Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 906028, 11 pages
http://dx.doi.org/10.1155/2014/906028
Research Article

A Memetic Approach for Improving Minimum Cost of Economic Load Dispatch Problems

Department of Energy IT, Gachon University, Seongnam 461-701, Republic of Korea

Received 21 October 2013; Revised 16 December 2013; Accepted 7 January 2014; Published 23 February 2014

Academic Editor: Swagatam Das

Copyright © 2014 Jinho Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. F. Bard, “Short-term scheduling of thermal-electric generators using Lagrangian relaxation,” Operations Research, vol. 36, no. 5, pp. 756–766, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. Z. X. Liang and J. D. Glover, “A zoom feature for a dynamic programming solution to economic dispatch including transmission losses,” IEEE Transactions on Power Systems, vol. 7, no. 2, pp. 544–550, 1992. View at Publisher · View at Google Scholar · View at Scopus
  3. C. L. Chen and S. C. Wang, “Branch-and-bound scheduling for thermal generating units,” IEEE Transactions on Energy Conversion, vol. 8, no. 2, pp. 184–189, 1993. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Nanda, L. Hari, and M. L. Kothari, “Economic emission load dispatch with line flow constraints using a classical technique,” IET Generation, Transmission and Distribution, vol. 141, no. 1, pp. 1–10, 1994. View at Google Scholar · View at Scopus
  5. P. G. Lowery, “Generating unit commitment by dynamic programming,” IEEE Transactions on Power Apparatus and Systems, vol. 85, no. 5, pp. 422–426, 1996. View at Publisher · View at Google Scholar
  6. J. P. D. Chattopadhyay, “A multi-area linear programming approach for analysis of economic operation of the Indian power system,” IEEE Transactions on Power Systems, vol. 11, no. 1, pp. 52–58, 1996. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Y. Fan and L. Zhang, “Real-time economic dispatch with line flow and emission constraints using quadratic programming,” IEEE Transactions on Power Systems, vol. 13, no. 2, pp. 320–325, 1998. View at Publisher · View at Google Scholar · View at Scopus
  8. D. C. Walters and G. B. Sheble, “Genetic algorithm solution of economic dispatch with value point loading,” IEEE Transactions on Power Systems, vol. 8, no. 3, pp. 1325–1332, 1993. View at Publisher · View at Google Scholar · View at Scopus
  9. P. H. Chen and H. C. Chang, “Large-scale economic dispatch by genetic algorithm,” IEEE Transactions on Power Systems, vol. 10, no. 4, pp. 1919–1926, 1995. View at Publisher · View at Google Scholar · View at Scopus
  10. G. B. Sheble and K. Brittig, “Refined genetic algorithm-economic dispatch example,” IEEE Transactions on Power Systems, vol. 10, no. 1, pp. 117–124, 1995. View at Publisher · View at Google Scholar · View at Scopus
  11. K. S. Swarup and S. Yamashiro, “Unit commitment solution methodology using genetic algorithm,” IEEE Transactions on Power Systems, vol. 17, no. 1, pp. 87–91, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. I. G. Damousis, A. G. Bakirtzis, and P. S. Dokopoulos, “Network-constrained economic dispatch using real-coded genetic algorithm,” IEEE Transactions on Power Systems, vol. 18, no. 1, pp. 198–205, 2003. View at Publisher · View at Google Scholar · View at Scopus
  13. C. L. Chiang, “Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels,” IEEE Transactions on Power Systems, vol. 20, no. 4, pp. 1690–1699, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. C. L. Chiang, “Genetic-based algorithm for power economic load dispatch,” IET Generation, Transmission and Distribution, vol. 1, no. 2, pp. 261–269, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Kumar and R. Naresh, “Nonconvex economic load dispatch using an efficient real-coded genetic algorithm,” Applied Soft Computing Journal, vol. 9, no. 1, pp. 321–329, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. H. T. Yang, P. C. Yang, and C. L. Huang, “Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions,” IEEE Transactions on Power Systems, vol. 11, no. 1, pp. 112–118, 1996. View at Publisher · View at Google Scholar · View at Scopus
  17. K. P. Wong and J. Yuryevich, “Evolutionary-programming-based algorithm for environmentally-constrained economic dispatch,” IEEE Transactions on Power Systems, vol. 13, no. 2, pp. 301–306, 1998. View at Publisher · View at Google Scholar · View at Scopus
  18. N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay, “Evolutionary programming techniques for economic load dispatch,” IEEE Transactions on Evolutionary Computation, vol. 7, no. 1, pp. 83–94, 2003. View at Publisher · View at Google Scholar · View at Scopus
