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

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  • Ali Tuncel
  • Felisa Preciado
  • Ronald Rardin
  • Mark Langer
  • Jean-Philippe Richard

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. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Ali Tuncel & Felisa Preciado & Ronald Rardin & Mark Langer & Jean-Philippe Richard, 2012. "Strong valid inequalities for fluence map optimization problem under dose-volume restrictions," Annals of Operations Research, Springer, vol. 196(1), pages 819-840, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:819-840:10.1007/s10479-010-0759-1
    DOI: 10.1007/s10479-010-0759-1
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    2. Eva Lee & Tim Fox & Ian Crocker, 2003. "Integer Programming Applied to Intensity-Modulated Radiation Therapy Treatment Planning," Annals of Operations Research, Springer, vol. 119(1), pages 165-181, March.
    3. Michael C. Ferris & Robert R. Meyer & Warren D’Souza, 2006. "Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches," International Series in Operations Research & Management Science, in: Gautam Appa & Leonidas Pitsoulis & H. Paul Williams (ed.), Handbook on Modelling for Discrete Optimization, chapter 0, pages 317-340, Springer.
    4. Felisa Preciado-Walters & Mark Langer & Ronald Rardin & Van Thai, 2006. "Column generation for IMRT cancer therapy optimization with implementable segments," Annals of Operations Research, Springer, vol. 148(1), pages 65-79, November.
    5. Hanif D. Sherali & Suvrajeet Sen, 1985. "Technical Note—On Generating Cutting Planes from Combinatorial Disjunctions," Operations Research, INFORMS, vol. 33(4), pages 928-933, August.
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    Cited by:

    1. Kelsey Maass & Minsun Kim & Aleksandr Aravkin, 2022. "A Nonconvex Optimization Approach to IMRT Planning with Dose–Volume Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1366-1386, May.
    2. Feng Qiu & Shabbir Ahmed & Santanu S. Dey & Laurence A. Wolsey, 2014. "Covering Linear Programming with Violations," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 531-546, August.

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