One important problem in radiation therapy for cancer treatment is the selection of the set of beam angles radiation will be delivered from. A primary goal in this problem is to find a beam angle configuration (BAC) that leads to a clinically acceptable treatment plan. Further, this process must be done within clinically acceptable times. Since the problem of selecting beam angles in radiation therapy is known to be extremely hard to solve as well as time-consuming, both exact algorithms and population-based heuristics might not be suitable to solve this problem. In this paper, we compare two matheuristic methods based on local search algorithms, to approximately solve the beam angle optimisation problem (BAO). Although the steepest descent algorithm is able to find locally optimal BACs for the BAO problem, it takes too long before convergence, which is not acceptable in clinical practice. Thus, we propose to use a next descent algorithm that converges quickly to good quality solutions although no (local) optimality guarantee is given. We apply our two matheuristic methods on a prostate case which considers two organs at risk, namely, the rectum and the bladder. Results show that the matheuristic algorithm based on the next descent local search is able to quickly find solutions as good as the ones found by the steepest descent algorithm.
A self-adaptive hybrid steepest descent algorithm for solving a class of variational inequalities
