Local minima in anatomic aperture-based IMRT optimization

Purpose: An anatomic aperture‐based IMRT optimization program, named Ballista, was recently developed at our institution. Even though studies previously published concluded local minima in full‐IMRT optimization were not problematic, early observations with Ballista revealed their nuisance in the case of simplified IMRT. The purpose of this study was to evaluate the extent of local minima and their impact on the optimization process.Method and Materials: In Ballista beam weights are optimized by a bound‐constrained quasi‐Newton algorithm, which cannot escape local minima, even with a quadratic dose‐based objective function. Therefore, a high number (20 000) of descents were launched with random initial weights to explore the solution space for a varying number of beams. Actual treatment plan DVHs corresponding to different local minima were analyzed, yielding information on the nature of those minima. Results: When only four beam weights were optimized, only a few but very distinctive local minima were found. For a more realistic case of 20 beam weights, the optimization revealed an astonishing number of local minima, almost forming a continuum in the objective function value space. DVH analysis showed local minima generally favor one or more organs‐at‐risk (OARs) while the other objectives, especially those concerning the target volume, are less than optimal compared with the global minimum. Also, all minima lie on the boundary of the solution space. It was found that limiting the initial beam weights to small values eliminates the vast majority of the solution space containing local minima. Conclusion: With Ballista local minima proved to be a major problem. Plans corresponding to different minima differed drastically. In order to give the optimization a “clear shot” at the global minimum, initial beam weights must be limited to small values. This focuses the optimization on improving the target volume objectives since all OARs objectives are initially met. © 2005, American Association of Physicists in Medicine. All rights reserved.