deterministic Global Optimization: Theory, Methods and Applications Kluwer Academic Publishers Dordrecht, The Netherlands
R. Horst H. Tuy (1996) Global Optimization: Deterministic Approaches EditionNumber3 Springer-Verlag Berlin
ILOG, Inc. (2000). ILOG CPLEX 7.0 User’s Manual.
Kallrath, J. (2003). Exact Computation of Global Minima of a Nonconvex Portfolio Optimization Problem. In: Floudas, C.A. and Pardalos, P.M. (eds.). Frontiers in Global Optimization, Kluwer Academic Publishers.
H.S. Ryoo N.V. Sahinidis (1996) ArticleTitleA Branch-and-Reduce Approach to Global Optimization Journal of Global Optimization 8 107–138 Occurrence Handle10.1007/BF00138689
E.M.B. Smith C.C. Pantelides (1999) ArticleTitleA Symbolic Reformulation/Spatial Branch-and-Bound Algorithm for the Global Optimization of Nonconvex MINLPs Computers and Chemical Engineering 23 457–478 Occurrence Handle10.1016/S0098-1354(98)00286-5
T. Westerlund H. Skrifvars I. Harjunkoski R. Porn (1998) ArticleTitleAn Extended Cutting Plane Method for a Class of Non-Convex MENLP Problems Computers and Chemical Engineering 22 357–365 Occurrence Handle10.1016/S0098-1354(97)00000-8
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Lin, X., Floudas, C.A. & Kallrath, J. Global Solution Approach for a Nonconvex MINLP Problem in Product Portfolio Optimization. J Glob Optim 32, 417–431 (2005). https://doi.org/10.1007/s10898-004-5903-5
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DOI: https://doi.org/10.1007/s10898-004-5903-5