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paper/paper.tex

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@@ -27,7 +27,7 @@ \section{Introduction}
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Within the optimization community, there is a high volume of ongoing research that relies on GDP to formulate models for a variety of applications. Due to the combinatorial nature of system design problems, the GDP paradigm has been applied to the synthesis of complex processes and networks \cite{MATOVU2022107856, ZHOU202269}, the planning and optimal control of energy systems \cite{CHO2022841, kim2022generalized}, and the modeling of chemical synthesis under uncertainty \cite{CHEN2022107616}. These and numerous other applications of GDP illustrate the benefit of having a robust package for GDP that removes much of the overhead associated with developing and testing GDP models. Although packages with GDP capabilities exist for \verb|Pyomo| \cite{chen2022pyomo} and \verb|GAMS| \cite{vecchietti1999logmip}, having such a package available in Julia can greatly accelerate research in optimization, where packages like \verb|JuMP.jl| \cite{dunning_huchette_lubin_2017} are gaining significant traction.
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This paper provides background on the GDP paradigm, and the techniques for reformulating and solving such models. It then presents the package \verb|DisjunctiveProgramming.jl| as an extension to \verb|JuMP.jl| for creating models for optimization that follow the GDP modeling paradigm and can be solved using the vast list of supported solvers \cite{DunningHuchetteLubin2017}. A case study demonstrates the use of the package for chemical process superstructure optimization.
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This paper provides background on the GDP paradigm, and the techniques for reformulating and solving such models. It then presents the package \verb|DisjunctiveProgramming.jl| as an extension to \verb|JuMP.jl| for creating models for optimization that follow the GDP modeling paradigm and can be solved using the vast list of supported solvers \cite{dunning_huchette_lubin_2017}. A case study demonstrates the use of the package for chemical process superstructure optimization.
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\section{Generalized Disjunctive Programming}
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The GDP form of modeling is an abstraction that uses both algebraic and logical constraints to capture the fundamental rules governing a system. The two main reformulation strategies to transform GDP models into their equivalent MIP models are the Big-M reformulation \cite{nemhauser_1999, TRESPALACIOS201598} and the Hull reformulation \cite{LEE20002125}, the latter of which yields tighter models at the expense of larger model sizes \cite{grossmann_lee_2003}.

