AbstractID: 8222 Title: Acceleration of IMRT Optimization using Objective Function... without Replacement

AbstractID: 8222 Title: Acceleration of IMRT Optimization using Objective Function Random Sampling
without Replacement
In the optimization portion of IMRT planning, a large fraction of the computational time is spent evaluating the objective function. At
each iteration, the objective function is computed as a sum of means (1/Nj) Σi fj(Di), where fj(Di) is the objective function contribution
of the ith voxel in the jth organ containing Nj voxels. If the distribution of voxel dose functions is viewed as a statistical sample for a
finite population, we may think of computing the objective function as calculating the population mean at each iteration. By randomly
selecting a subset of voxels without replacement from the set of all relevant voxels and calculating a mean for this subset, an estimate
of the true objective function value may be obtained in a fraction of the computational time. We applied this idea to an optimization of
a C-shaped target surrounding a critical structure. Using the simulated annealing algorithm and a quadratic objective function, we
found a 50% reduction in the optimization time when just 1/8th of the Nj voxels are sampled. The final dose distributions obtained
with the randomly sampled subset of Nj voxels are comparable to those produced when the full set of voxels is sampled. We present
the mathematical justification of random sampling without replacement in a finite population and discuss the broad applicability of
this technique to IMRT optimization problems.