A Comprehensive Review of Particle Swarm Optimization

Article Preview

Abstract:

Particle swarm optimization (PSO) is a heuristic global optimization method. PSO was motivated by the social behavior of organisms, such as bird flocking, fish schooling and human social relations. Its properties of low constraint on the continuity of objective function and the ability to adapt various dynamic environments, makes PSO one of the most important swarm intelligence algorithms and ostensibly the most commonly used optimization technique. This survey presents a comprehensive investigation of PSO and in particular, a proposed theoretical framework to improve its implementation. We hope that this survey would be beneficial to researchers studying PSO algorithms and would also serve as the substratum for future research in the study area, particularly those pursuing their career in artificial intelligence. In the end, some important conclusions and possible research directions of PSO that need to be studied in the future are proposed.

You might also be interested in these eBooks

Info:

Pages:

141-161

Citation:

Online since:

April 2016

Export:

Price:

* - Corresponding Author

[1] C. -J. Ting, K. -C. Wu, and H. Chou, Particle swarm optimization algorithm for the berth allocation problem, Expert Systems with Applications, vol. 41, pp.1543-1550, (2014).

DOI: 10.1016/j.eswa.2013.08.051

Google Scholar

[2] Z. Li, T. T. Nguyen, S. Chen, and T. K. Truong, A hybrid algorithm based on particle swarm and chemical reaction optimization for multi-object problems, Applied Soft Computing, vol. 35, pp.525-540, (2015).

DOI: 10.1016/j.asoc.2015.06.036

Google Scholar

[3] R. C. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, in Proceedings of the sixth international symposium on micro machine and human science, 1995, pp.39-43.

DOI: 10.1109/mhs.1995.494215

Google Scholar

[4] M. Talukdar, Stable Drug Designing by Minimizing Drug-Protein Interaction Energy using PSO, JADAVPUR UNIVERSITY, (2014).

Google Scholar

[5] M. Abido, Optimal power flow using particle swarm optimization, International Journal of Electrical Power & Energy Systems, vol. 24, pp.563-571, (2002).

DOI: 10.1016/s0142-0615(01)00067-9

Google Scholar

[6] Z. -L. Gaing, Particle swarm optimization to solving the economic dispatch considering the generator constraints, Power Systems, IEEE Transactions on, vol. 18, pp.1187-1195, (2003).

DOI: 10.1109/tpwrs.2003.814889

Google Scholar

[7] A. Salman, I. Ahmad, and S. Al-Madani, Particle swarm optimization for task assignment problem, Microprocessors and Microsystems, vol. 26, pp.363-371, (2002).

DOI: 10.1016/s0141-9331(02)00053-4

Google Scholar

[8] D. Saha, S. Banerjee, and N. D. Jana, Multi-objective Particle Swarm Optimization based on adaptive mutation, in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, 2015, pp.1-5.

DOI: 10.1109/c3it.2015.7060214

Google Scholar

[9] N. Netjinda, T. Achalakul, and B. Sirinaovakul, Particle Swarm Optimization inspired by starling flock behavior, Applied Soft Computing, vol. 35, pp.411-422, (2015).

DOI: 10.1016/j.asoc.2015.06.052

Google Scholar

[10] C. Grosan, A. Abraham, and M. Chis, Swarm intelligence in data mining: Springer, (2006).

Google Scholar

[11] I. Fister, X. -S. Yang, and J. Brest, A comprehensive review of firefly algorithms, Swarm and Evolutionary Computation, vol. 13, pp.34-46, (2013).

DOI: 10.1016/j.swevo.2013.06.001

Google Scholar

[12] H. X. Peng, M. X. Du, B. Wang, and P. Wang, Acquisition of Swarm Intellegence (SI) Principle in Practice Teaching of Automation Disciplines, in Advanced Materials Research, 2014, pp.4443-4446.

DOI: 10.4028/www.scientific.net/amr.926-930.4443

Google Scholar

[13] L. Goel and V. Panchal, Feature Extraction through Information Sharing in Swarm Intelligence Techniques, Knowledge-Based Processes in Software Development, p.151, (2013).

