Global optimization of large-scale mixed-integer linear fractional programming problems: A reformulation-linearization method and process scheduling applications

Mixed‐integer linear fractional program (MILFP) is a class of mixed‐integer nonlinear programs (MINLP) where the objective function is the ratio of two linear functions and all constraints are linear. Global optimization of large‐scale MILFPs can be computationally intractable due to the presence of...

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Bibliographic Details
Published in:AIChE journal Vol. 59; no. 11; pp. 4255 - 4272
Main Authors: Yue, Dajun, Guillén-Gosálbez, Gonzalo, You, Fengqi
Format: Journal Article
Language:English
Published: New York Blackwell Publishing Ltd 01.11.2013
American Institute of Chemical Engineers
Subjects:
Algorithms
Batch processing
Integer programming
linearization
Mathematical functions
Mathematical problems
mixed-integer fractional programming
mixed-integer linear programs
mixed-integer nonlinear programs
Objective function
Optimization algorithms
reformulation
Scheduling
ISSN:0001-1541, 1547-5905
Online Access:Get full text
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Summary:Mixed‐integer linear fractional program (MILFP) is a class of mixed‐integer nonlinear programs (MINLP) where the objective function is the ratio of two linear functions and all constraints are linear. Global optimization of large‐scale MILFPs can be computationally intractable due to the presence of discrete variables and the pseudoconvex/pseudoconcave objective function. We propose a novel and efficient reformulation–linearization method, which integrates Charnes–Cooper transformation and Glover's linearization scheme, to transform general MILFPs into their equivalent mixed‐integer linear programs (MILP), allowing MILFPs to be globally optimized effectively with MILP methods. Extensive computational studies are performed to demonstrate the efficiency of this method. To illustrate its applications, we consider two batch scheduling problems, which are modeled as MILFPs based on the continuous‐time formulations. Computational results show that the proposed approach requires significantly shorter CPU times than various general‐purpose MINLP methods and shows similar performance than the tailored parametric algorithm for solving large‐scale MILFP problems. Specifically, it performs with respect to the CPU time roughly a half of the parametric algorithm for the scheduling applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4255–4272, 2013
Bibliography:Argonne National Laboratory via a Northwestern-Argonne Early Career Investigator Award for Energy Research
ark:/67375/WNG-ZBTBQBK9-7
ArticleID:AIC14185
istex:C9A2DF117AED517238B7B9C94B28AB173E87A809
Initiative for Sustainability and Energy at Northwestern University (ISEN)
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0001-1541
1547-5905
DOI:10.1002/aic.14185