Logic-Based Outer-Approximation and Benders Decomposition Algorithms for the Synthesis of Process Networks

  • Metin Türkay
  • Ignacio E. Grossmann
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 7)


In this paper the MINLP problem for the optimal synthesis of process networks is modeled as a discrete optimization problem involving logic disjunctions with nonlinear equations and pure logic relations. The logic disjunctions allow the conditional modeling of equations. The outer approximation algorithm is used as a basis to derive a logic-based OA solution method which naturally gives rise to NLP subproblems that avoid zero flows and a disjunctive LP master problem. The NLP subproblems are selected through a set covering problem for which we consider both the cases of disjunctive and conjunctive normal form logic. The master problem, on the other hand, is converted to mixed-integer form using a convex-hull representation. Furthermore, based on some interesting relations of outer-approximation with Generalized Benders Decomposition it is also shown that it is possible to derive a logic-based method for the latter algorithm. The performance of the proposed algorithms illustrated with two process network problems.


Propositional Logic Master Problem Boolean Variable Bender Decomposition Disjunctive Normal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Metin Türkay
    • 1
  • Ignacio E. Grossmann
    • 1
  1. 1.Department of Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA

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