A hybrid approach to beam angle optimization in intensity-modulated radiation therapy

D. Bertsimas, V. Cacchiani*, D. Craft, O. Nohadani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


Intensity-Modulated Radiation Therapy is the technique of delivering radiation to cancer patients by using non-uniform radiation fields from selected angles, with the aim of reducing the intensity of the beams that go through critical structures while reaching the dose prescription in the target volume. Two decisions are of fundamental importance: to select the beam angles and to compute the intensity of the beams used to deliver the radiation to the patient. Often, these two decisions are made separately: first, the treatment planners, on the basis of experience and intuition, decide the orientation of the beams and then the intensities of the beams are optimized by using an automated software tool. Automatic beam angle selection (also known as Beam Angle Optimization) is an important problem and is today often based on human experience. In this context, we face the problem of optimizing both the decisions, developing an algorithm which automatically selects the beam angles and computes the beam intensities. We propose a hybrid heuristic method, which combines a simulated annealing procedure with the knowledge of the gradient. Gradient information is used to quickly find a local minimum, while simulated annealing allows to search for global minima. As an integral part of this procedure, the beam intensities are optimized by solving a Linear Programming model. The proposed method presents a main difference from previous works: it does not require to have on input a set of candidate beam angles. Indeed, it dynamically explores angles and the only discretization that is necessary is due to the maximum accuracy that can be achieved by the linear accelerator machine. Experimental results are performed on phantom and real-life case studies, showing the advantages that come from our approach.

Original languageEnglish (US)
Pages (from-to)2187-2197
Number of pages11
JournalComputers and Operations Research
Issue number9
StatePublished - Sep 2013


  • Beam angle optimization
  • Computational experiments
  • Gradient descent
  • Heuristic algorithm
  • Intensity-modulated radiation therapy
  • Linear programming
  • Simulated annealing

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research


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