UBC Undergraduate Research

An Application of the Extended Cutting Angle Method in Radiation Therapy Koch, Valentin


Global optimization of continuous, non-linear functions are very hard problems, especially when the functions are multivariate and when analytical information is not available. Heuristic methods like simulated annealing provide good results. However, if time is a critical factor, those methods may deliver suboptimal solutions and give little information about the quality of the solutions. Methods of Lipschitz optimization allow one to nd and con rm the global minimum of multivariate Lipschitz functions using a nite number of function evaluations. The Extended Cutting Angle Method (ECAM), proposed by Gleb Beliakov, is a fast method to optimize a Lipschitz function over multiple dimensions. The first objective was to fully implement the proposed algorithm and to test it on a family of classic global optimization problems. A second objective was to apply the algorithm to the problem of optimizing the radiation treatment for cancer patients. In radiotherapy, several x-ray beams are delivered to the tumor from di erent angles around the patient. The ECAM was tested against a simulated annealing algorithm to nd the optimal angles of the beams in order to deliver the prescribed radiation dose to the tumor and to minimize the damage to healthy tissue.

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