DOI: 10.4018/978-1-4666-4229-4.ch010

Google Scholar

[14] T. Dokeroglu, U. Tosun, and A. Cosar, Particle Swarm Intelligence as a new heuristic for the optimization of distributed database queries, in Application of Information and Communication Technologies (AICT), 2012 6th International Conference on, 2012, pp.1-7.

DOI: 10.1109/icaict.2012.6398467

Google Scholar

[15] N. Tabassum and M. Haque, Accelerating ant colony optimization by using local search, (2015).

Google Scholar

[16] D. Singh, J. P. Choudhary, and M. De, An effort to select a preferable metaheuristic model for knowledge discovery in data mining, International Journal of Metaheuristics, vol. 4, pp.57-90, (2015).

DOI: 10.1504/ijmheur.2015.071763

Google Scholar

[17] J. Tillett, T. Rao, F. Sahin, and R. Rao, Darwinian particle swarm optimization, (2005).

Google Scholar

[18] J. Sabatier, O. P. Agrawal, and J. T. Machado, Advances in fractional calculus vol. 4: Springer, (2007).

Google Scholar

[19] I. Ramirez, P. Sprechmann, and G. Sapiro, Classification and clustering via dictionary learning with structured incoherence and shared features, in Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on, 2010, pp.3501-3508.

DOI: 10.1109/cvpr.2010.5539964

Google Scholar

[20] K. Yu, Y. Lin, and J. Lafferty, Learning image representations from the pixel level via hierarchical sparse coding, in Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on, 2011, pp.1713-1720.

DOI: 10.1109/cvpr.2011.5995732

Google Scholar

[21] J. -L. Deneubourg, S. Aron, S. Goss, and J. M. Pasteels, The self-organizing exploratory pattern of the argentine ant, Journal of insect behavior, vol. 3, pp.159-168, (1990).

DOI: 10.1007/bf01417909

Google Scholar

[22] K. Ramsch, C. R. Reid, M. Beekman, and M. Middendorf, A mathematical model of foraging in a dynamic environment by trail-laying Argentine ants, Journal of theoretical biology, vol. 306, pp.32-45, (2012).

DOI: 10.1016/j.jtbi.2012.04.003

Google Scholar

[23] P. Sharkey, Ant Colony Optimisation: Algorithms and Applications, (2014).

Google Scholar

[24] L. M. Gambardella and M. Dorigo, Coupling ant colony system with local search, (2015).

Google Scholar

[25] J. -L. Deneubourg, S. Goss, N. Franks, A. Sendova-Franks, C. Detrain, and L. Chrétien, The dynamics of collective sorting robot-like ants and ant-like robots, in Proceedings of the first international conference on simulation of adaptive behavior on From animals to animats, 1991, pp.356-363.

DOI: 10.7551/mitpress/3115.003.0048

Google Scholar

[26] R. Beckers, O. Holland, and J. -L. Deneubourg, From local actions to global tasks: Stigmergy and collective robotics, in Artificial life IV, 1994, p.189.

DOI: 10.7551/mitpress/1428.003.0022

Google Scholar

[27] S. Garnier, C. Jost, J. Gautrais, M. Asadpour, G. Caprari, R. Jeanson, et al., The embodiment of cockroach aggregation behavior in a group of micro-robots, Artificial Life, vol. 14, pp.387-408, (2008).

DOI: 10.1162/artl.2008.14.4.14400

Google Scholar

[28] E. D. Lumer and B. Faieta, Diversity and adaptation in populations of clustering ants, in Proceedings of the third international conference on Simulation of adaptive behavior: from animals to animats 3: from animals to animats 3, 1994, pp.501-508.

DOI: 10.7551/mitpress/3117.003.0011

Google Scholar

[29] E. Bonabeau, M. Dorigo, and G. Theraulaz, Swarm intelligence: from natural to artificial systems: Oxford university press, (1999).

