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
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-010-0759-1

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.