Combinatorially Accelerated Branch-and-Bound Method for Solving the MIP Model of Process Network Synthesis
Process network synthesis (PNS) has enormous practical impact; however, its mixed integer programming (MIP) model is tedious to solve because it usually involves a large number of binary variables. The present work elucidates the recently proposed accelerated branch-and- bound algorithm that exploits the unique feature of the MIP model of PNS. Implementation of the algorithm is based on the so-called decision-mapping that consistently organizes the system of complex decisions. The accelerated branch-and-bound algorithm of PNS reduces both the number and size of the partial problems. The efficacy of the algorithm is demonstrated with a realistic example.
KeywordsProcess network synthesis mixed integer programming branch-and-bound combinatorial acceleration
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- 1.Floudas, C. A. and I. E. Grossmann, Algorithmic Approaches to Process Synthesis: Logic and Global Optimization, International Symposium on Foundations of Computer Aided Process Design, Snowmass Village, CO, U.S.A., July 10–15, 1994 (in press).Google Scholar
- 2.Floudas, C. A. and P. M. Pardalos, A Collection of Test Problems for Constrained Global Optimization Algorithms, In: Lecture Notes in Computer Science ( Eds: G. Goos and J. Hartmanis) Springer-Verlag, 1990.Google Scholar
- 3.Friedler, F., L. T. Fan, and B. Imreh, Process Network Synthesis: Problem Definition, accepted for publication in Networks, 1995.Google Scholar
- 4.Friedler, F., K. Tarjan, Y. W. Huang, and L. T. Fan, Combinatorial Algorithms for Process Synthesis, ESCAPE-1 Conference, Elsinore, Denmark, May 24–28, 1992; Computers chem. Engng, 16, Suppl., S313–20, 1992.Google Scholar
- 7.Friedler, F., J. B. Varga, and L. T. Fan, Decision-Mapping: A Tool for Consistent and Complete Decisions in Process Synthesis, accepted for publication in Chem. Engng Sci., 1995.Google Scholar
- 8.Friedler, F., J. B. Varga, and L. T. Fan, Decision-Mapping for Design and Synthesis of Chemical Processes: Application to Reactor-Network Synthesis, International Symposium on Foundations of Computer Aided Process Design, Snowmass Village, CO, U.S.A., July 10–15, 1994 (in press).Google Scholar
- 9.Grossmann, I. E., V. T. Voudouris, O. Ghattas, Mixed-Integer Linear Programming Reformulations for Some Nonlinear Discrete Design Optimization Problems, In: Recent Advances in Global Optimization (Eds: C. A. Floudas and P. M. Pardalos) Princeton University Press, New Jersey, 1992.Google Scholar
- 10.Guisewite, G. M, Network Problems, In: Handbook of Global Optimization, Nonconvex Optimization and Its Applications, 2, (Eds: R. Horst and P. M. Pardalos) Kluwer Academic Publishers, Dordrecht/Boston/London, pp. 609–648, 1995.Google Scholar