A matheuristic approach to solve the multiobjective beam angle optimization problem in intensity-modulated radiation therapy

Selecting a suitable set of beam angles is an important but difficult task in intensity-modulated radiation therapy (IMRT) for cancer treatment. From a single objective point of view, this problem, known as the beam angle optimization (BAO) problem, is solved by finding a beam angle configuration (BAC) that leads to the best dose distribution, according to some objective function. As there exists a trade-off between the main goals in IMRT (to irradiate the tumor according to some prescription and to avoid surrounding healthy tissue), it makes sense to solve this problem from a multiobjective (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 that 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 for selecting 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 nonlinear programming algorithm. During the second phase, a set of nondominated points is generated for each promising locally optimal BAC and a dominance analysis among them is performed. The output of the procedure is a set of (approximately) efficient BACs that lead to good dose distributions. To demonstrate the viability of the method, the two-phase strategy is applied to a prostate case.