Systematic modeling of discrete‐continuous optimization models through generalized disjunctive programming
Identifieur interne : 005C63 ( Main/Exploration ); précédent : 005C62; suivant : 005C64Systematic modeling of discrete‐continuous optimization models through generalized disjunctive programming
Auteurs : Ignacio E. Grossmann [États-Unis] ; Francisco Trespalacios [États-Unis]Source :
- AIChE Journal [ 0001-1541 ] ; 2013-09.
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- topic : Coût d'investissement.
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- 2ceq 2craw, 5true, Aiche, Aiche journal, Aiche journal september, Aiche september, Algebraic, Algebraic equations, Algebraic form, Algorithm, Basic step, Basic steps, Binaries number, Binary, Binary variables, Boolean, Boolean variables, Carnegie mellon university, Chem, Color figure, Comput, Comput chem, Constraint, Constraints number, Continuous relaxation, Continuous relaxations, Continuous variables, Convex, Convex hull, Craw, Craw craw, Disaggregated, Disaggregated variables, Disjunction, Disjunctive, Disjunctive branch, Disjunctive programming, Falseg, Feasible region, Feed tray, Ftrue, Gdp1, Generalized disjunctive programming, Global, Global constraints, Global optimization, Grossmann, Hull relaxation, I2dk, Inequality, Investment cost, Linear case, Linear constraints, Logic constraints, Logic proposition, Logic propositions, Lower bounds, Milp, Minlp, Modeling, Nodes solution time, Nonconvex, Nonlinear, Objective function, Online issue, Optimal design, Optimal solution, Optimization, Optimization problems, Particular case, Perfect formulation, Problem size, Process network, Process synthesis, Process systems engineering, Processing times, Programming, Propositional logic, Reformulation, Reformulations, Relaxation, Relaxation number, Ruiz, Sawaya, Scheduling, September, Small example, Solver, Superstructure, Systematic modeling framework, Tighter, Variables number, Yrawa, Yrawa yrawb, Yrawb.
- Teeft :
- 2ceq 2craw, 5true, Aiche, Aiche journal, Aiche journal september, Aiche september, Algebraic, Algebraic equations, Algebraic form, Algorithm, Basic step, Basic steps, Binaries number, Binary, Binary variables, Boolean, Boolean variables, Carnegie mellon university, Chem, Color figure, Comput, Comput chem, Constraint, Constraints number, Continuous relaxation, Continuous relaxations, Continuous variables, Convex, Convex hull, Craw, Craw craw, Disaggregated, Disaggregated variables, Disjunction, Disjunctive, Disjunctive branch, Disjunctive programming, Falseg, Feasible region, Feed tray, Ftrue, Gdp1, Generalized disjunctive programming, Global, Global constraints, Global optimization, Grossmann, Hull relaxation, I2dk, Inequality, Investment cost, Linear case, Linear constraints, Logic constraints, Logic proposition, Logic propositions, Lower bounds, Milp, Minlp, Modeling, Nodes solution time, Nonconvex, Nonlinear, Objective function, Online issue, Optimal design, Optimal solution, Optimization, Optimization problems, Particular case, Perfect formulation, Problem size, Process network, Process synthesis, Process systems engineering, Processing times, Programming, Propositional logic, Reformulation, Reformulations, Relaxation, Relaxation number, Ruiz, Sawaya, Scheduling, September, Small example, Solver, Superstructure, Systematic modeling framework, Tighter, Variables number, Yrawa, Yrawa yrawb, Yrawb.
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
Url:
DOI: 10.1002/aic.14088
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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</div></front></TEI><affiliations><list><country><li>États-Unis</li></country><region><li>Pennsylvanie</li></region><settlement><li>Pittsburgh</li></settlement></list><tree><country name="États-Unis"><region name="Pennsylvanie"><name sortKey="Grossmann, Ignacio E" sort="Grossmann, Ignacio E" uniqKey="Grossmann I" first="Ignacio E." last="Grossmann">Ignacio E. Grossmann</name></region><name sortKey="Grossmann, Ignacio E" sort="Grossmann, Ignacio E" uniqKey="Grossmann I" first="Ignacio E." last="Grossmann">Ignacio E. Grossmann</name><name sortKey="Trespalacios, Francisco" sort="Trespalacios, Francisco" uniqKey="Trespalacios F" first="Francisco" last="Trespalacios">Francisco Trespalacios</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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