Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming

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 th...

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Vydané v:AIChE journal Ročník 59; číslo 9; s. 3276 - 3295
Hlavní autori: Grossmann, Ignacio E., Trespalacios, Francisco
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Blackwell Publishing Ltd 01.09.2013
American Institute of Chemical Engineers
Predmet:
Algebra
Boolean algebra
logic-based optimization
Mathematical analysis
Mathematical models
mixed-integer programming
Nonlinear programming
Optimization
Programming
Representations
Systems engineering
ISSN:0001-1541, 1547-5905
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Popis
Shrnutí: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
Bibliografia:National Science Foundation - No. OCI-0750826
istex:73C8F92B1065F93CED2670F7AD7AD82B0B5B621A
ark:/67375/WNG-BGR1L9WP-Q
ArticleID:AIC14088
This article is dedicated to the memory of Professor Neil Amundson, who pioneered the application of mathematical modeling and analysis in chemical engineering.
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ISSN:0001-1541
1547-5905
DOI:10.1002/aic.14088