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.

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

The Hybrid Differential Evolution with Dynamic Scaling Mutation and Wrapper Local Search for Optimization Problems

2013 ◽  
Vol 479-480 ◽  
pp. 989-995
Author(s):  
Chun Liang Lu ◽  
Shih Yuan Chiu ◽  
Chih Hsu Hsu ◽  
Shi Jim Yen
Keyword(s):  
Local Search ◽  
Differential Evolution ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Optimization Problems ◽  
Search Space ◽  
Dynamic Scaling ◽  
Multi Objective ◽  
Wide Range ◽  
Single Objective

In this paper, an improved hybrid Differential Evolution (DE) is proposed to enhance optimization performance by cooperating Dynamic Scaling Mutation (DSM) and Wrapper Local Search (WLS) schemes. When evolution speed is standstill, DSM can improve searching ability to achieve better balance between exploitation and exploration in the search space. Furthermore, WLS can disturb individuals to fine tune the searching range around and then properly find better solutions in the evolution progress. The effective particle encoding representation named Particle Segment Operation-Machine Assignment (PSOMA) that we previously published is also applied to always produce feasible candidate solutions for hybrid DE model to solve the Flexible Job-Shop Scheduling Problem (FJSP). To test the performance of the proposed hybrid method, the experiments contain five frequently used CEC 2005 numerical functions and three representative FJSP benchmarks for single-objective and multi-objective optimization verifications, respectively. Compare the proposed method with the other related published algorithms, the simulation results indicate that our proposed method exhibits better performance for solving most the test functions for single-objective problems. In addition, the wide range of Pareto-optimal solutions and the more Gantt chart diversities can be obtained for the multi-objective FJSP in practical decision-making considerations.

scholarly journals A Multi-objective Version of the Lin-Kernighan Heuristic for the Traveling Salesman Problem

2018 ◽  
Vol 25 (1) ◽  
pp. 48
Author(s):  
Emerson Bezerra De Carvalho ◽  
Elizabeth Ferreira Gouvêa Goldbarg ◽  
Marco Cesar Goldbarg
Keyword(s):  
Local Search ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
Symmetric Case ◽  
Traveling Salesman ◽  
Weighted Sum ◽  
Pareto Dominance ◽  
Multi Objective ◽  
The Traveling Salesman Problem ◽  
Single Objective

The Lin and Kernighan’s algorithm for the single objective Traveling Salesman Problem (TSP) is one of the most efficient heuristics for the symmetric case. Although many algorithms for the TSP were extended to the multi-objective version of the problem (MTSP), the Lin and Kernighan’s algorithm was still not fully explored. Works that applied the Lin and Kernighan’s algorithm for the MTSP were driven to weighted sum versions of the problem. We investigate the LK from a Pareto dominance perspective. The multi-objective LK was implemented within two local search schemes and applied to 2 to 4-objective instances. The results  showed that the proposed algorithmic variants obtained better results than a state-of-the-art algorithm.

Supplier Selection Problem: A Multi-Objective Model Considering both All-Unit and Incremental Discounts with Multiple-Item

2014 ◽  
Vol 606 ◽  
pp. 271-275
Author(s):  
Ismed Iskandar ◽  
Soroush Avakh Darestani ◽  
S. Ghavami ◽  
Amir Azizi
Keyword(s):  
Supplier Selection ◽  
Mathematical Formulation ◽  
Selection Problem ◽  
Special Importance ◽  
Multi Objective ◽  
Numerical Example ◽  
Multiple Item ◽  
Objective Model ◽  
Supplier Selection Problem ◽  
Single Objective

In supply chain management, supplier selection has a special importance. In this paper, a multi-objective model is developed based on decisions on quality, service level and cost of purchased goods. The difference of this research is to consider discount parameter into the model. A numerical example for three proposed suppliers is interpreted. The model has been solved in two steps: 1-single-objective, 2-multi-objective approach. According to Lpmetric solution, results can predict optimum selection of suppliers as well as the purchased goods amount. The results show that the single objective problem has better result than multi-objective function. This paper is organized by six sections: in next section, some previous studies and researches on supplier selection problem considering discount and non-considering discount have been discussed. In section 3, mathematical formulation of the supplier selection model considering all-unit and incremental with multiple-item is presented. In section 4, aLP metrics solution is dedicated. In section 5, a numerical example is given and the results are presented. Finally in section 6, conclusions of this research are discussed.

scholarly journals Multi-Objective Test Case Selection: Local Search Approaches for the NSGA-II algorithm

2020 ◽  
Author(s):  
Luciano Soares De Souza
Keyword(s):  
Local Search ◽  
Software Testing ◽  
Search Algorithms ◽  
Selection Problem ◽  
Objective Test ◽  
Test Case ◽  
Nsga Ii ◽  
Test Case Selection ◽  
Multi Objective ◽  
Case Selection

The software testing process can be very expensive and it is important to find ways in order to reduce its costs. Test case selection techniques can be used in order to reduce the amount of tests to execute and this way reducing the costs. Search algorithms are very promising approach to deal with the test case selection problem. This work proposes new hybrid algorithms for multiobjective test case selection by adding local search mechanisms into the NSGAII algorithm. The results showed that some of the mechanisms were capable of improve the NSGA-II algorithm.

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