On column generation approaches for approximate solutions of quadratic programs in intensity-modulated radiation therapy

Fredrik Carlsson () and Anders Forsgren ()

Annals of Operations Research, 2014, vol. 223, issue 1, 481 pages

Abstract: 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. Copyright Springer Science+Business Media New York 2014

Keywords: Column generation; Conjugate-gradient method; Intensity-modulated radiation therapy; Step-and-shoot delivery (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10479-013-1360-1

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