In this paper, an effective meta-heuristic technique called Quasi-Oppositional Symbiotic Organisms Search is applied for solving non-convex economic dispatch problems. Symbiotic Organisms Search is a soft computing technique, inspired by organisms in the ecosystem. This technique is implemented for improving the solution quality in minimum time. In order to improve convergence rate, quasi-reflected numbers are used here instead of pseudo-random numbers. Different equality and inequality constraints such as transmission loss, load demand, prohibited operating zone, generator operating limits and boundary of ramp rate are considered here. Presence of multiple fuels and valve point are also considered in some cases. This algorithm is applied to four different test systems. Simulation results are compared with many recently developed optimization techniques to show the superiority and consistency of this method. Simulation results also show that the computational efficiency of this algorithm is much better than the other meta-heuristic methods available in the literature.
Fanshel, S. and Lynes, E.S. Economic power generation using linear programming", IEEE Trans. Power Appar. Syst., 83(4), pp. 347{356 (1964). DOI: 10.1109/TPAS/.1964.4766011 2. Bellman, R., The Theory of Dynamic Programming, Rand Corp Santa Monica CA (1954). D. Das et al./Scientia Iranica, Transactions D: Computer Science & ... 27 (2020) 3096{3117 3115 3. Wood, J. and Wollenberg, B.F., Power Generation, Operation, and Control, John Wiley and Sons, 2nd Edn., Wiley New York (1984). 4. Ingber, L. Simulated annealing : Practice versus Theory", Mathl. Comput. Modeling l, 18(11), pp. 29{ 57 (1993). DOI: 10.1016/0895-7177(93)90204-C 5. Panigrahi, C.K., Chattopadhyay, P.K., and Chakrabarti, R.N., et al. Simulated annealing technique for dynamic economic dispatch", Electr. Power Compon. Syst., 34(5), pp. 577{586 (2006). DOI: 10.1080/15325000500360843 6. Walters, D.C. and Sheble, G.B. Genetic algorithm solution of economic dispatch with valve point loadings", IEEE Trans. Power Syst., 8(3), pp. 1325{1331 (1993). DOI: 10.1109/59.260861 7. Chiang, C.L. Improved genetic algorithm for power economic dispatch of units with valve-point e_ects and multiple fuels", IEEE Trans. Power Syst., 20(4), pp. 1690{1699 (2005). DOI: 10.1109/TPWRS.2005.857924 8. Kennedy, J. and Eberhart, R. Particle swarm optimization", In Pro. IEEE Int. Conf. Neural Networks, IV, pp. 1942{1948 (1995). DOI: 10.1109/ICNN.1995.488968 9. Gaing, Z.-L. Particle swarm optimization to solving the economic dispatch considering the generator constraints", IEEE Trans. Power Syst., 18(3), pp. 1187{ 1195 (2003). DOI: 10.1109/TPWRS.2003.814889 10. Selvakumar, I. and Thanushkodi, K. A new particle swarm optimization solution to nonconvex economic dispatch problems", IEEE Trans. Power Syst., 22(1), pp. 42{51 (2007). DOI: 10.1109/TPWRS.2006.889132 11. Panigrahi, B.K., Pandi, V.R., and Das, S. Adaptive particle swarm optimization approach for static and dynamic economic load dispatch", Energy Convers. Manage., 49(6), pp. 1407{1415 (2008). DOI: 10.1016/j.enconman.2007.12.023 12. Vlachogiannis, J.K. and Lee, K.Y. Economic load dispatch - a comparative study on heuristic optimization techniques with an improved coordinated aggregationbased PSO", IEEE Trans. Power Syst., 24(2), pp. 991{ 1001 (2009). DOI: 10.1109/TPWRS.2009.2016524 13. Park, J.B., Jeong, Y.W., Shin, J.R., et al. An improved particle swarm optimization for non-convex economic dispatch problems", IEEE Trans. Power Syst., 25 (1), pp. 156{166 (2010). DOI: 10.1109/TPWRS. 