DOI: 10.1093/oso/9780195131581.001.0001

Google Scholar

[30] G. Theraulaz and E. Bonabeau, A brief history of stigmergy, Artificial life, vol. 5, pp.97-116, (1999).

DOI: 10.1162/106454699568700

Google Scholar

[31] J. Kennedy, J. F. Kennedy, R. C. Eberhart, and Y. Shi, Swarm intelligence: Morgan Kaufmann, (2001).

Google Scholar

[32] R. Schoonderwoerd, O. E. Holland, J. L. Bruten, and L. J. Rothkrantz, Ant-based load balancing in telecommunications networks, Adaptive behavior, vol. 5, pp.169-207, (1997).

DOI: 10.1177/105971239700500203

Google Scholar

[33] G. Di Caro and M. Dorigo, AntNet: Distributed stigmergetic control for communications networks, Journal of Artificial Intelligence Research, pp.317-365, (1998).

DOI: 10.1613/jair.530

Google Scholar

[34] G. Di Caro, F. Ducatelle, L. M. Gambardella, and M. Dorigo, AntHocNet: an adaptive nature-inspired algorithm for routing in mobile ad hoc networks, European Transactions on Telecommunications, vol. 16, pp.443-455, (2005).

DOI: 10.1002/ett.1062

Google Scholar

[35] M. Clerc and J. Kennedy, The particle swarm-explosion, stability, and convergence in a multidimensional complex space, Evolutionary Computation, IEEE Transactions on, vol. 6, pp.58-73, (2002).

DOI: 10.1109/4235.985692

Google Scholar

[36] A. P. Engelbrecht, Fundamentals of computational swarm intelligence: John Wiley & Sons, (2006).

Google Scholar

[37] M. Clerc, Particle Swarm Optimization; ISTE Ltd, London, UK, (2006).

Google Scholar

[38] R. Poli, J. Kennedy, and T. Blackwell, Particle swarm optimization, Swarm intelligence, vol. 1, pp.33-57, (2007).

DOI: 10.1007/s11721-007-0002-0

Google Scholar

[39] J. Kennedy and R. C. Eberhart, A discrete binary version of the particle swarm algorithm, in Systems, Man, and Cybernetics, 1997. Computational Cybernetics and Simulation., 1997 IEEE International Conference on, 1997, pp.4104-4108.

DOI: 10.1109/icsmc.1997.637339

Google Scholar

[40] J. Kennedy, Bare bones particle swarms, " in Swarm Intelligence Symposium, 2003. SIS, 03. Proceedings of the 2003 IEEE, 2003, pp.80-87.

DOI: 10.1109/sis.2003.1202251

Google Scholar

[41] R. Mendes, J. Kennedy, and J. Neves, The fully informed particle swarm: simpler, maybe better, Evolutionary Computation, IEEE Transactions on, vol. 8, pp.204-210, (2004).

DOI: 10.1109/tevc.2004.826074

Google Scholar

[42] Y. Del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J. -C. Hernandez, and R. G. Harley, Particle swarm optimization: basic concepts, variants and applications in power systems, Evolutionary Computation, IEEE Transactions on, vol. 12, pp.171-195, (2008).

DOI: 10.1109/tevc.2007.896686

Google Scholar

[43] M. S. Couceiro, R. P. Rocha, N. F. Ferreira, and J. T. Machado, Introducing the fractional-order Darwinian PSO, Signal, Image and Video Processing, vol. 6, pp.343-350, (2012).

DOI: 10.1007/s11760-012-0316-2

Google Scholar

[44] D. Floreano and C. Mattiussi, Bio-inspired artificial intelligence: theories, methods, and technologies: MIT press, (2008).

Google Scholar

[45] D. Verma and R. Shrivas, Survey Paper on A Hybrid Approach using Particle Swarm Optimization with Linear Crossover to Solve Continuous Optimization Problem, (2015).

Google Scholar

[46] Y. Shi and R. C. Eberhart, Fuzzy adaptive particle swarm optimization, in Evolutionary Computation, 2001. Proceedings of the 2001 Congress on, 2001, pp.101-106.

