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

Ali T. Tuncel, Felisa Preciado, Ronald L. Rardin, Mark Langer, Jean Philippe P Richard

Research output: Contribution to journalArticle

12 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)819-840
Number of pages22
JournalAnnals of Operations Research
Volume196
Issue number1
DOIs
StatePublished - Jul 2012

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Optimization problem
Mixed integer programming
Valid inequalities
Linear programming
Radiation
NP-hard
Planning
Therapy
Programming

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Decision Sciences(all)

Cite this

Strong valid inequalities for fluence map optimization problem under dose-volume restrictions. / Tuncel, Ali T.; Preciado, Felisa; Rardin, Ronald L.; Langer, Mark; Richard, Jean Philippe P.

In: Annals of Operations Research, Vol. 196, No. 1, 07.2012, p. 819-840.

Research output: Contribution to journalArticle

Tuncel, Ali T. ; Preciado, Felisa ; Rardin, Ronald L. ; Langer, Mark ; Richard, Jean Philippe P. / Strong valid inequalities for fluence map optimization problem under dose-volume restrictions. In: Annals of Operations Research. 2012 ; Vol. 196, No. 1. pp. 819-840.
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