Radiotherapy treatment planning is a challenging large-scale optimization problem plagued by uncertainty. Following the robust optimization methodology, we propose a novel, spatially based uncertainty set for robust modeling of radiotherapy planning, producing solutions that are immune to unexpected changes in biological conditions. Our proposed uncertainty set realistically captures biological radiosensitivity patterns that are observed using recent advances in imaging, while its parameters can be personalized for individual patients. We exploit the structure of this set to devise a compact reformulation of the robust model. We develop a row-generation scheme to solve real, large-scale instances of the robust model. This method is then extended to a relaxation-based scheme for enforcing challenging, yet clinically important, dose-volume cardinality constraints. The computational performance of our algorithms, as well as the quality and robustness of the computed treatment plans, are demonstrated on simulated and real imaging data. Based on accepted performance measures, such as minimal target dose and homogeneity, these examples demonstrate that the spatially robust model achieves almost the same performance as the nominal model in the nominal scenario, and otherwise, the spatial model outperforms both the nominal and the box-uncertainty models.

翻译：放射治疗计划是一个受不确定性困扰的具有挑战性的大规模优化问题。遵循稳健优化方法论，我们提出了一种新颖的基于空间的不确定性集，用于放射治疗计划的稳健建模，生成能够抵御生物条件意外变化的解决方案。我们提出的不确定性集真实地捕捉了利用最新成像技术观察到的生物放射敏感性模式，同时其参数可根据患者个体进行个性化设置。我们利用该集合的结构，对稳健模型进行了紧凑重构。我们开发了一种行生成方案来解决真实大规模稳健模型实例。该方法随后扩展为基于松弛的方案，用于强制执行具有挑战性但临床重要的剂量-体积基数约束。我们的算法计算性能以及所计算治疗计划的质量和稳健性已在模拟和真实成像数据上得到验证。基于最小靶区剂量和均匀性等公认性能指标，这些示例表明，空间稳健模型在名义场景下取得了与名义模型几乎相同的性能，而在其他情况下，空间模型的表现优于名义模型和箱式不确定性模型。