A Matheuristic Approach to Solve the Multi-objective Beam Angle Optimisation Problem in Intensity Modulated Radiation Therapy Guillermo Cabrera G. 1,2, * , Matthias Ehrgott 3 , Andrew Mason 1 , and Andrea Raith 1 1 Department of Engineering Science, University of Auckland (New Zealand) 2 Escuela de Ingenier´ıa Inform´atica, Pontificia Universidad Cat´ olica de Valpara´ıso (Chile) 3 Management School, Lancaster University (United Kingdom) Received: date / Accepted: date Abstract Selecting a suitable set of beam angles is an important but difficult task in intensity modulated radiation therapy (IMRT) for cancer treat- ment. From a single objective point of view this problem, known as beam angle optimisation (BAO) problem, is solved by finding a beam angle configuration (BAC) that leads to the best dose distribution, according to some objective function. Because there exists a trade-off between the main goals in IMRT (to irradiate the tumour according to some prescrip- tion and to avoid surrounding healthy tissue) it makes sense to solve this problem from a multi-objective (MO) point of view. When doing so, a solution of the BAO problem is no longer a single BAC but instead a set of BACs which lead to a set of dose distributions that, depending on both dose prescription and physician preferences, can be selected as the preferred treatment. We solve this MO problem using a two-phase strategy. During the first phase, a deterministic local search algorithm is used to select a set of locally optimal BACs, according to a single objective function. During this search, an optimal dose distribution for each BAC, with respect to the single objective function, is calculated using an exact non-linear pro- gramming algorithm. During the second phase a set of non-dominated * Please address correspondence to guillermo.cabrera@ucv.cl 1