In this study, a hybrid approach combining trust region (TR) algorithm and particle swarm optimization (PSO) is proposed to solve multi-objective optimization problems (MOOPs). The proposed approach integrates the merits of both TR and PSO. Firstly, the MOOP converting by weighted method to a single objective optimization problem (SOOP) and some of the points in the search space are generated. Secondly, TR algorithm is applied to solve the SOOP to obtain a point on the Pareto frontier. Finally, all the points that have been obtained by TR are used as particles position for PSO; where homogeneous PSO is applied to get all nondominated solutions on the Pareto frontier. In addition, to restrict velocity of the particles and control it, a dynamic constriction factor is presented. Various kinds of multiobjective (MO) benchmark problems have been reported to show the importance of hybrid algorithm in generating Pareto optimal set. The results have demonstrated the superiority of the proposed algorithm to solve MOOPs.
| Published in | American Journal of Applied Mathematics (Volume 3, Issue 3) |
| DOI | 10.11648/j.ajam.20150303.11 |
| Page(s) | 81-89 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Multi-Objective Optimization, Trust Region algorithm, Particle Swarm Optimization, Pareto Optimal Set, Weighted Method
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APA Style
M. A. El-Shorbagy. (2015). Weighted Method Based Trust Region-Particle Swarm Optimization for Multi-Objective Optimization. American Journal of Applied Mathematics, 3(3), 81-89. https://doi.org/10.11648/j.ajam.20150303.11
ACS Style
M. A. El-Shorbagy. Weighted Method Based Trust Region-Particle Swarm Optimization for Multi-Objective Optimization. Am. J. Appl. Math. 2015, 3(3), 81-89. doi: 10.11648/j.ajam.20150303.11
AMA Style
M. A. El-Shorbagy. Weighted Method Based Trust Region-Particle Swarm Optimization for Multi-Objective Optimization. Am J Appl Math. 2015;3(3):81-89. doi: 10.11648/j.ajam.20150303.11
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Download@article{10.11648/j.ajam.20150303.11,
author = {M. A. El-Shorbagy},
title = {Weighted Method Based Trust Region-Particle Swarm Optimization for Multi-Objective Optimization},
journal = {American Journal of Applied Mathematics},
volume = {3},
number = {3},
pages = {81-89},
doi = {10.11648/j.ajam.20150303.11},
url = {https://doi.org/10.11648/j.ajam.20150303.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.11},
abstract = {In this study, a hybrid approach combining trust region (TR) algorithm and particle swarm optimization (PSO) is proposed to solve multi-objective optimization problems (MOOPs). The proposed approach integrates the merits of both TR and PSO. Firstly, the MOOP converting by weighted method to a single objective optimization problem (SOOP) and some of the points in the search space are generated. Secondly, TR algorithm is applied to solve the SOOP to obtain a point on the Pareto frontier. Finally, all the points that have been obtained by TR are used as particles position for PSO; where homogeneous PSO is applied to get all nondominated solutions on the Pareto frontier. In addition, to restrict velocity of the particles and control it, a dynamic constriction factor is presented. Various kinds of multiobjective (MO) benchmark problems have been reported to show the importance of hybrid algorithm in generating Pareto optimal set. The results have demonstrated the superiority of the proposed algorithm to solve MOOPs.},
year = {2015}
}
TY - JOUR T1 - Weighted Method Based Trust Region-Particle Swarm Optimization for Multi-Objective Optimization AU - M. A. El-Shorbagy Y1 - 2015/04/14 PY - 2015 N1 - https://doi.org/10.11648/j.ajam.20150303.11 DO - 10.11648/j.ajam.20150303.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 81 EP - 89 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20150303.11 AB - In this study, a hybrid approach combining trust region (TR) algorithm and particle swarm optimization (PSO) is proposed to solve multi-objective optimization problems (MOOPs). The proposed approach integrates the merits of both TR and PSO. Firstly, the MOOP converting by weighted method to a single objective optimization problem (SOOP) and some of the points in the search space are generated. Secondly, TR algorithm is applied to solve the SOOP to obtain a point on the Pareto frontier. Finally, all the points that have been obtained by TR are used as particles position for PSO; where homogeneous PSO is applied to get all nondominated solutions on the Pareto frontier. In addition, to restrict velocity of the particles and control it, a dynamic constriction factor is presented. Various kinds of multiobjective (MO) benchmark problems have been reported to show the importance of hybrid algorithm in generating Pareto optimal set. The results have demonstrated the superiority of the proposed algorithm to solve MOOPs. VL - 3 IS - 3 ER -
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