On column generation approaches for approximate solutions of quadratic programs in intensity-modulated radiation therapy
2014 (English)In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 223, no 1, 471-481 p.Article in journal (Refereed) Published
This paper deals with numerical behavior of a recently presented column generation approach for optimization of so called step-and-shoot radiotherapy treatment plans. The approach and variants of it have been reported to be efficient in practice, finding near-optimal solutions by generating only a low number of columns. The impact of different restrictions on the columns in a column generation method is studied, and numerical results are given for quadratic programs corresponding to three patient cases. In particular, it is noted that with a bound on the two-norm of the columns, the method is equivalent to the conjugate-gradient method. Further, the above-mentioned column generation approach for radiotherapy is obtained by employing a restriction based on the infinity-norm and non-negativity. The column generation method has weak convergence properties if restricted to generating feasible step-and-shoot plans, with a "tailing-off" effect for the objective values. However, the numerical results demonstrate that, like the conjugate-gradient method, a rapid decrease of the objective value is obtained in the first few iterations. For the three patient cases, the restriction on the columns to generate feasible step-and-shoot plans has small effect on the numerical efficiency.
Place, publisher, year, edition, pages
2014. Vol. 223, no 1, 471-481 p.
Column generation, Conjugate-gradient method, Intensity-modulated radiation therapy, Step-and-shoot delivery
IdentifiersURN: urn:nbn:se:kth:diva-158803DOI: 10.1007/s10479-013-1360-1ISI: 000345073400024OAI: oai:DiVA.org:kth-158803DiVA: diva2:785288
FunderSwedish Research Council
QC 201502022015-02-022015-01-122015-02-02Bibliographically approved