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Copy file name to clipboardExpand all lines: paper/paper.tex
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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}.
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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