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

• 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

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...