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

doi:10.1007/s10479-010-0759-1

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 journal › Article › peer-review

14 Scopus citations

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 language	English (US)
Pages (from-to)	819-840
Number of pages	22
Journal	Annals of Operations Research
Volume	196
Issue number	1
DOIs	https://doi.org/10.1007/s10479-010-0759-1
State	Published - Jul 2012
Externally published	Yes

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10.1007/s10479-010-0759-1

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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.",

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AU - Preciado, Felisa

AU - Rardin, Ronald L.

AU - Langer, Mark

AU - Richard, Jean Philippe P.

PY - 2012/7

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AB - 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.

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JO - Annals of Operations Research

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

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