DOI: 10.1109/cec.2001.934377

Google Scholar

[47] B. R. Secrest and G. B. Lamont, Visualizing particle swarm optimization-Gaussian particle swarm optimization, " in Swarm Intelligence Symposium, 2003. SIS, 03. Proceedings of the 2003 IEEE, 2003, pp.198-204.

DOI: 10.1109/sis.2003.1202268

Google Scholar

[48] E. S. Pires, J. T. Machado, P. de Moura Oliveira, J. B. Cunha, and L. Mendes, Particle swarm optimization with fractional-order velocity, Nonlinear Dynamics, vol. 61, pp.295-301, (2010).

DOI: 10.1007/s11071-009-9649-y

Google Scholar

[49] T. M. Blackwell and P. Bentley, Don't push me! Collision-avoiding swarms, " in Evolutionary Computation, 2002. CEC, 02. Proceedings of the 2002 Congress on, 2002, pp.1691-1696.

DOI: 10.1109/cec.2002.1004497

Google Scholar

[50] T. Krink, J. S. VesterstrOm, and J. Riget, Particle swarm optimisation with spatial particle extension, in wcci, 2002, pp.1474-1479.

DOI: 10.1109/cec.2002.1004460

Google Scholar

[51] V. Miranda and N. Fonseca, New evolutionary particle swarm algorithm (EPSO) applied to voltage/VAR control, in Proc. 14th Power Syst. Comput. Conf, 2002, pp.3816-3821.

Google Scholar

[52] M. Lovbjerg and T. Krink, Extending particle swarm optimisers with self-organized criticality, in wcci, 2002, pp.1588-1593.

DOI: 10.1109/cec.2002.1004479

Google Scholar

[53] C. M. Fernandes, J. J. Merelo, and A. C. Rosa, A Time-Varying Inertia Weight Strategy for Particles Swarms Based on Self-Organized Criticality, in Computational Intelligence, ed: Springer, 2015, pp.49-62.

DOI: 10.1007/978-3-319-11271-8_4

Google Scholar

[54] C. -F. Juang, A hybrid of genetic algorithm and particle swarm optimization for recurrent network design, Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol. 34, pp.997-1006, (2004).

DOI: 10.1109/tsmcb.2003.818557

Google Scholar

[55] F. Lei and W. Wei, Research of PSO/Genetic Algorithms and Development of its Hybrid Algorithm, International Journal of Digital Content Technology & its Applications, vol. 6, (2012).

Google Scholar

[56] V. Singh, I. Elamvazuthi, V. Jeoti, and J. George, Automatic Ultrasound Image Segmentation Framework Based on Darwinian Particle Swarm Optimization, in Proceedings of the 18th Asia Pacific Symposium on Intelligent and Evolutionary Systems, Volume 1, 2015, pp.225-236.

DOI: 10.1007/978-3-319-13359-1_18

Google Scholar

[57] M. Couceiro and P. Ghamisi, Fractional-Order Darwinian PSO, in Fractional Order Darwinian Particle Swarm Optimization, ed: Springer, 2016, pp.11-20.

DOI: 10.1007/978-3-319-19635-0_2

Google Scholar

[58] M. Couceiro, J. M. A. Luz, C. M. Figueiredo, N. F. Ferreira, and G. Dias, Parameter estimation for a mathematical model of the golf putting, in Proceedings of WACI-Workshop Applications of Computational Intelligence. ISEC. IPC. Coimbra, 2010, pp.1-8.

Google Scholar

[59] M. S. Couceiro, R. P. Rocha, and N. M. Ferreira, A novel multi-robot exploration approach based on particle swarm optimization algorithms, in Safety, Security, and Rescue Robotics (SSRR), 2011 IEEE International Symposium on, 2011, pp.327-332.

DOI: 10.1109/ssrr.2011.6106751

Google Scholar

[60] S. Lahmiri and M. Boukadoum, An evaluation of particle swarm optimization techniques in segmentation of biomedical images, in Proceedings of the 2014 conference companion on Genetic and evolutionary computation companion, 2014, pp.1313-1320.