paper/ref.bib

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@@ -4,6 +4,7 @@ @inproceedings{agarwal2010automating
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booktitle={International Symposium on Practical Aspects of Declarative Languages},
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pages={134--148},
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year={2010},
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doi="10.1007/978-3-642-11503-5\_12",
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organization={Springer}
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}
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@article{huangfu2018parallelizing,
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number={1},
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pages={119--142},
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year={2018},
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doi={10.1007/s12532-017-0130-5},
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publisher={Springer}
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}
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@article{chen2022pyomo,
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number={4-5},
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pages={555--565},
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year={1999},
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doi={10.1016/s0098-1354(98)00293-2},
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publisher={Elsevier}
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}
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@article{trespalacios_grossmann_2016,
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@Inbook{E.Grossmann2009,
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author="E. Grossmann, Ignacio",
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title="Logic-based outer approximationLogic-Based Outer Approximation",
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title="Logic-based outer approximation",
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bookTitle="Encyclopedia of Optimization",
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year="2009",
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publisher="Springer US",
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pages = {13-25},
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year = {2014},
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issn = {0098-1354},
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doi = {https://doi.org/10.1016/j.compchemeng.2014.03.014},
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doi = {10.1016/j.compchemeng.2014.03.014},
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url = {https://www.sciencedirect.com/science/article/pii/S0098135414000957},
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author = {Miguel A. Navarro-Amorós and Rubén Ruiz-Femenia and José A. Caballero},
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keywords = {Process synthesis, Generalized Disjunctive Programming, Modular simulators, Logic-based optimization algorithm},
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number={3},
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pages={219--260},
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year={2011},
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doi={10.1007/s12532-011-0026-8},
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publisher={Springer}
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}
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year = {2022},
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booktitle = {32nd European Symposium on Computer Aided Process Engineering},
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issn = {1570-7946},
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doi = {https://doi.org/10.1016/B978-0-323-95879-0.50141-7},
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doi = {10.1016/B978-0-323-95879-0.50141-7},
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url = {https://www.sciencedirect.com/science/article/pii/B9780323958790501417},
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author = {Seolhee Cho and Ignacio E. Grossmann},
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keywords = {Reliability, Expansion Planning, Power systems, Optimization},
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pages = {107616},
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year = {2022},
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issn = {0098-1354},
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doi = {https://doi.org/10.1016/j.compchemeng.2021.107616},
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doi = {10.1016/j.compchemeng.2021.107616},
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url = {https://www.sciencedirect.com/science/article/pii/S009813542100394X},
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author = {Ying Chen and Yixin Ye and Zhihong Yuan and Ignacio E. Grossmann and Bingzhen Chen},
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keywords = {Reliability-based superstructure optimization, Stochastic programming, Endogenous and exogenous uncertainties, Logic-based outer approximation algorithm},
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pages = {107856},
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year = {2022},
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issn = {0098-1354},
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doi = {https://doi.org/10.1016/j.compchemeng.2022.107856},
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doi = {10.1016/j.compchemeng.2022.107856},
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url = {https://www.sciencedirect.com/science/article/pii/S0098135422001946},
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author = {Fahad Matovu and Shuhaimi Mahadzir and Rasel Ahmed and Nor Erniza Mohammad Rozali},
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keywords = {Multilevel refrigeration, GDP Modelling, Synthesis and optimization, Logic based branch and bound},
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pages = {69-83},
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year = {2022},
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issn = {0263-8762},
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doi = {https://doi.org/10.1016/j.cherd.2022.08.027},
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doi = {10.1016/j.cherd.2022.08.027},
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url = {https://www.sciencedirect.com/science/article/pii/S0263876222004397},
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author = {Wenjin Zhou and Kashif Iqbal and Xiaogang Sun and Dinghui Gan and Chun Deng and José María Ponce-Ortega and Chunmao Chen},
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keywords = {Mathematicalv programming: Water supply network: Multi-source: Desalination: Optimum design},
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@article{dunning_huchette_lubin_2017,
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title={Jump: A modeling language for mathematical optimization},
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volume={59},
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DOI={10.1137/15m1020575},
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number={2},
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journal={SIAM Review},
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author={Dunning,
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Miles},
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year={2017},
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pages={295–320},
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URL = {https://doi.org/10.1137/15M1020575},
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eprint = {https://doi.org/10.1137/15M1020575},
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doi = {10.1137/15M1020575},
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abstract = {JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes advantage of advanced features of the Julia programming language to offer unique functionality while achieving performance on par with commercial modeling tools for standard tasks. In this work we will provide benchmarks, present the novel aspects of the implementation, and discuss how JuMP can be extended to new problem classes and composed with state-of-the-art tools for visualization and interactivity.}
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}
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number = {9},
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pages = {3276-3295},
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keywords = {optimization, mixed-integer programming, logic-based optimization},
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doi = {https://doi.org/10.1002/aic.14088},
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doi = {10.1002/aic.14088},
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url = {https://aiche.onlinelibrary.wiley.com/doi/abs/10.1002/aic.14088},
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eprint = {https://aiche.onlinelibrary.wiley.com/doi/pdf/10.1002/aic.14088},
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abstract = {Discrete-continuous optimization problems are commonly modeled in algebraic form as mixed-integer linear or nonlinear programming models. Since these models can be formulated in different ways, leading either to solvable or nonsolvable problems, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models. This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. An overview is provided of major research results that have emerged in this area. Basic concepts are emphasized as well as the major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixed-integer optimization models that exhibit strong continuous relaxations, which often translates into shorter computational times. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3276–3295, 2013},
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year = {2013}
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}
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pages = {98-103},
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year = {2015},
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issn = {0098-1354},
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doi = {https://doi.org/10.1016/j.compchemeng.2015.02.013},
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doi = {10.1016/j.compchemeng.2015.02.013},
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url = {https://www.sciencedirect.com/science/article/pii/S0098135415000587},
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author = {Francisco Trespalacios and Ignacio E. Grossmann},
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keywords = {Disjunctive programming, Mixed-integer programming, Big-M},
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pages = {2125-2141},
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year = {2000},
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issn = {0098-1354},
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doi = {https://doi.org/10.1016/S0098-1354(00)00581-0},
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doi = {10.1016/S0098-1354(00)00581-0},
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url = {https://www.sciencedirect.com/science/article/pii/S0098135400005810},
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author = {Sangbum Lee and Ignacio E. Grossmann},
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keywords = {Generalized disjunctive programming, Branch and bound, Mixed-integer nonlinear programming, Nonlinear convex hull},
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pages = {1891-1913},
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year = {2005},
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issn = {0098-1354},
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doi = {https://doi.org/10.1016/j.compchemeng.2005.04.004},
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doi = {10.1016/j.compchemeng.2005.04.004},
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url = {https://www.sciencedirect.com/science/article/pii/S0098135405000992},
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author = {Nicolas W. Sawaya and Ignacio E. Grossmann},
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keywords = {MIP, Disjunctive Programming, Cutting planes, Mixed integer linear programming, Strip-packing, Retrofit planning, Job-shop scheduling},

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