2009.2030293 14. Hosseinnezhad, V., Ra_ee, M., Ahmadian, M., et al. Species-based quantum particle swarm optimization for economic load dispatch", Int. J. Electr. Power & Energy Syst., 63, pp. 311{322 (2014). DOI: 10.1016/j.ijepes.2014.05.066 15. Storn, R. and Price, K.V. Di_erential evolution a simple and e_cient heuristic for global optimization over continuous spaces", J. Global Optim., 11(4), pp. 341{359 (1997). DOI: 10.1023/A:100820282 16. Noman, N. and Iba, H. Di_erential evolution for economic load dispatch problems", Electr. Power Syst. Res., 78(3), pp. 1322{1331 (2008). DOI: 10.1016/j.epsr.2007.11.007 17. Coelho, L.D.S. and Mariani, V.C. Combining of chaotic di_erential evolution and quadratic programming for economic dispatch optimization with valvepoint e_ect", IEEE Trans. Power Syst., 21 (2), pp. 989{996 (2006). DOI: 10.1109/TPWRS.2006.873410 18. Parouha, R.P. and Das, K.N. A novel hybrid optimizer for solving economic load dispatch problem", Int. J. Electr. Power & Energy Syst., 78, pp. 108{126 (2016). DOI: 10.1016/j.ijepes.2015.11.058 19. Zou, D., Li, S., Wang, G-G., et al. An improved di_erential evolution algorithm for the economic load dispatch problems withor without valvepoint e_ects", Appl. Energy, 181, pp. 375{390 (2016). DOI: 10.1016/j.apenergy.2016.08.067 20. Jayabharathi, T., Jayaprakash, K., Jeyakumar, N., et al. Evolutionary programming techniques for different kinds of economic dispatch problems", Electr. Power Syst. Res., 73(2), pp. 169{176 (2005). DOI: 10.1016/j.epsr.2004.08.001 21. Sinha, N., Chakrabarti, R., and Chattopadhyay, P.K. Evolutionary programming techniques for economic load dispatch", IEEE Trans. Evol. Comput., 7(1), pp. 83{94 (2003). DOI: 10.1109/TEVC.2002.806788 22. Panigrahi, B.K. and Pandi, V.R. Bacterial foraging optimization Nelder-Mead hybrid algorithm for economic load dispatch", IET Generation, Transm. Distrib., 2(4), pp. 556{65 (2008). DOI: 10.1049/ietgtd: 20070422 23. Simon, D. Biogeography-based optimization", IEEE Trans. Evol. Comput., 12(6), pp. 702{713 (2008). DOI: 10.1109/TEVC.2008.919004 24. Bhattacharya, A. and Chattopadhyay, P.K. Biogeography-based optimization for di_erent economic load dispatch problems", IEEE Trans. Power Syst., 25(2), pp. 1064{1077 (2010). DOI: 10.1109/TPWRS.2009.2034525 25. Bhattacharya, A. and Chattopadhyay, P.K. Hybrid di_erential evolution with biogeography-based optimization for solution of economic load dispatch", IEEE Trans. Power Syst., 25(4), pp. 1955{1964 (2010). DOI: 10.1109/TPWRS.2010.2043270 26. Lam, A.Y.S. and Li, V.O.K. Chemical-reactioninspired metaheuristic for optimization", IEEE Trans. Evol. Comput., 14(3) pp. 381{399 (2010). DOI: 10.1109/TEVC.2009.2033580 27. Bhattacharjee, K., Bhattacharya, A., and Dey, S.H.N. Chemical reaction optimisation for di_erent economic dispatch problems", IET Gener. Transm. Distrib., 8(3), pp. 530{541 (2014). DOI: 10.1049/ietgtd. 