We provide a framework for integrating two stages of radiation treatment planning (RTP): beam-angle selection (BAS) and dose optimization (DO). The framework is applied to both classical three-dimensional conformal radiotherapy and advanced intensity-modulated radiation therapy. Automated BAS and improved dose distribution are achieved within the framework. A metaheuristic approach, nested partitions, is applied. Alternative BAS and DO algorithms or commercial RTP software and clinical experience can be embedded within the framework to provide new methods for warm starts and evaluations of the quality of beam-angle set samples. Computational efficiency is achieved by utilizing high-throughput computing via the Condor system. Computational results show that our framework has led to a significant improvement in terms of solution quality and delivery time compared with current clinical practice.

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We present a simple, elegant algorithm for finding an optimal solution to a general min-max sequencing problem. This problem assumes many well-known scheduling problems as special cases, including problems with regular objectives (e.g., maximum lateness, maximum tardiness) as well as ones with non-regular objectives (e.g., maximum earliness-tardiness). Our algorithm is a dichotomy procedure in which highly efficient methods for the single-machine min-max lateness problem are leveraged. Despite the NP-hard nature of the problem in question, our method proves to be effective even for large-scale problem instances with hundreds of jobs. Through extensive numerical experiments, we demonstrate the working of our method on three different problem types, i.e., the maximum weighted completion time problem, the maximum weighted lateness problem, and the maximum weighted earliness-tardiness problem. The results show that the proposed method is effective for min-max sequencing problems.Index Terms -Min-Max sequencing, single machine, scheduling.