DOI: 10.1145/2598394.2609855

Google Scholar

[61] S. Wu, S. P. Weinstein, E. F. Conant, and D. Kontos, Automated fibroglandular tissue segmentation and volumetric density estimation in breast MRI using an atlas-aided fuzzy C-means method, Medical physics, vol. 40, p.122302, (2013).

DOI: 10.1118/1.4829496

Google Scholar

[62] J. -l. Fan and F. Zhao, Two-dimensional Otsu's curve thresholding segmentation method for gray-Level images, Dianzi Xuebao(Acta Electronica Sinica), vol. 35, pp.751-755, (2007).

Google Scholar

[63] F. HAMDAOUI, A. SAKLY, and A. MTIBAA, An efficient multithresholding method for image segmentation based on PSO, Proceedings-Copyright IPCO, pp.203-213, (2014).

Google Scholar

[64] D. -K. Lim, D. -K. Woo, H. -K. Yeo, S. -Y. Jung, J. -S. Ro, and H. -K. Jung, A Novel Surrogate-Assisted Multi-Objective Optimization Algorithm for an Electromagnetic Machine Design, IEEE TRANSACTIONS ON MAGNETICS, vol. 51, p.8200804, (2015).

DOI: 10.1109/tmag.2014.2359452

Google Scholar

[65] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 198, XV-XXIV, ed: Academic Press, (1999).

Google Scholar

[66] L. Debnath, Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, vol. 2003, pp.3413-3442, (2003).

DOI: 10.1155/s0161171203301486

Google Scholar

[67] E. Elshehawey, E. M. Elbarbary, N. Afifi, and M. El-Shahed, On the solution of the endolymph equation using fractional calculus, Applied mathematics and computation, vol. 124, pp.337-341, (2001).

DOI: 10.1016/s0096-3003(00)00094-1

Google Scholar

[68] R. F. Camargo, A. O. Chiacchio, and E. C. de Oliveira, Differentiation to fractional orders and the fractional telegraph equation, Journal of Mathematical Physics, vol. 49, p.033505, (2008).

DOI: 10.1063/1.2890375

Google Scholar

[69] J. T. Machado, A. M. Galhano, and J. J. Trujillo, Science metrics on fractional calculus development since 1966, Fractional Calculus and Applied Analysis, vol. 16, pp.479-500, (2013).

DOI: 10.2478/s13540-013-0030-y

Google Scholar

[70] J. Tenreiro Machado, M. F. Silva, R. S. Barbosa, I. S. Jesus, C. M. Reis, M. G. Marcos, et al., Some applications of fractional calculus in engineering, Mathematical Problems in Engineering, vol. 2010, (2009).

DOI: 10.1155/2010/639801

Google Scholar

[71] P. Ghamisi, M. S. Couceiro, J. A. Benediktsson, and N. M. Ferreira, An efficient method for segmentation of images based on fractional calculus and natural selection, Expert Systems with Applications, vol. 39, pp.12407-12417, (2012).

DOI: 10.1016/j.eswa.2012.04.078

Google Scholar

[72] B. Ghansah, S. Wu, and N. Ghansah, Rankboost-Based Result Merging, in Computer and Information Technology; Ubiquitous Computing and Communications; Dependable, Autonomic and Secure Computing; Pervasive Intelligence and Computing (CIT/IUCC/DASC/PICOM), 2015 IEEE International Conference on, 2015, pp.907-914.

DOI: 10.1109/cit/iucc/dasc/picom.2015.136

Google Scholar

[73] D. L. Donoho and M. Elad, Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization, Proceedings of the National Academy of Sciences, vol. 100, pp.2197-2202, (2003).

DOI: 10.1073/pnas.0437847100

Google Scholar

[74] E. S. Pires, P. Oliveira, J. T. Machado, and J. B. Cunha, Particle swarm optimization versus genetic algorithm in manipulator trajectory planning, in 7th Portuguese conference on automatic control, (2006).

