Reprint of: On convergence analysis of particle swarm optimization algorithm

Journal of Computational and Applied Mathematics - Tập 340 - Trang 709-717 - 2018
Gang Xu1, Guosong Yu1
1Department of Mathematics, Nanchang University, Nanchang 330031, China

Tài liệu tham khảo

J. Kennedy, R.C. Eberhart, Particle swarm optimization, in: Proceedings of the IEEE International Conference on Neural Networks, 1995, pp. 1942–1948. Banks, 2007, A review of particle swarm optimization. Part I: background and development, Nat. Comput., 6, 467, 10.1007/s11047-007-9049-5 AlRashidi, 2009, A survey of particle swarm optimization applications in electric power systems, IEEE Trans. Evol. Comput., 14, 913, 10.1109/TEVC.2006.880326 Clerc, 2002, The particle swarm-explosion, stability and convergence in a multidimensional complex space, IEEE Trans. Evol. Comput., 6, 58, 10.1109/4235.985692 Kadirkamanathan, 2006, Stability analysis of the particle dynamics in particle swarm optimizer, IEEE Trans. Evol. Comput., 10, 245, 10.1109/TEVC.2005.857077 van den Bergh, 2006, A study of particle swarm optimization particle trajectories, Inform. Sci., 176, 937, 10.1016/j.ins.2005.02.003 Liu, 2015, Order-2 stability analysis of particle swarm optimization, Evol. Comput., 23, 187, 10.1162/EVCO_a_00129 Jiang, 2007, Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm, Inform. Process. Lett., 102, 8, 10.1016/j.ipl.2006.10.005 R. Poli, W.B. Langdon, Markov chain models of bare-bones particle swarm optimizers, in: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, 2007, pp. 142–149. Cai, 2009, Convergence improvement of particle swarm optimization based on the expanding attaining-state set, J. Huazhong Univ. Sci. Technol. Nat. Sci., 37, 44 Solis, 1981, Minimization by random search techniques, Math. Oper. Res., 6, 19, 10.1287/moor.6.1.19 van den Bergh, 2010, A convergence proof for the particle swarm optimiser, Fund. Inform., 105, 341 Dirk, 2010, Runtime analysis of a binary particle swarm optimizer, Theoret. Comput. Sci., 411, 2084, 10.1016/j.tcs.2010.03.002 Sun, 2012, Convergence analysis and improvements of quantum-behaved particle swarm optimization, Inform. Sci., 193, 81, 10.1016/j.ins.2012.01.005 Per, 2013, Finite first hitting time versus stochastic convergence in particle swarm optimization, Adv. Metaheuristics, 53, 1, 10.1007/978-1-4614-6322-1_1 Ren, 2011, The global convergence analysis of particle swarm optimization algorithm based on markov chain, Control Theory Appl., 28, 462 Pan, 2013, Analysis of standard particle swarm optimization algorithm based on Markov Chain, Acta Automat. Sinica, 39, 381, 10.1016/S1874-1029(13)60037-3 Tian, 2013, A review of convergence analysis of particle swarm optimization, Int. J. Grid Distrib. Comput., 6, 117, 10.14257/ijgdc.2013.6.6.10 Yuan, 2015, Analyzing convergence and rates of convergence of particle swarm optimization algorithms using stochastic approximation methods, IEEE Trans. Automat. Control, 60, 1760, 10.1109/TAC.2014.2381454 Y.H. Shi, R.C. Eberhart, Empirical study of particle swarm optimization, in: Proceedings of the Congress on Evolutionary Computation, 1999,pp. 1945–1950. J. Kennedy, R. Mendes, Population structure and particle swarm performance, in: Proceedings of the Congress on Evolutionary Computation, 2002,pp. 1671–1676. J.J. Liang, P.N. Suganthan, Dynamic multi-swarm particle swarm optimizer, in: Proceedings of the IEEE Swarm Intelligence Symposium, 2005,pp. 124–129. J. Sun, B. Feng, W.B. Xu, Particle swarm optimization with particles having quantum behavior, in: Proceedings of the 2004 Congress on Evolutionary Computation, CEC’04, Portland, USA, 2004, pp. 326–331. Parrott, 2006, Locating and tracking multiple dynamic optima by a particle swarm model using speciation, IEEE Trans. Evol. Comput., 10, 440, 10.1109/TEVC.2005.859468 Brits, 2007, Locating multiple optima using particle swarm optimization, Appl. Math. Comput., 189, 1859 Zhao, 2010, A perturbed particle swarm algorithm for numerical optimization, Appl. Soft. Comput., 10, 119, 10.1016/j.asoc.2009.06.010 Tang, 2011, Feedback learning particle swarm optimization, Appl. Soft. Comput., 11, 4713, 10.1016/j.asoc.2011.07.012 Wang, 2012, A memetic particle swarm optimization algorithm for multimodal optimization problems, Inform. Sci., 197, 38, 10.1016/j.ins.2012.02.016 Huang, 2012, Example-based learning particle swarm optimization for continuous optimization, Inform. Sci., 182, 125, 10.1016/j.ins.2010.10.018 Lawler, 2006 Xiao, 2014, Moment convergence rates in the law of logarithm for moving average process under dependence, Stochastics, 86, 1, 10.1080/17442508.2012.748057 Kao, 1997 Yu, 2008, A new approach to estimating the expected first hitting time of evolutionary algorithms, Artificial Intelligence, 172, 1809, 10.1016/j.artint.2008.07.001