A comparison of mixed integer programming and fast simulated annealing for optimizing beam weights in radiation therapy

M. Langer, S. Morrill, R. Brown, O. Lee, R. Lane

Research output: Contribution to journalArticle

38 Scopus citations


Two competing methods for assigning intensities to radiation treatment beams were tested. One method was derived from mixed integer programming and the other was based on simulated annealing. The methods faced a common objective and identical constraints. The goal was to maximize the minimum tumor dose while keeping the dose in required fractions of normal organ volumes below a threshold for damage. The minimum tumor doses of the two methods were compared when all the dose-volume constraints were satisfied. A mixed integer linear program gave a minimum tumor dose that was at least 1.8 Gy higher than that given by simulated annealing in 7 of 19 trials. The difference was ≥5.4 Gy in 4 of 19 trials. In no case was the mixed integer solution one fraction size (1.8 Gy) worse than that of simulated annealing. The better solution provided by the mixed integer program allows tumor dose to increase without violating the dose-volume limits of normal tissues.

Original languageEnglish (US)
Pages (from-to)957-964
Number of pages8
JournalMedical physics
Issue number6
StatePublished - Jun 1996



  • dose-volume limits
  • mixed integer programming
  • optimization
  • radiation therapy planning
  • simulated annealing

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging

Cite this