Strong valid inequalities for fluence map optimization problem under dose-volume restrictions

Fluence map optimization problems are commonly solved in intensity modulated radiation therapy (IMRT) planning. We show that, when subject to dose-volume restrictions, these problems are NP-hard and that the linear programming relaxation of their natural mixed integer programming formulation can be...

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Published in:Annals of operations research Vol. 196; no. 1; pp. 819 - 840
Main Authors: Tuncel, Ali T., Preciado, Felisa, Rardin, Ronald L., Langer, Mark, Richard, Jean-Philippe P.
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2012
Springer Science + Business Media
Springer
Springer Nature B.V
Subjects:
Business and Management
Combinatorics
Constrictions
Fluence
Formulations
Inequalities
Inequalities (Mathematics)
Integer programming
Linear programming
MAP (programming language)
Mappings (Mathematics)
Mathematical optimization
Mixed integer
Nuclear radiation
Operations research
Operations Research/Decision Theory
Optimization
Planning
Programming
Radiation therapy
Radiotherapy
Restrictions
Studies
Theory of Computation
United States
Iran
Mixed Integer Programming Solver
Separation Heuristic
Valid Inequality
Intensity Modulate Radiation Therapy
Mixed Integer Programming Formulation
ISSN:0254-5330, 1572-9338
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Abstract Fluence map optimization problems are commonly solved in intensity modulated radiation therapy (IMRT) planning. We show that, when subject to dose-volume restrictions, these problems are NP-hard and that the linear programming relaxation of their natural mixed integer programming formulation can be arbitrarily weak. We then derive strong valid inequalities for fluence map optimization problems under dose-volume restrictions using disjunctive programming theory and show that strengthening mixed integer programming formulations with these valid inequalities has significant computational benefits.
AbstractList Fluence map optimization problems are commonly solved in intensity modulated radiation therapy (IMRT) planning. We show that, when subject to dose-volume restrictions, these problems are NP-hard and that the linear programming relaxation of their natural mixed integer programming formulation can be arbitrarily weak. We then derive strong valid inequalities for fluence map optimization problems under dose-volume restrictions using disjunctive programming theory and show that strengthening mixed integer programming formulations with these valid inequalities has significant computational benefits.
Fluence map optimization problems are commonly solved in intensity modulated radiation therapy (IMRT) planning. We show that, when subject to dose-volume restrictions, these problems are NP-hard and that the linear programming relaxation of their natural mixed integer programming formulation can be arbitrarily weak. We then derive strong valid inequalities for fluence map optimization problems under dose-volume restrictions using disjunctive programming theory and show that strengthening mixed integer programming formulations with these valid inequalities has significant computational benefits.[PUBLICATION ABSTRACT]
Audience Academic
Author Langer, Mark
Tuncel, Ali T.
Richard, Jean-Philippe P.
Preciado, Felisa
Rardin, Ronald L.
Author_xml – sequence: 1
  givenname: Ali T.
  surname: Tuncel
  fullname: Tuncel, Ali T.
  email: atuncel@purdue.edu
  organization: IBM Global Business Services
– sequence: 2
  givenname: Felisa
  surname: Preciado
  fullname: Preciado, Felisa
  organization: Smeal College of Business, Penn State University
– sequence: 3
  givenname: Ronald L.
  surname: Rardin
  fullname: Rardin, Ronald L.
  organization: Department of Industrial Engineering, University of Arkansas
– sequence: 4
  givenname: Mark
  surname: Langer
  fullname: Langer, Mark
  organization: School of Medicine, Indiana University
– sequence: 5
  givenname: Jean-Philippe P.
  surname: Richard
  fullname: Richard, Jean-Philippe P.
  organization: Department of Industrial and Systems Engineering, University of Florida
BackLink http://www.econis.eu/PPNSET?PPN=722922493$$DView this record in ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften
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COPYRIGHT 2012 Springer
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Keywords Mixed Integer Programming Solver
Separation Heuristic
Valid Inequality
Intensity Modulate Radiation Therapy
Mixed Integer Programming Formulation
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Snippet Fluence map optimization problems are commonly solved in intensity modulated radiation therapy (IMRT) planning. We show that, when subject to dose-volume...
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SubjectTerms Business and Management
Combinatorics
Constrictions
Fluence
Formulations
Inequalities
Inequalities (Mathematics)
Integer programming
Linear programming
MAP (programming language)
Mappings (Mathematics)
Mathematical optimization
Mixed integer
Nuclear radiation
Operations research
Operations Research/Decision Theory
Optimization
Planning
Programming
Radiation therapy
Radiotherapy
Restrictions
Studies
Theory of Computation
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Title Strong valid inequalities for fluence map optimization problem under dose-volume restrictions
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