  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.
