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A hierarchy of relaxations for linear generalized disjunctive programming

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  • Sawaya, Nicolas
  • Grossmann, Ignacio

Abstract

Generalized disjunctive programming (GDP), originally developed by Raman and Grossmann (1994), is an extension of the well-known disjunctive programming paradigm developed by Balas in the mid 70s in his seminal technical report (Balas, 1974). This mathematical representation of discrete-continuous optimization problems, which represents an alternative to the mixed-integer program (MIP), led to the development of customized algorithms that successfully exploited the underlying logical structure of the problem. The underlying theory of these methods, however, borrowed only in a limited way from the theories of disjunctive programming, and the unique insights from Balas’ work have not been fully exploited.

Suggested Citation

  • Sawaya, Nicolas & Grossmann, Ignacio, 2012. "A hierarchy of relaxations for linear generalized disjunctive programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 70-82.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:1:p:70-82
    DOI: 10.1016/j.ejor.2011.07.018
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    Cited by:

    1. Francisco Trespalacios & Ignacio E. Grossmann, 2015. "Algorithmic Approach for Improved Mixed-Integer Reformulations of Convex Generalized Disjunctive Programs," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 59-74, February.
    2. Yinrun Lyu & Li Chen & Changyou Zhang & Dacheng Qu & Nasro Min-Allah & Yongji Wang, 2018. "An interleaved depth-first search method for the linear optimization problem with disjunctive constraints," Journal of Global Optimization, Springer, vol. 70(4), pages 737-756, April.
    3. Peter Kirst & Fabian Rigterink & Oliver Stein, 2017. "Global optimization of disjunctive programs," Journal of Global Optimization, Springer, vol. 69(2), pages 283-307, October.
    4. Dimitri J. Papageorgiou & Francisco Trespalacios, 2018. "Pseudo basic steps: bound improvement guarantees from Lagrangian decomposition in convex disjunctive programming," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 55-83, March.
    5. Novas, Juan M. & Ramello, Juan Ignacio & Rodríguez, María Analía, 2020. "Generalized disjunctive programming models for the truck loading problem: A case study from the non-alcoholic beverages industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    6. Li Chen & Yinrun Lyu & Chong Wang & Jingzheng Wu & Changyou Zhang & Nasro Min-Allah & Jamal Alhiyafi & Yongji Wang, 2017. "Solving linear optimization over arithmetic constraint formula," Journal of Global Optimization, Springer, vol. 69(1), pages 69-102, September.
    7. Francisco Trespalacios & Ignacio E. Grossmann, 2016. "Cutting Plane Algorithm for Convex Generalized Disjunctive Programs," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 209-222, May.

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