Google Scholar

[75] K. Yasuda, N. Iwasaki, G. Ueno, and E. Aiyoshi, Particle swarm optimization: a numerical stability analysis and parameter adjustment based on swarm activity, IEEJ Transactions on Electrical and Electronic Engineering, vol. 3, pp.642-659, (2008).

DOI: 10.1002/tee.20326

Google Scholar

[76] Y. Wakasa, K. Tanaka, and Y. Nishimura, Control-theoretic analysis of exploitation and exploration of the PSO algorithm, in Computer-Aided Control System Design (CACSD), 2010 IEEE International Symposium on, 2010, pp.1807-1812.

DOI: 10.1109/cacsd.2010.5612763

Google Scholar

[77] F. Van den Bergh and A. P. Engelbrecht, A study of particle swarm optimization particle trajectories, Information sciences, vol. 176, pp.937-971, (2006).

DOI: 10.1016/j.ins.2005.02.003

Google Scholar

[78] J. Kennedy, R, Eberhart, Particle swarm optimization, vol. 1, (1995).

Google Scholar

[79] R. Poli, Analysis of the publications on the applications of particle swarm optimisation, Journal of Artificial Evolution and Applications, vol. 2008, p.3, (2008).

DOI: 10.1155/2008/685175

Google Scholar

[80] N. Franken and A. P. Engelbrecht, Investigating binary pso parameter influence on the knights cover problem, in Evolutionary Computation, 2005. The 2005 IEEE Congress on, 2005, pp.282-289.

DOI: 10.1109/cec.2005.1554696

Google Scholar

[81] C. -J. Lin and S. -J. Hong, The design of neuro-fuzzy networks using particle swarm optimization and recursive singular value decomposition, Neurocomputing, vol. 71, pp.297-310, (2007).

DOI: 10.1016/j.neucom.2006.12.016

Google Scholar

[82] R. Mehran, A. Fatehi, C. Lucas, and B. N. Araabi, Particle swarm extension to LOLIMOT, " in Intelligent Systems Design and Applications, 2006. ISDA, 06. Sixth International Conference on, 2006, pp.969-974.

DOI: 10.1109/isda.2006.253743

Google Scholar

[83] M. G. Omran, A. P. Engelbrecht, and A. Salman, A color image quantization algorithm based on particle swarm optimization, Informatica, vol. 29, (2005).

Google Scholar

[84] S. Ujjin and P. J. Bentley, Particle swarm optimization recommender system, " in Swarm Intelligence Symposium, 2003. SIS, 03. Proceedings of the 2003 IEEE, 2003, pp.124-131.

DOI: 10.1109/sis.2003.1202257

Google Scholar

[85] B. C. Chang, A. Ratnaweera, S. K. Halgamuge, and H. C. Watson, Particle swarm optimisation for protein motif discovery, Genetic Programming and Evolvable Machines, vol. 5, pp.203-214, (2004).

DOI: 10.1023/b:genp.0000023688.42515.92

Google Scholar

[86] Y. -T. Hsiao, C. -L. Chuang, and J. -A. Jiang, Particle swarm optimization approach for multiple biosequence alignment, in Proceedings of the IEEE international workshop on genomic signal processing and statistics, (2005).

Google Scholar

[87] M. P. Wachowiak, R. Smolíková, Y. Zheng, J. M. Zurada, and A. S. Elmaghraby, An approach to multimodal biomedical image registration utilizing particle swarm optimization, Evolutionary Computation, IEEE Transactions on, vol. 8, pp.289-301, (2004).

DOI: 10.1109/tevc.2004.826068

Google Scholar

[88] Y. Li, D. Yao, J. Yao, and W. Chen, A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning, Physics in medicine and biology, vol. 50, p.3491, (2005).

DOI: 10.1088/0031-9155/50/15/002

Google Scholar

[89] S. Das, A. Konar, and U. K. Chakraborty, An efficient evolutionary algorithm applied to the design of two-dimensional IIR filters, in Proceedings of the 7th annual conference on Genetic and evolutionary computation, 2005, pp.2157-2163.

