TY - JOUR

T1 - Local Search Algorithms for the Beam Angles' Selection Problem in Radiotherapy

AU - Cabrera-Guerrero, Guillermo

AU - Rodriguez, Nibaldo

AU - Lagos, Carolina

AU - Cabrera, Enrique

AU - Johnson, Franklin

N1 - Funding Information:
Guillermo Cabrera-Guerrero wishes to acknowledge both DI 039.416/2017 Project and CONICYT/FONDECYT/INICIA-CION/11170456 Project for partially supporting this research.
Publisher Copyright:
© 2018 Guillermo Cabrera-Guerrero et al.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85047628350&partnerID=8YFLogxK

U2 - 10.1155/2018/4978703

DO - 10.1155/2018/4978703

M3 - Article

AN - SCOPUS:85047628350

VL - 2018

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 4978703

ER -