Abstract
Particle swarm optimization (PSO) and differential evolution (DE) have their similarities and compatibility in the design update process, such that a new design vector is determined by using neighborhood designs under algorithm control parameters. The paper deals with an integrated method of a hybrid PSO (HPSO) algorithm combined with DE in order to refine the optimization performance. PSO and DE also possess common characteristics compared with genetic algorithm (GA). The crossover- and mutation-like operators are suggested in the HPSO. A bounce back method is also implemented to prevent the design from locating out of design spaces during the optimization process. For the purpose of further enhancing the search capabilities, such HPSO is combined with the Q-learning that is one of efficient reinforcement learning methods. Using a number of nonlinear multimodal functions and engineering optimization problems, the proposed algorithms of HPSO and HPSO with Q-learning are compared with PSO DE and GA.
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References
J. Kennedy and R. C. Eberhart, Particle Swarm Optimization, Proceedings of the IEEE International Conference on Neural Networks, 4 (1995) 1942–194.
P. C. Fourie and A. A. Groenwold, The Particle Swarm Algorithm in Topology Optimization, Proceedings of the 4th World Congress of Structural and Multidisciplinary Optimization, pp. 52–53, Dalian, China, 2001.
A. A. Groenwold and P. C. Fourie, The Particle Swarm Optimization in Size and Shape Optimization, Structural and Multidisciplinary Optimization, 23 (2002) 259–267.
J. F. Schuttle and A. A. Groenwold, A Study of Global Optimization Using Particle Swarms, Journal of Global Optimization, 31(1) (2005) 93–108.
J. F. Schuttle, B.-I. Koh, J. A. Reinbolt, R. T. Haftka, A. D. George and B. J. Fregly, Evaluation of a Particle Swarm Algorithm for Biomechanical Optimization, ASME Transactions, Journal of Biomechanical Engineering, 27 (2005) 465–474.
R. M. Storn and K. V. Price, Differential Evolution — A Simple and Efficient Heuristic for Global Optimization over Continuous Space, Journal of Global Optimization, 11(4) (1997) 341–359.
J. A. Lampinen and I. Zelinka, Mechanical Engineering Design Optimization by Differential Evolution, MaGraw-Hill’s Advanced Topics in Computer Science Series: New Ideas in Optimization, pp. 127–146, McGraw-Hill, United Kingdom, 1999.
K. V. Price, R. M. Storn and J. A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization, Springer, 2005.
S. Das, A. Konar and U. K. Chakraborty, Improved Differential Evolution Algorithms for Handling Noisy Optimization Problems, Proceedings of the 2005 IEEE Congress on Evolutionary Computation, 2 (2005) 1691–1698.
J. Lee, S. Kim and S. Kang, Evolutionary Fuzzy Modeling in Global Approximate Optimization, International Journal of Vehicle Design, 28(3) (2002) 81–97.
J. Lee and S. Kim, Optimal Design of Engine Mount Rubber Considering Stiffness and Fatigue Strength, Proceedings of the Institution of Mechanical Engineers, Part D — Journal of Automobile Engineering, 221(7) (2007) 823–835.
T. Hendtlass, A Combined Swarm Differential Evolution Algorithm for Optimization Problems, Lecture Notes in Computer Science, 20 (2001) 11–18.
W. J. Zhang and X. F. Xie, DEPSO: Hybrid Particle Swarm with Differential Evolution Operator, Proceeding of IEEE International Conference on Systems, Man and Cybernetics, 4 (2003) 3816–3821.
A. Stacey, M. Jancic and I. Grundy, Particle Swarm Optimization with Mutation, Proceedings of Congress on Evolutionary Computation (CEC’ 03), 1425–1430, 2003.
H. J. Meng, P. Zheng, R. Y. Wu, X. J. Hao and Z. Xie, A Hybrid Particle Swarm Algorithm with Embedded Chaotic Search, Proceedings of Conference on Cybernetics and Intelligent Systems, 1 (2004) 367–371.
T. O. Ting, M. V. C. Rao and C. K. Loo, A Novel Approach for Unit Commitment Problem Via an Effective Hybrid Particle Swarm Optimization, IEEE Transactions on Power Systems, 21(1) (2006) 411–418.
M. Khajenejad, F. Afshinmanesh, A. Marandi and B. N. Araabi, Intelligent Particle Swarm Optimization Using Q-Learning, Proceedings of IEEE Swarm Intelligence Symposium, Indianapolis, IN, 2006.
J. Ilonen, J.-K. Kamarainen and J. A. Lampinen, Differential Evolution Training Algorithm for Feed-Forward Neural Networks, Neural Processing Letters, 17(1) (2003) 93–105.
A. Ratnaweera, S. K. Halgamuge and H. C. Watson, Self-Organizing Hierarchical Particle Swarm Optimizer with Time-Varying Acceleration Coefficients, IEEE Transactions on Evolutionary Computation, 8(3) (2004) 240–255.
T. Takahama and S. Sakai, Solving Constrained Optimization Problems by the ɛ-Constrained Particle Swarm Optimizer with Adaptive Velocity Limit Control, Proceedings of IEEE Conference on Cybernetics and Intelligent Systems, 1425–1430, 2006.
J.-S. Jang, C.-T. Sun and E. Mizutani, Neuro-Fuzzy and Soft Computing, Prentice Hall, Upper Saddle River, NJ, 1997.
R. T. Haftka and Z. Gürdal, Elements of Structural Optimization, Kluwer Academic Publishers, The Netherlands, 1993.
G. N. Vanderplaats, DOT (Design Optimization Tools) User’s Manual, Version 4.20, VR&D, 1995.
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This paper was recommended for publication in revised form by Associate Editor Tae Hee Lee
Jongsoo Lee received a B.S. degree in Mechanical Engineering from Yonsei University in 1988. He then went on to receive his M.S. degree from University of Minnesota in 1992 and Ph.D. degree from Rensselaer Polytechnic Institute in 1996. Dr. Lee is currently a Professor at the School of Mechanical Engineering at Yonsei University in Seoul, Korea. He is currently serving as a committee member of the division of CAE and Applied Mechanics in the Korean Society of Mechanical Engineers. Dr. Lee’s research interests are in the area of engineering design optimization, fluidstructure interactions, and reliability based robust product design.
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Kim, P., Lee, J. An integrated method of particle swarm optimization and differential evolution. J Mech Sci Technol 23, 426–434 (2009). https://doi.org/10.1007/s12206-008-0917-4
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DOI: https://doi.org/10.1007/s12206-008-0917-4