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International Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) Techniques in Constraint Programming

CPAIOR 2010: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems pp 56–70Cite as

Hybrid Methods for the Multileaf Collimator Sequencing Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6140))

Abstract

The multileaf collimator sequencing problem is an important component of the effective delivery of intensity modulated radiotherapy used in the treatment of cancer. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. In this paper we extend the state-of-the-art optimisation methods for this problem, which are based on constraint programming and decomposition. Specifically, we propose two alternative hybrid methods: one based on Lagrangian relaxation and the other on column generation. Empirical evaluation on both random and clinical problem instances shows that these approaches can out-perform the state-of-the-art by an order of magnitude in terms of time. Larger problem instances than those within the capability of other approaches can also be solved with the methods proposed.

This work was supported by Science Foundation Ireland under Grant Number 05/IN/I886.

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References

  1. Agazaryan, N., Solberg, T.D.: Segmental and dynamic intensity-modulated radiotherapy delivery techniques for micro-multileaf collimator. Medical Physics 30(7), 1758–1767 (2003)

    Article  Google Scholar 

  2. Ahuja, R.K., Hamacher, H.W.: A network flow algorithm to minimize beamon time for unconstrained multileaf collimator problems in cancer radiation therapy. Netw. 45(1), 36–41 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Baatar, D., Boland, N., Brand, S., Stuckey, P.J.: Minimum cardinality matrix decomposition into consecutive-ones matrices: CP and IP approaches. In: Van Hentenryck, P., Wolsey, L.A. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 1–15. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Baatar, D., Hamacher, H.W., Ehrgott, M., Woeginger, G.J.: Decomposition of integer matrices and multileaf collimator sequencing. Discrete Applied Mathematics 152(1-3), 6–34 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bahr, G.K., Kereiakes, J.G., Horwitz, H., Finney, R., Galvin, J., Goode, K.: The method of linear programming applied to radiation therapy planning. Radiology 91, 686–693 (1968)

    Google Scholar 

  6. Boland, N., Hamacher, H.W., Lenzen, F.: Minimizing beam-on time in cancer radiation treatment using multileaf collimators. Networks 43(4), 226–240 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bortfeld, T.R., Kahler, D.L., Waldron, T.J., Boyer, A.L.: X-ray field compensation with multileaf collimators. International Journal of Radiation Oncology Biology Physics 28(3), 723–730 (1994)

    Google Scholar 

  8. Boyd, S., Xiao, L., Mutapic, A.: Subgradient methods. In: Notes for EE392o, Standford University (2003)

    Google Scholar 

  9. Brand, S.: The sum-of-increments constraints in the consecutive-ones matrix decomposition problem. In: SAC 2009: 24th Annual ACM Symposium on Applied Computing (2009)

    Google Scholar 

  10. Cambazard, H., O’Mahony, E., O’Sullivan, B.: A shortest path-based approach to the multileaf collimator sequencing problem. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 41–55. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Collins, M.J., Kempe, D., Saia, J., Young, M.: Nonnegative integral subset representations of integer sets. Inf. Process. Lett. 101(3), 129–133 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Desaulniers, G., Desrosiers, J., Solomon, M.M.: Column Generation. Springer, Heidelberg (2005)

    Book  MATH  Google Scholar 

  13. du Merle, O., Villeneuve, D., Desrosiers, J., Hansen, P.: Stabilized column generation. Discrete Math. 194(1-3), 229–237 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ehrgott, M., Güler, Ç., Hamacher, H.W., Shao, L.: Mathematical optimization in intensity modulated radiation therapy. 4OR 6(3), 199–262 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Engel, K.: A new algorithm for optimal multileaf collimator field segmentation. Discrete Applied Mathematics 152(1-3), 35–51 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ernst, A.T., Mak, V.H., Mason, L.A.: An exact method for the minimum cardinality problem in the planning of imrt. INFORMS Journal of Computing (2009) (to appear)

    Google Scholar 

  17. Focacci, F., Lodi, A., Milano, M.: Cost-based domain filtering. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 189–203. Springer, Heidelberg (1999)

    Google Scholar 

  18. Hamacher, H.W., Ehrgott, M.: Special section: Using discrete mathematics to model multileaf collimators in radiation therapy. Discrete Applied Mathematics 152(1-3), 4–5 (2005)

    Article  MathSciNet  Google Scholar 

  19. Kalinowski, T.: The complexity of minimizing the number of shape matrices subject to minimal beam-on time in multileaf collimator field decomposition with bounded fluence. Discrete Applied Mathematics (in press)

    Google Scholar 

  20. Kalinowski, T.: A duality based algorithm for multileaf collimator field segmentation with interleaf collision constraint. Discrete Applied Mathematics 152(1-3), 52–88 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Langer, M., Thai, V., Papiez, L.: Improved leaf sequencing reduces segments or monitor units needed to deliver imrt using multileaf collimators. Medical Physics 28(12), 2450–2458 (2001)

    Article  Google Scholar 

  22. Lübbecke, M.E., Desrosiers, J.: Selected topics in column generation. Oper. Res. 53(6), 1007–1023 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  23. Menana, J., Demassey, S.: Sequencing and counting with the multicost-regular constraint. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 178–192. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  24. Sellmann, M.: Theoretical foundations of CP-based lagrangian relaxation. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 634–647. Springer, Heidelberg (2004)

    Google Scholar 

  25. Caner Taskin, Z., Cole Smith, J., Edwin Romeijn, H., Dempsey, J.F.: Collimator leaf sequencing in imrt treatment planning. Operations Research 119 (2009) (submitted)

    Google Scholar 

  26. Wake, G.M.G.H., Boland, N., Jennings, L.S.: Mixed integer programming approaches to exact minimization of total treatment time in cancer radiotherapy using multileaf collimators. Comput. Oper. Res. 36(3), 795–810 (2009)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Cork Constraint Computation Centre, Department of Computer Science, University College Cork, Ireland

    Hadrien Cambazard, Eoin O’Mahony & Barry O’Sullivan

Authors
  1. Hadrien Cambazard
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  2. Eoin O’Mahony
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  3. Barry O’Sullivan
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Editor information

Editors and Affiliations

  1. DEIS, University of Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

    Andrea Lodi , Michela Milano  & Paolo Toth ,  & 

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Cambazard, H., O’Mahony, E., O’Sullivan, B. (2010). Hybrid Methods for the Multileaf Collimator Sequencing Problem. In: Lodi, A., Milano, M., Toth, P. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2010. Lecture Notes in Computer Science, vol 6140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13520-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-13520-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13519-4

  • Online ISBN: 978-3-642-13520-0

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