Abstract
Particle swarm optimizer (PSO) is an effective tool for solving many optimization problems. However, it may easily get trapped into local optimumwhen solving complex multimodal nonseparable problems. This paper presents a novel algorithm called distributed learning particle swarm optimizer (DLPSO) to solve multimodal nonseparable problems. The strategy for DLPSO is to extract good vector information from local vectors which are distributed around the search space and then to form a new vector which can jump out of local optima and will be optimized further. Experimental studies on a set of test functions show that DLPSO exhibits better performance in solving optimization problems with few interactions between variables than several other peer algorithms.
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References
Eberhart R C, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the 6th International Symposium of Micromachine Human Science. 1995, 39–43
Kennedy J, Eberhart R C. Particle swarm optimization. In: Proceedings of IEEE International Conferences on Neural Networks. 1995, 1942–1948
Liang J J, Qin A K, Suganthan P N, Baskar S. Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Transactions on Evolutionary Computation, 2006, 10(3): 281–295
Ho S Y, Lin H S, Liauh WH, Ho S J. OPSO: orthogonal particle swarm optimization and its application to task assignment problems. IEEE Transactions on Systems, Man, and Cybernetics, Part A (Systems and Humans), 2008, 38(2): 288–298
Zhan Z H, Zhang J, Li Y, Shi Y H. Orthogonal learning particle swarm optimization. IEEE Transactions on Evolutionary Computation, 2011, 15(6): 832–847
Zhang G, Li Y M. Parallel and cooperative particle swarm optimizer for multimodal problems. Mathematical Problems in Engineering, 2015, 2015: 743671
Ho S Y, Shu L S, Chen J H. Intelligent evolutionary algorithms for large parameter optimization problems. IEEE Transactions on Evolutionary Computation, 2004, 8(6), 522–541
Van den Bergh F, Engelbrecht A P. A cooperative approach to particle swarm optimization. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 225–239
Shi Y H, Eberhart R C. A modified particle swarm optimizer. In: Proceedings of IEEEWorld Congress on Evolutionary Computation. 1998, 69–73
Shi Y H, Eberhart R C. Parameter selection in particle swarm optimizer. In: Proceedings of the 7th Conference on Evolutionary Programming. 1998, 591–600
Suganthan P N. Particle swarm optimizer with neighborhood operator. In: Proceedings of IEEE World Congress on Evolutionary Computation. 1999, 1958–1962
Li C H, Yang S X, Nguyen T T. A Self-learning particle swarm optimizer for global optimization problems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2012, 42(3): 627–643
Shi Y H, Eberhart R C. Population diversity of particle swarms. In: Proceedings of IEEE World Congress on Evolutionary Computation. 2008, 1063–1067
Shi Y H, Eberhart R C. Monitoring of particle swarm optimization. Frontiers of Computer Science in China, 2009, 3(1): 31–37
Wu Z J, Zhou J Z. A self-adaptive particle swarm optimization algorithm with individual coefficient adjustment. In: Proceedings of International Conference on Computational Intelligence and Security. 2007, 133–136
Parsopoulos K E, Vrahatis M N. UPSO: a unified particle swarm optimization scheme. Lecture Series on Computational Sciences, 2004, 868–873
Li X D. Niching without niching parameters: Particle swarm optimization using a ring topology. IEEE Transactions on Evolutionary Computation, 2010, 14(1): 150–169
Kennedy J. Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: Proceedings of IEEE World Congress on Evolutionary Computation. 1999, 1931–1938
Kennedy J, Mendes R. Population structure and particle swarm performance. In: Proceedings of IEEE World Congress on Evolutionary Computation. 2002, 1671–1676
Jason J, Middendorf M. A hierarchical particle swarm optimizer and its adaptive variant. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2005, 35(6): 1272–1282
Liang J J, Suganthan P N. Dynamic multi-swarm particle optimizer. In: Proceedings of IEEE Congress on Evolutionary Computation. 2005, 124–129
Mendes R, Kennedy J, Neves J. The fully informed particle swarm: simpler, maybe better. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 204–210
Peram T, Veeramachaneni K, Mohan C K. Fitness-distance-ratio based particle swarm optimization. In: Proceedings of IEEE Swarm Intelligence Symposium. 2003, 174–181
Angeline P J. Using selection to improve particle swarm optimization. In: Proceedings of IEEE World Congress on Evolutionary Computation. 1998, 84–89
Juang C F. A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2004, 34(2): 997–1006
