Comparing Local Search Algorithms for the Beam Angles Selection in Radiotherapy

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 of 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 three matheuristic methods based on local search algorithms, namely, steepest descent (SD), next descent (ND), and tabu search (TS) to approximately solve the beam angle optimisation problem (BAO). Although the SD algorithm is able to find locally optimal BACs for the BAO problem, it takes too long before convergence. For this reason, we try the ND algorithm as it has been shown to converge quickly to good quality solutions, although no (local) optimality guarantee is given. Finally, the well-known tabu search is also applied to the BAO problem in order to evaluate its performance. A prostate case which considers two organs at risk, namely the rectum and the bladder is considered in this paper. Results show that the ND finds solutions as good as the ones found by the SD algorithm. TS outperforms both the SD and the ND algorithms. Convergence curves for the all three algorithms are studied.