Author: Yang Sheng, Qingrong Jackie Wu, Qiuwen Wu, Xin Wu, Dongrong Yang 👨🔬
Affiliation: Duke University Medical Center 🌍
Purpose: Convergence speed is crucial for an optimizer. Faster convergence leads to better solutions with fewer iterations and less time. Recently, a machine learning (ML)-assisted framework employing a one-layer neural network has demonstrated feasibility for IMRT FMO. This study evaluates its convergence speed advantages by comparing results with classical optimization under multiple convergence criteria, an optimization hyperparameter often hidden in most treatment planning systems.
Methods: Both ML and classical optimizers were tested using a 1e-4 convergence criterion, meaning the optimization stopped when the relative change in objective value was less than 1e-4. Initial fluence map configurations included reference plans (beamlets through targets set to 1) and 1000 random plans (beamlet fluence initialized randomly between 0 and 2) to simulate different starting conditions, with non-target beamlets set to 0 and normalization applied. Extended runs using a strict 1e-10 convergence criterion were also conducted. For each optimizer, 3D gamma analysis was performed on final dose. Both DVH- and gEUD-based objectives were formulated in quadratic form and optimized for prostate and head-and-neck cases.
Results: 1) Random initialization often caused classical optimization to converge prematurely, while ML-assisted framework consistently avoided such traps, achieving solutions closer to reference plan indicated by final objective values. 2) Under 1e-4 convergence criterion, classical optimization left many regions of solution space unexplored, particularly for gEUD-based objectives. While stricter convergence criteria such as 1e-10 improved classical optimizer's results but required thousands more iterations and significantly longer time. In contrast, ML-assisted optimization already achieved near-optimal solutions under 1e-4 criteria, minimizing the need for stricter criteria and avoiding excessive iterations or time.
Conclusion: The ML-assisted framework demonstrates superior convergence speed and robustness. It avoids premature convergence and reduces computational demands, making it a competitive alternative to classical optimization. The convergence criterion should be selected specifically to each optimizer to achieve similar results.