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Optimal configuration of gamma ray machine radiosurgery units: the sphere covering subproblem

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Abstract

We use reformulation techniques to model and solve a complex sphere covering problem occurring in the configuration of a gamma ray machine radiotherapy equipment unit.

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References

  1. Audet C., Hansen P., Jaumard B., Savard G.: Links between linear bilevel and mixed 0-1 programming problems. J. Optim. Theory Appl. 93(2), 273–300 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Brook A., Kendrick D., Meeraus A.: Gams, a user’s guide. ACM SIGNUM Newsl. 23(3-4), 10–11 (1988)

    Article  Google Scholar 

  3. Ferris, M., Shepard, D.: Optimization of gamma knife radiosurgery. In: Du, D.Z., Pardalos, P., Wang, J., (eds.) Discrete Mathematical Problems with Medical Applications, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 55, pp. 27–44. AMS (2000)

  4. Ferris M., Voelker M.: Neuro-dynamic programming for radiation treatment planning. Ann. Oper. Res. 119, 247–260 (2003)

    Article  MATH  Google Scholar 

  5. Ferris M., Lim J., Shepard D.: An optimization approach for the radiosurgery treatment planning. SIAM J. Optim. 13(3), 921–937 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Floudas C.: Deterministic Global Optimization. Kluwer Academic Publishers, Dordrecht (2000)

    Google Scholar 

  7. Fortet R.: Applications de l’algèbre de boole en recherche opérationelle. Revue Française de Recherche Opérationelle 4, 17–26 (1960)

    Google Scholar 

  8. Fourer R., Gay D.: The AMPL Book. Duxbury, Pacific Grove (2002)

    Google Scholar 

  9. ILOG: ILOG CPLEX 10.1 User’s Manual. ILOG S.A., Gentilly, France (2006)

  10. Jitprapaikulsarn, S.: An optimization-based treatment planner for gamma knife radiosurgery. Ph.D. Thesis, Case Western Reserve University (2005)

  11. Leyffer S.: User Manual for minlp_bb. Technical Report, University of Dundee, UK (1999)

  12. Liberti, L.: Writing global optimization software. In: Liberti and Maculan [16], pp. 211–262 (2006)

  13. Liberti L.: Compact linearization of binary quadratic problems. 4OR 5(3), 231–245 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. Liberti, L.: Reformulation techniques in mathematical programming. Thèse d’Habilitation à Diriger des Recherches (2007)

  15. Liberti, L., Dražic, M.: Variable neighbourhood search for the global optimization of constrained nlps. In: Proceedings of GO Workshop, Almeria, Spain (2005)

  16. Liberti, L.,Maculan, N. (eds.): Global Optimization: from Theory to Implementation. Springer, Berlin (2006)

  17. Lim, J.: Optimization in radiation treatment planning. Ph.D. Thesis, University of Wisconsin-Madison (2002)

  18. Olafsson A., Wright S.: Linear programming formulations and algorithms for radiotherapy treatment planning. Optim. Methods Softw. 21(2), 201–231 (2004)

    Article  MathSciNet  Google Scholar 

  19. Soutou A., Dai Y.: Global optimization approach to unequal sphere packing problems in 3D. J. Optim. Theory Appl. 114(3), 671–694 (2002)

    Article  MathSciNet  Google Scholar 

  20. Tawarmalani M., Sahinidis N.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

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Authors and Affiliations

  1. LIX, École Polytechnique, 91128, Palaiseau, France

    Leo Liberti

  2. COPPE, Systems Engineering, Federal University of Rio de Janeiro, P. O. Box 68511, 21941-972, Rio de Janeiro, Brazil

    Nelson Maculan

  3. Physics Department, Wuhan University, Wuhan, 430072, People’s Republic of China

    Yue Zhang

Authors
  1. Leo Liberti
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  2. Nelson Maculan
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  3. Yue Zhang
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Correspondence to Leo Liberti.

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Liberti, L., Maculan, N. & Zhang, Y. Optimal configuration of gamma ray machine radiosurgery units: the sphere covering subproblem. Optim Lett 3, 109–121 (2009). https://doi.org/10.1007/s11590-008-0095-4

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  • DOI: https://doi.org/10.1007/s11590-008-0095-4

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