TRUST REGION-PARTICLE SWARM FOR MULTI-OBJECTIVE ENGINEERING COMPONENT DESIGN PROBLEMS

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Mohamed A. El-Shorbagy

Abstract

In this paper, we apply a proposed approach for solving multi-objective engineering design problem (MOEDP) with multiple objectives. In the proposed approach, a reference point based multi-objective optimization (MOO) using a combination between trust region (TR) algorithm and particle swarm optimization (PSO). The integration of TR and PSO has improved the quality of the founded solutions, also it guarantees the faster converge to the Pareto optimal solution. TR has provided the initial set (close to the Pareto set as possible) followed by PSO to improve the quality of the solutions and get all the points on the Pareto frontier. Detailed numerical results on three different MOEDP are reported to demonstrate the effectiveness and advantages of the proposed algorithm for solving practical MOEDP.

Keywords: Multi-objective engineering design problem; trust region; particle swarm optimization;

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How to Cite
El-Shorbagy, M. A. (2013). TRUST REGION-PARTICLE SWARM FOR MULTI-OBJECTIVE ENGINEERING COMPONENT DESIGN PROBLEMS. Journal of Global Research in Mathematical Archives(JGRMA), 1(3), 04–15. Retrieved from https://jgrma.com/index.php/jgrma/article/view/37
Section
Research Paper

References

C. C. Coello, “An Updated Survey of GA-Based Multiobjective Optimization Techniquesâ€, ACM Computing Surveys, ACM Press, Vol. 32, No. 2, pp. 109--143, June 2000.

M. Ahookhosh, K. Amini, "A Nonmonotone trust region method with adaptive radius for unconstrained optimization problems", Computers & Mathematics with Applications 60(3): 411-422 (2010).

B. El-Sobky, A Global Convergence Theory for Trust-Region Algorithm for General Nonlinear Programming Problem, Publicities in Fourth Saudi Science Conference, Al-Madinah Al-Munawarah, Kingdom of Saudi Arabia, March, 21st -24th, 2010.

J. Kennedy, R. C. Eberhart, and Y. Shi, "Swarm Intelligence", Morgan Kaufmann, 2001.

K. Miettinen, Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Boston, 1999.

K. Deb, A. Pratap, S. Moitra " Mechanical Component Design for multi-objective using Elitist non-dominated sorting GA." KanGAL Report No. 200002, 2000.

Y. Wang, S. Yang, G. Ni, S.L. Ho, Z.J. Liu, “An emigration genetic algorithm and its application to multiobjective optimal designs of electromagnetic devicesâ€, IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 2, MARCH 2004.

A. Osyczka, “Multicriteria optimization for engineering designâ€, In John S. Gero, editor, Design Optimization, pages 193–227. Academic Press, 1985.

V. Pareto, “Cours d’Économie politiqueâ€, volume I and II. F. Rouge, Lausanne, 1896-97.

K. Deb, J. Sundar, Udaya Bhaskara Rao N. and Shamik Chaudhuri, Reference Point Based Multi-Objective Optimization Using Evolutionary Algorithms, International Journal of Computational Intelligence Research, Vol.2, No.3 (2006), pp. 273–286.

X. W. Liu and Y. X. Yuan, "A robust trust region algorithm for solving general nonlinear programming", J. Comput. Math., 19: 309-322 (2001).

F. Wang, K. Zhang, C. Wang, L. Wang, A variant of trust-region methods for unconstrained optimization, Applied Mathematics and Computation 203(1): 297-307 (2008).

M. Ahookhosh, K. Amini, M. R. Peyghami, "A nonmonotone trust-region line search method for large-scale unconstrained optimization", Applied Mathematical Modelling, 36: 478–487 (2012).

Z. Shi, J. Guo, "A new trust region method for unconstrained optimization", Journal of Computational and Applied Mathematics 213: 509 – 520 (2008).

J. Zhang, K. Zhang, S. Qu, "A nonmonotone adaptive trust region method for unconstrained optimization based on conic model", Applied Mathematics and Computation 217(8): 4265-4273 (2010).

B. El-Sobky, "A global convergence theory for an active trust region algorithm for solving the general nonlinear programming problem", Applied Mathematics and computation archive,144 (1):127-157 (2003).

Y. Ji, K. Zhang, S. Qu, Y. Zhou, "A trust-region method by active-set strategy for general nonlinear optimization", Computers and Mathematics with Applications 54: 229–241 (2007).

S. Kim, J. Ryu, "A Trust-Region Algorithm for Bi-Objective Stochastic Optimization", Procedia Computer Science, 4: 1422-1430 (2011).

B. El-Sobky, "An Active-Set Trust-Region Algorithm for Solving Constrained Multi-Objective Optimization Problem", Applied Mathematical Sciences, 6: 1599 – 1612 (2012).

M. R. Sierra, and C. C. Coello, “Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the- Artâ€, International Journal of Computational Intelligence Research, 2(3): 287-308, 2006.

A. M. J. Skulimowski, “Classiï¬cation and properties of dominating points in vector optimizationâ€, In P. Klein-schmidt, F. J. Radermacher, W. Scweitzer, and H. Wil¬dermann, editors, Methods of Operations Research 58, pages 99–112. Frankfurt am Main, Germany: Athenum Verlag, 1989.

A. A. El-Sawy, Z. M. Hendawy, M. A. El-Shorbagy, Combining Trust-Region Algorithm and local search for Multi-objective Optimization, 3rd European Conference of Civil Engineering (ECCIE'12), Paris, France, December, 11-12, 2012.

R. Byrd, "Robust Trust Region methods for Nonlinearly Constrained Optimization", A talk presented at the second SIAM conference on optimization, Houston, TX (1987).

E. Omojokun, "Trust-region strategies for optimization with nonlinear equality and inequality constraints", PhD thesis, Department of Computer Science, University of Colorado, Boulder, Colorado, 1989. ditor, Spares Matrices and Thier Uses, pages 57-87. Academic Press, New York.

M. El-Alem, "A robust trust-region algorithm with a non-monotonic penalty parameter scheme for constrained optimization", SIAM J. Optim. 5 (2): 348-378 (1995).

J. Dennis, M. El-Alem, and K. Williamson, "A trust-region approach to nonlinear systems of equalities and inequalities", SIAM J Optimization, 9: 291-315 (1999).

S. K. Hwang, K. Koo, and J. S. Lee, "Homogeneous Particle Swarm Optimizer for Multi-objective Optimization Problem", ICGST International Journal on Artificial Intelligence and Machine Learning, AIML, 2006.

W. F. Abd-El-Wahed, A. A. Mousa, M. A. El-Shorbagy, "Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems", J. Computational Applied Mathematics 235(5): 1446-1453 (2011).

I. S. Duff, J. Nocedal, and J.K. Reid, â€The use of linear programming for the solution of sparse sets of nonlinear equationsâ€, SIAM J. Sci. Stat. Comput. 8: 99-108 (1987).

R. Fletcher, "Practical Methods of Optimization", (second edition) (JohnWiley and Sons, Chichester, 1987).