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Weighted Method Based Trust Region-Particle Swarm Optimization for Multi-Objective Optimization
American Journal of Applied Mathematics
Volume 3, Issue 3, June 2015, Pages: 81-89
Received: Feb. 28, 2015; Accepted: Apr. 3, 2015; Published: Apr. 14, 2015
Author
M. A. El-Shorbagy, Department of Basic Engineering Science, Faculty of Engineering, Menoufiya University, Shebin El-Kom, Egypt
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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.
Keywords
Multi-Objective Optimization, Trust Region algorithm, Particle Swarm Optimization, Pareto Optimal Set, Weighted Method
M. A. El-Shorbagy, Weighted Method Based Trust Region-Particle Swarm Optimization for Multi-Objective Optimization, American Journal of Applied Mathematics. Vol. 3, No. 3, 2015, pp. 81-89. doi: 10.11648/j.ajam.20150303.11
References
[1]
Y. Ou, “A hybrid trust region algorithm for unconstrained optimization,” Applied Numerical Mathem., vol. 61, pp. 900–909, 2011.
[2]
M. Ahookhosh, K. Amini and M.R. Peyghami, “A nonmonotone trust-region line search method for large-scale unconstrained optimization.” Applied Mathem. Modell., vol. 36, pp. 478–487, 2012.
[3]
M. Ahookhosh, and K. Amini, “A Nonmonotone trust region method with adaptive radius for unconstrained optimization problems,” Comput Mathem. Applications, vol. 60, pp. 411–422, 2010.
[4]
J. Zhang, K. Zhang and S. Qu, “A nonmonotone adaptive trust region method for unconstrained optimization based on conic model,” Applied Mathem. Computation, vol. 217, pp. 4265–4273, 2010.
[5]
B. El-Sobky, “A multiplier active-set trust-region algorithm for solving constrained optimization problem,” Applied Mathem. and Computation, vol. 219, pp. 928–946, 2012.
[6]
S. Kim, and J. Ryu, “A trust-region algorithm for bi-objective stochastic optimization,” Procedia Comput. Sci., vol. 4, pp. 1422–1430, 2011.
[7]
A.A. El-Sawy, Z.M. Hendawy, M.A. El-Shorbagy, “Trust-Region Algorithm based local search for Multi-objective Optimization”, IEEE 1st International Conference on Innovative Engineering Systems (IEEE-RAS ICIES2012), Alexandria, Egypt, December, 7-9, 2012.
[8]
J. Kennedy, R.C. Eberhart and Y. Shi, “Swarm Intelligence,” Morgan Kaufmann, 2001.
[9]
K.E. Parsopoulos, and M.N. Vrahatis, “Particle swarm optimization method in multiobjective problems,” Proceedings of the ACM 2002 Symposium on Applied Computing, pp. 603–607, 2002.
[10]
A.A. Mousa, M.A. El-Shorbagy and W.F. Abd-El-Wahed, “Local search based hybrid particle swarm optimization algorithm for multiobjective optimization,” Swarm Evolutionary Computation, vol. 3, pp. 1–14, 2012.
[11]
M.R. Sierra, and C.C. Coello, “Multi-objective particle swarm optimizers: a survey of the state-of-the-art,” Int. J. Computational Intell. Res., vol. 2, pp. 287–308, 2006.
[12]
L. Tang, “A Hybrid Multiobjective Evolutionary Algorithm for Multiobjective Optimization Problems,” IEEE Transactions on Evolutionary Computation, vol. 17, pp. 20–45, 2013.
[13]
C.A. Coello, D.A.V. Veldhuizen, G.B. Lamount, “Evolutionary Algorithms for Solving Multi-Objective Problems,” Kluwer Academic Publishers, 2001.
[14]
T. Friedrich, T. Kroeger, and F. Neumann, “Weighted preferences in evolutionary multi-objective optimization,” Int. J. Mach. Learn. & Cyber, vol. 4, pp. 139–148, 2013.
[15]
J. Dennis, M. El-Alem and K. Williamson, “A trust-region approach to nonlinear systems of equalities and inequalities,” SIAM J. Optimization, vol. 9, pp. 291–315, 1999.
[16]
W.F. Abd-El-Wahed, A.A. Mousa and M.A. El-Shorbagy, “Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems,” J. Computational Applied Mathem., vol. 235, pp. 1446–1453, 2011.
[17]
K. Deb, “Multi-objective Using Evolutionary Algorithms,” 1 st ed., John Wiley & Sons, LTD, New York, 2001.
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