2013.0122 28. Bhattacharjee, K., Bhattacharya, A., and Dey, S.H. Oppositional real coded chemical reaction optimization for di_erent economic dispatch problems", Int. J. 3116 D. Das et al./Scientia Iranica, Transactions D: Computer Science & ... 27 (2020) 3096{3117 Electr. Power Energy Syst., 55, pp. 378{391 (2014). DOI: 10.1016/j.ijepes.2013.09.033 29. Rao, R.V., Savsani, V.J., and Vakharia, D.P. Teaching-learning based optimization: a novel method for constrained mechanical design optimization problems", Comp. Aided Design, 43(3), pp. 303{ 315 (2011). DOI: 10.1016/j.cad.2010.12.015 30. Bhattacharjee, K., Bhattacharya, A., and Dey, S.H.N. Teaching learning based optimization for di_erent economic dispatch problems", Scientia Iranica, 21(3), pp. 870{884 (2013). 31. Banerjee, S., Maity, D., and Chanda, C.K. Teaching learning based optimization for economic load dispatch problem considering valve point loading e_ect", Int. J. Electr. Power & Energy Syst., 73, pp. 456{464 (2015). DOI: 10.1016/j.ijepes.2015.05.036 32. He, X., Rao, Y., and Huang, J. A novel algorithm for economic dispatch of power systems", Neurocomputing, 171, pp. 1454{1461 (2016). DOI: 10.1016/j.neucom.2015.07.107 33. Mirjalili, S., Mirjalili, S.M., and Lewis, A. Grey wolf optimizer", Adv. Eng. Softw., 69, pp. 46{61 (2014). DOI: 10.1016/j.advengsoft.2013.12.007 34. Kamboj, V.K., Bath, S.K., and Dhillon, J.S. Solution of non-convex economic load dispatch problem using grey wolf optimizer", Neural Comput & Applic., 27(5), pp. 1301{1316 (2006). DOI: 10.1007/s00521-015-1934- 8 35. Rajagopalan, A., Sengoden, V., and Govindasamy, R. Solving economic load dispatch problems using chaotic self-adaptive di_erential harmony search algorithm", Int. Trans. Electr. Energ. Syst., 25(5), pp. 845{858 (2014). DOI: 10.1002/etep.1877 36. Mandal, B., Roy, P.K., and Mandal, S. Economic load dispatch using krill herd algorithm", Int. J. Electr. Power Energy Syst., 57, pp. 1{10 (2014). DOI: 10.1016/j.ijepes.2013.11.016 37. Barisal, A.K. and Prusty, R.C. Large scale economic dispatch of power systems using oppositional invasive weed optimization", Appl. Soft Comput., 29, pp. 122{ 137 (2015). DOI: 10.1016/j.asoc.2014.12.014 38. Mirjalili, S. The ant lion optimizer", Adv Eng Softw., 83, pp. 80{98 (2015). DOI: 10.1016/j.advengsoft.2015.01.010 39. Kamboj, V.K., Bhadoria, A., and Bath, S.K. Solution of non-convex economic load dispatch problem for small-scale power systems using ant lion optimizer", Neural Comput & Applic., 28, pp. 2181{2192 (2016). DOI: 10.1007/s00521-015-2148-9 40. Subathra, M.S.P., Easter, S.E., Victoire, T.A., et al. A hybrid with cross-entropy method and sequential quadratic programming to solve economic load dispatch problem", IEEE Sys. Journal, 9(3), pp. 1031{ 1044 (2015). DOI: 10.1109/JSYST.2013.2297471 41. Al-Betar, M.A., Awadallah, M.A., Khader, A.T., et al. Tournament based harmony search algorithm for non-convex economic load dispatch problem", Appl. Soft comput., 47, pp. 449{459 (2016). DOI: 10.1016/j.asoc.2016.05.034 42. Ghorbani, N. and Babaei, E. Exchange market algorithm for economic load dispatch", Int. J. Electr. Power Energy Syst., 75, pp. 19{27 (2016). DOI: 10.1016/j.ijepes.2015.08.013 43. Mohammadi, F. and Abdi, H. A modi_ed crow search algorithm (MCSA) for solving economic load dispatch problem", Appl. Soft Comput., 71, pp. 51{65 (2018). DOI: 