DOI: 10.1145/1068009.1068364

Google Scholar

[90] S. Das, A. Konar, and U. K. Chakraborty, Improving particle swarm optimization with differentially perturbed velocity, in Proceedings of the 7th annual conference on Genetic and evolutionary computation, 2005, pp.177-184.

DOI: 10.1145/1068009.1068037

Google Scholar

[91] N. Khemka, C. Jacob, and G. Cole, Making soccer kicks better: a study in particle swarm optimization, in Proceedings of the 7th annual workshop on Genetic and evolutionary computation, 2005, pp.382-385.

DOI: 10.1145/1102256.1102342

Google Scholar

[92] P. Ko and P. Lin, A hybrid swarm intelligence based mechanism for earning forecast, Asian Journal of Information Technology, vol. 3, pp.180-187, (2004).

Google Scholar

[93] J. Nenortaite, Computation improvement of stockmarket decision making model through the application of grid, Inf Technol Control, vol. 34, pp.269-275, (2005).

Google Scholar

[94] J. Nenortaitė, COMPUTATION IMPROVEMENT OF STOCKMARKET DECISION MAKING MODEL THROUGHTHE APPLICATION OF GRID, Information Technology And Control, vol. 34, (2015).

Google Scholar

[95] G. Kendall and Y. Su, A Particle Swarm Optimisation Approach in the Construction of Optimal Risky Portfolios, in Artificial Intelligence and Applications, 2005, pp.140-145.

Google Scholar

[96] J. Nenortaite and R. Simutis, Stocks' trading system based on the particle swarm optimization algorithm, in Computational Science-ICCS 2004, ed: Springer, 2004, pp.843-850.

DOI: 10.1007/978-3-540-25944-2_109

Google Scholar

[97] H. H. Balci and J. F. Valenzuela, Scheduling electric power generators using particle swarm optimization combined with the Lagrangian relaxation method, International Journal of Applied Mathematics and Computer Science, vol. 14, pp.411-422, (2004).

Google Scholar

[98] T. -O. Ting, M. Rao, C. K. Loo, and S. Ngu, Solving unit commitment problem using hybrid particle swarm optimization, Journal of Heuristics, vol. 9, pp.507-520, (2003).

DOI: 10.1023/b:heur.0000012449.84567.1a

Google Scholar

[99] Y. Foo, S. Chien, A. Low, C. Teo, and Y. Lee, New strategy for optimizing wavelength converter placement, Optics express, vol. 13, pp.545-551, (2005).

DOI: 10.1364/opex.13.000545

Google Scholar

[100] A. Brabazon, A. Silva, T. F. de Sousa, M. O'Neill, R. Matthews, and E. Costa, Investigating strategic inertia using OrgSwarm, Informatica, vol. 29, (2005).

Google Scholar

[101] S. Kauffman and S. Levin, Towards a general theory of adaptive walks on rugged landscapes, Journal of theoretical Biology, vol. 128, pp.11-45, (1987).

DOI: 10.1016/s0022-5193(87)80029-2

Google Scholar

[102] A. Kaur, J. Kaushal, and P. Basak, Areview on microgrid central controller, Renewable and Sustainable Energy Reviews, vol. 55, pp.338-345, (2016).

DOI: 10.1016/j.rser.2015.10.141

Google Scholar

[103] P. Prakash and D. K. Khatod, Optimal sizing and siting techniques for distributed generation in distribution systems: A review, Renewable and Sustainable Energy Reviews, vol. 57, pp.111-130, (2016).

DOI: 10.1016/j.rser.2015.12.099

Google Scholar

[104] C. Gamarra and J. M. Guerrero, Computational optimization techniques applied to microgrids planning: a review, Renewable and Sustainable Energy Reviews, vol. 48, pp.413-424, (2015).

DOI: 10.1016/j.rser.2015.04.025

Google Scholar