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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Bibliographic Details
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
Online Access:Get full text
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Summary: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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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-010-0759-1