Pareto local search algorithms for the multi-objective beam angle optimisation problem

2018 ◽  
Vol 24 (2) ◽  
pp. 205-238 ◽  
Author(s):  
Guillermo Cabrera-Guerrero ◽  
Andrew J. Mason ◽  
Andrea Raith ◽  
Matthias Ehrgott
Keyword(s):  
Local Search ◽  
Search Algorithms ◽  
Beam Angle ◽  
Local Search Algorithms ◽  
Multi Objective ◽  
Pareto Local Search

scholarly journals Comparing Multi-Objective Local Search Algorithms for the Beam Angle Selection Problem

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 159
Author(s):  
Guillermo Cabrera-Guerrero ◽  
Carolina Lagos
Keyword(s):  
Local Search ◽  
Organs At Risk ◽  
Intensity Modulated Radiation Therapy ◽  
Selection Problem ◽  
Large Set ◽  
Beam Angle ◽  
Local Search Algorithms ◽  
Multi Objective ◽  
Single Objective ◽  
Therapy Treatment

In intensity-modulated radiation therapy, treatment planners aim to irradiate the tumour according to a medical prescription while sparing surrounding organs at risk as much as possible. Although this problem is inherently a multi-objective optimisation (MO) problem, most of the models in the literature are single-objective ones. For this reason, a large number of single-objective algorithms have been proposed in the literature to solve such single-objective models rather than multi-objective ones. Further, a difficulty that one has to face when solving the MO version of the problem is that the algorithms take too long before converging to a set of (approximately) non-dominated points. In this paper, we propose and compare three different strategies, namely random PLS (rPLS), judgement-function-guided PLS (jPLS) and neighbour-first PLS (nPLS), to accelerate a previously proposed Pareto local search (PLS) algorithm to solve the beam angle selection problem in IMRT. A distinctive feature of these strategies when compared to the PLS algorithms in the literature is that they do not evaluate their entire neighbourhood before performing the dominance analysis. The rPLS algorithm randomly chooses the next non-dominated solution in the archive and it is used as a baseline for the other implemented algorithms. The jPLS algorithm first chooses the non-dominated solution in the archive that has the best objective function value. Finally, the nPLS algorithm first chooses the solutions that are within the neighbourhood of the current solution. All these strategies prevent us from evaluating a large set of BACs, without any major impairment in the obtained solutions’ quality. We apply our algorithms to a prostate case and compare the obtained results to those obtained by the PLS from the literature. The results show that algorithms proposed in this paper reach a similar performance than PLS and require fewer function evaluations.

scholarly journals Local Search Algorithms for the Beam Angles’ Selection Problem in Radiotherapy

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Guillermo Cabrera-Guerrero ◽  
Nibaldo Rodriguez ◽  
Carolina Lagos ◽  
Enrique Cabrera ◽  
Franklin Johnson
Keyword(s):  
Radiation Therapy ◽  
Local Search ◽  
Organs At Risk ◽  
Treatment Plan ◽  
Search Algorithms ◽  
Steepest Descent ◽  
Beam Angle ◽  
Local Search Algorithms ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm

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.

The Local Search Algorithms for Maximum 3-Satisfiablility Problem

2010 ◽  
Vol 33 (7) ◽  
pp. 1127-1139
Author(s):  
Da-Ming ZHU ◽  
Shao-Han MA ◽  
Ping-Ping ZHANG
Keyword(s):  
Local Search ◽  
Search Algorithms ◽  
Local Search Algorithms
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