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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This work was supported in part by NCI STTR grant number 1 R01 CA12345-01.
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Tuncel, A.T., Preciado, F., Rardin, R.L. et al. Strong valid inequalities for fluence map optimization problem under dose-volume restrictions. Ann Oper Res 196, 819–840 (2012). https://doi.org/10.1007/s10479-010-0759-1
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DOI: https://doi.org/10.1007/s10479-010-0759-1