A comparison of three optimization algorithms for intensity modulated radiation therapy

In intensity modulated treatment techniques, the modulation of each treatment field is obtained using an optimization algorithm. Multiple optimization algorithms have been proposed in the literature, e.g. steepest descent, conjugate gradient, quasi-Newton methods to name a few. The standard optimization algorithm in our in-house inverse planning tool KonRad is a quasi-Newton algorithm. Although this algorithm yields good results, it also has some drawbacks. Thus we implemented an improved optimization algorithm based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) routine. In this paper the improved optimization algorithm is described. To compare the two algorithms, several treatment plans are optimized using both algorithms. This included photon (IMRT) as well as proton (IMPT) intensity modulated therapy treatment plans. To present the results in a larger context the widely used conjugate gradient algorithm was also included into this comparison. On average, the improved optimization algorithm was six times faster to reach the same objective function value. However, it resulted not only in an acceleration of the optimization. Due to the faster convergence, the improved optimization algorithm usually terminates the optimization process at a lower objective function value. The average of the observed improvement in the objective function value was 37%. This improvement is clearly visible in the corresponding dose-volume-histograms. The benefit of the improved optimization algorithm is particularly pronounced in proton therapy plans. The conjugate gradient algorithm ranked in between the other two algorithms with an average speedup factor of two and an average improvement of the objective function value of 30%.