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Two Effective Heuristics for Beam Angle Optimization in Radiation Therapy

In radiation therapy, mathematical methods have been used for optimizing treatment planning for delivery of sufficient dose to the cancerous cells while keeping the dose to critical surrounding structures minimal. This optimization problem can be modeled using mixed integer programming (MIP) whose solution gives the optimal beam orientation as well as optimal beam intensity. The challenge, however, is the computation time for this large scale MIP. We propose and investigate two novel heuristic approaches to reduce the computation time considerably while attaining high-quality solutions. We introduce a family of heuristic cuts based on the concept of 'adjacent beams' and a beam elimination scheme based on the contribution of each beam to deliver the dose to the tumor in the ideal plan in which all potential beams can be used simultaneously. We show the effectiveness of these heuristics for intensity modulated radiation therapy (IMRT) and stereotactic body radiation therapy (SBRT) on a clinical liver case.