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Pareto local search algorithms for the multi-objective beam angle optimisation problem

Author

Listed:
  • Guillermo Cabrera-Guerrero

    (Pontificia Universidad Católica de Valparaíso
    University of Auckland)

  • Andrew J. Mason

    (University of Auckland)

  • Andrea Raith

    (University of Auckland)

  • Matthias Ehrgott

    (Lancaster University Management School)

Abstract

Due to inherent trade-offs between tumour control and sparing of organs at risk, optimisation problems arising in intensity modulated radiation therapy planning are naturally modelled as multi-objective optimisation problems. Nevertheless, the vast majority of studies in the literature consider single objective approaches to these problems. The beam angle optimisation problem, that we address ion this paper, is one of these problems. It attempts to identify “good” beam angle configurations that allow the delivery of efficient treatment plans. In this paper two bi-objective local search algorithms are developed for the bi-objective beam angle optimisation problem, namely Pareto local search (PLS) and a variation of PLS we call adaptive PLS (aPLS). Both algorithms are able to find a set of (approximately) efficient beam angle configurations. While the PLS algorithm aims to find a set of efficient BACs by performing a very focused search over a specific region of the objective space, the aPLS algorithm aims to produce a set of efficient BACs that are well-distributed over the objective space. We test both algorithms on two prostate cancer cases and compare them to our previously proposed single objective local search algorithm.

Suggested Citation

  • Guillermo Cabrera-Guerrero & Andrew J. Mason & Andrea Raith & Matthias Ehrgott, 2018. "Pareto local search algorithms for the multi-objective beam angle optimisation problem," Journal of Heuristics, Springer, vol. 24(2), pages 205-238, April.
    • Handle: RePEc:spr:joheur:v:24:y:2018:i:2:d:10.1007_s10732-018-9365-1
    DOI: 10.1007/s10732-018-9365-1
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    References listed on IDEAS

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    1. Joana Dias & Humberto Rocha & Brígida Ferreira & Maria Lopes, 2014. "A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(3), pages 431-455, September.
    2. Dionne M. Aleman & H. Edwin Romeijn & James F. Dempsey, 2009. "A Response Surface Approach to Beam Orientation Optimization in Intensity-Modulated Radiation Therapy Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 62-76, February.
    3. Gino Lim & Laleh Kardar & Wenhua Cao, 2014. "A hybrid framework for optimizing beam angles in radiation therapy planning," Annals of Operations Research, Springer, vol. 217(1), pages 357-383, June.
    4. Robert Fourer & David M. Gay & Brian W. Kernighan, 1990. "A Modeling Language for Mathematical Programming," Management Science, INFORMS, vol. 36(5), pages 519-554, May.
    5. Hao Howard Zhang & Leyuan Shi & Robert Meyer & Daryl Nazareth & Warren D'Souza, 2009. "Solving Beam-Angle Selection and Dose Optimization Simultaneously via High-Throughput Computing," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 427-444, August.
    6. Misic, V.V. & Aleman, D.M. & Sharpe, M.B., 2010. "Neighborhood search approaches to non-coplanar beam orientation optimization for total marrow irradiation using IMRT," European Journal of Operational Research, Elsevier, vol. 205(3), pages 522-527, September.
    7. Margaret M. Wiecek & Matthias Ehrgott & Alexander Engau, 2016. "Continuous Multiobjective Programming," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 739-815, Springer.
    8. Lim, Gino J. & Cao, Wenhua, 2012. "A two-phase method for selecting IMRT treatment beam angles: Branch-and-Prune and local neighborhood search," European Journal of Operational Research, Elsevier, vol. 217(3), pages 609-618.
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    1. Guillermo Cabrera-Guerrero & Matthias Ehrgott & Andrew J. Mason & Andrea Raith, 2022. "Bi-objective optimisation over a set of convex sub-problems," Annals of Operations Research, Springer, vol. 319(2), pages 1507-1532, December.
    2. Guillermo Cabrera-Guerrero & Aníbal Álvarez & Joaquín Vásquez & Pablo A. Maya Duque & Lucas Villavicencio, 2022. "A VNS-Based Matheuristic to Solve the Districting Problem in Bicycle-Sharing Systems," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

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