Ling S H, Iu H H C, Chan K Y, Lam H K, Yeung B C W, Leung F H. Hybrid particle swarm optimization with wavelet mutation and its industrial applications. IEEE Transactions on Systems Man and Cyberntics Part B, 2008, 38(3): 743–763
Ren Z G, Zhang A M, Wen C Y, Feng Z R. A scatter learning particle swarm optimization algorithm for multimodal problems. IEEE Transactions on Cyberntics, 2014, 44(7): 1127–1140
Chen X, Li Y M. A modified PSO structure resulting in high exploration ability with convergence guaranteed. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2007, 37(5): 1271–1289
Chen X, Li Y.M. On convergence and parameters selection of an improved particle swarm optimization. International Journal of Control, Automation, and Systems, 2008, 6(4): 559–570
Ratnaweera A, Halgamuge S K, Watson H C. Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240–255
Shen Y X, Wei L N, Zeng C H. Swarm diversity analysis of particle swarm optimization. In: Tan Y, Shi Y H, Buarque F, et al. eds. Advances in Swarm and Computational Intelligence. Lecture Notes in Compute Science, Vol 9140. Springer, 2015, 99–106
Tang K, Yang P, Yao X. Negatively correlated search. IEEE Journal on Selected Areas in Communications, 2016, 34(3): 540–550
Montgomery D C. Design and Analysis of Experiments. 5th ed. New York: Wiley, 2000
Ho S Y, Shu L S, Chen J H. Intelligent evolutionary algorithms for large parameter optimization problems. IEEE Transaction on Evolutionary Computation, 2004, 8(6): 522–541
Liang J J, Suganthan P N, Deb K. Novel composition test functions for numerical global optimization. In: Proceedings of IEEE Swarm Intelligence Symposium. 2005, 68–75
Salomon R. Reevaluating genetic algorithm performance under coordinate rotation of benchmark functions. Biosystems, 1996, 39(3): 263–278
Lee K S, Green Z W. A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Computer Methods in Applied Mechanics and Engineering, 2005, 194(36): 3902–3933
Sun J Y, Zhang Q F, Tsang E P K. DE/EDA: a new evolutionary algorithm for global optimization. Information Science, 2004, 169(3): 249–262
Acknowledgements
The authors would like to acknowledge the financial support of the National Natural Science Foundation of China (Grant Nos. 51575544, 51275353), Macao Science and Technology Development Fund (108/2012/A3 and 110/2013/A3) and Research Committee of University of Macau (MYRG2015-00194-FST, MYRG203(Y1-L4)-FST11-LYM).
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Geng Zhang received the BS and MS degrees in electrical automation from Lanzhou University of Technology, China in 2004 and 2007, respectively, and the MS degree in electrical and electronic engineering from the University of Hong Kong, China in 2009. He is currently working toward the PhD degree at the University of Macau, China. His current research interests include particle swarm optimization, memetic algorithm and neural network.
Yangmin Li received the BS and MS degrees from Jilin University, China in 1985 and 1988, respectively, and the PhD degree from Tianjin University, China in 1994. He was a posdoctoral research associate at Purdue University, USA in 1997. He is currently a professor and director of the Mechatronics Laboratory at Dept. Electromech. Eng. at the University of Macau, China. His research interests include nanorobotics, micromanipulator, mobile and parallel robot, computational intelligence and control. He has authored over 360 papers in above areas. Prof. Li is an IEEE Senior member, ASME and CSME member. He is an editor of the Chinese Journal of Mechanical Engineering, an associate editor of the IEEE Transactions on Automation Science Engineering, Mechatronics, International Journal of Control, Automation and Systems, and IEEE Access.
Yuhui Shi is a professor in the Department of Electrical and Electronic Engineering at the Xi’an Jiaotong-Liverpool University (XJTLU), China since 2008. Dr. Shi was with the Electronic Data Systems Corporation (EDS), Indiana, USA from 1998 to 2007. He is an IEEE Fellow, the Editor-in-Chief of the International Journal of Swarm Intelligence Research, and an associate editor of the IEEE Transactions on Evolutionary Computation. Dr. Shi co-authored a book on Swarm Intelligence together with Dr. James Kennedy and Dr. Russell C. Eberhart, and another book on Computational Intelligence: Concept to Implementation together with Dr. Russell C. Eberhart.
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Zhang, G., Li, Y. & Shi, Y. Distributed learning particle swarm optimizer for global optimization of multimodal problems. Front. Comput. Sci. 12, 122–134 (2018). https://doi.org/10.1007/s11704-016-5373-1
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DOI: https://doi.org/10.1007/s11704-016-5373-1