10.1016/j.asoc.2018.06.040 44. Cheng, M.Y. and Prayogo, D. Symbiotic organisms search: A new metaheuristic optimization algorithm", Computers & Structures, 139, pp. 98{112 (2014). DOI: 10.1016/j.compstruc.2014.03.007 45. Duman, S. Symbiotic organisms search algorithm for optimal power ow problem based on valve-point e_ect and prohibited zones", Neural Comput & Applic, 28, pp. 3571{3585 (2016). DOI: 10.1007/s00521-016-2265- 0 46. Guvenc, U., Duman, S., Sonmez, Y., et al. Symbiotic organisms search algorithm for economic load dispatch problem with valve point e_ect", Scientia Iranica, 25(6), pp. 3490{3506 (2017). 47. Tizhoosh, H. Opposition-based learning: A new scheme for machine intelligence", In Proceedings of the International Conference on Computational Intelligence for Modelling Control and Automation, Austria, pp. 695{701 (2005). DOI: 10.1109/CIMCA.2005.1631345 48. Eegezer, M., Simon, D., and Du, D. Optimization", In Proceedings of the IEEE International Conference on Oppositional Biogeography-Based Systems, Man and Cybernetics, San Antonio, TX, USA, pp. 1009{1014 (2009). DOI: 10.1109/CEC.2011.5949792 49. Aragon, V.S., Esquivel, S.C., and Coello, C.A.C. An immune algorithm with power redistribution for solving economic load dispatch problems", Info. Sciences, 295, pp. 609{632 (2014). DOI: 10.1016/j.ins.2014.10.026 50. Ciornei, I. and Kyriakides, E. E_cient hybrid optimization solution for the economic dispatch with nonsmooth cost function", In Proc. IEEE Power Tech, Bucharest, Romania, pp. 1{7 (2009). DOI: 10.1109/PTC.2009.5282062 51. Reddy A.S. and Vaisakh, K. Shu_ed di_erential evolution for large scale economic dispatch", Electr. Power Syst. Res., 96, pp. 237{245 (2013). DOI: 10.1016/j.epsr.2012.11.010 52. Ciornei, I. and Kyriakides, E. A GA-API solution for the economic dispatch of generation in power system operation", IEEE Trans. Power Syst., 27(1), pp. 233{ 242 (2011). DOI: 10.1109/TPWRS.2011.2168833 53. Derac, J., Garcia, S., Molina, D., et al. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary D. Das et al./Scientia Iranica, Transactions D: Computer Science & ... 27 (2020) 3096{3117 3117 and swarm intelligence algorithms", Swarm and Evolutionary Computation, 1, pp. 3{18 (2011). DOI: 10.1016/j.swevo.2011.02.002 54. Shenkin, D.J., Hand Book of Parametric and No Parametric Statistical Procedures, 4th Ed., Chapman & Hall/CRC (2006).
Das, D., Bhattacharya, A., Narayan Ray, R. (2020). Quasi-oppositional symbiotic organisms search algorithm for different economic load dispatch problems. Scientia Iranica, 27(6), 3096-3117. doi: 10.24200/sci.2018.50766.1855
MLA
D. Das; A. Bhattacharya; R. Narayan Ray. "Quasi-oppositional symbiotic organisms search algorithm for different economic load dispatch problems". Scientia Iranica, 27, 6, 2020, 3096-3117. doi: 10.24200/sci.2018.50766.1855
HARVARD
Das, D., Bhattacharya, A., Narayan Ray, R. (2020). 'Quasi-oppositional symbiotic organisms search algorithm for different economic load dispatch problems', Scientia Iranica, 27(6), pp. 3096-3117. doi: 10.24200/sci.2018.50766.1855
VANCOUVER
Das, D., Bhattacharya, A., Narayan Ray, R. Quasi-oppositional symbiotic organisms search algorithm for different economic load dispatch problems. Scientia Iranica, 2020; 27(6): 3096-3117. doi: 10.24200/sci.2018.50766.1855
)