  19. A. Pereira-Neto, C. Unsihuay, and O. R. Saavedra, “Efficient evolutionary strategy optimization procedure to solve the nonconvex economic dispatch problem with generator constraints,” IET Generation, Transmission and Distribution, vol. 152, no. 5, pp. 653–660, 2005. View at Publisher · View at Google Scholar
  20. Z. L. Gaing, “Particle swarm optimization to solving the economic dispatch considering the generator constraints,” IEEE Transactions on Power Systems, vol. 18, no. 3, pp. 1187–1195, 2003. View at Publisher · View at Google Scholar · View at Scopus
  21. J. B. Park, K. S. Lee, J. R. Shin, and K. Y. Lee, “A particle swarm optimization for economic dispatch with nonsmooth cost functions,” IEEE Transactions on Power Systems, vol. 20, no. 1, pp. 34–42, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Cai, X. Ma, L. Li, and P. Haipeng, “Chaotic particle swarm optimization for economic dispatch considering the generator constraints,” Energy Conversion and Management, vol. 48, no. 2, pp. 645–653, 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. A. I. Selvakumar and K. Thanushkodi, “A new particle swarm optimization solution to nonconvex economic dispatch problems,” IEEE Transactions on Power Systems, vol. 22, no. 1, pp. 42–51, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. K. T. Chaturvedi, M. Pandit, and L. Srivastava, “Self-organizing hierarchical particle swarm optimization for nonconvex economic dispatch,” IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1079–1087, 2008. View at Publisher · View at Google Scholar · View at Scopus
  25. A. I. Selvakumar and K. Thanushkodi, “Anti-predatory particle swarm optimization: solution to nonconvex economic dispatch problems,” Electric Power Systems Research, vol. 78, no. 1, pp. 2–10, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. K. T. Chaturvedi, M. Pandit, and L. Srivastava, “Particle swarm optimization with crazy particles for nonconvex economic dispatch,” Applied Soft Computing Journal, vol. 9, no. 3, pp. 962–969, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. J. G. Vlachogiannis and K. Y. Lee, “Economic load dispatch—a comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO,” IEEE Transactions on Power Systems, vol. 24, no. 2, pp. 991–1001, 2009. View at Publisher · View at Google Scholar · View at Scopus
  28. S. S. S. Hosseini and A. H. Gandomi, “Discussion of “Economic load dispatch—a comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO”,” IEEE Transactions on Power Systems, vol. 25, no. 1, p. 590, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. W. M. Lin, F. S. Cheng, and M. T. Tsay, “An improved tabu search for economic dispatch with multiple minima,” IEEE Transactions on Power Systems, vol. 17, no. 1, pp. 108–112, 2002. View at Publisher · View at Google Scholar · View at Scopus
  30. D. Liu and Y. Cai, “Taguchi method for solving the economic dispatch problem with nonsmooth cost functions,” IET Generation, Transmission and Distribution, vol. 1, no. 5, pp. 793–803, 2007. View at Publisher · View at Google Scholar
  31. B. K. Panigrahi and V. R. Pandi, “Bacterial foraging optimisation: Nelder-Mead hybrid algorithm for economic load dispatch,” IET Generation, Transmission and Distribution, vol. 2, no. 4, pp. 556–565, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. A. Bhattacharya and P. K. Chattopadhyay, “Solving complex economic load dispatch problems using biogeography-based optimization,” Expert Systems with Applications, vol. 37, no. 5, pp. 3605–3615, 2010. View at Publisher · View at Google Scholar · View at Scopus
  33. X. S. Yang, S. S. S. Hosseini, and A. H. Gandomi, “Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect,” Applied Soft Computing Journal, vol. 12, no. 3, pp. 1180–1186, 2012. View at Publisher · View at Google Scholar · View at Scopus
  34. T. Niknam, H. D. Mojarrad, H. Z. Meymand, and B. B. Firouzi, “A new honey bee mating optimization algorithm for non-smooth economic dispatch,” Energy, vol. 36, no. 2, pp. 896–908, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. L. D. S. Coelho and V. C. Mariani, “An improved harmony search algorithm for power economic load dispatch,” Energy Conversion and Management, vol. 50, no. 10, pp. 2522–2526, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. B. K. Panigrahi, V. R. Pandi, S. Das, Z. Cui, and R. Sharma, “Economic load dispatch using population-variance harmony search algorithm,” Transactions of the Institute of Measurement and Control, vol. 34, no. 6, pp. 746–754, 2011. View at Publisher · View at Google Scholar
  37. K. P. Wong and Y. W. Wong, “Thermal generator scheduling using hybrid genetic/simulated-annealing approach,” IET Generation, Transmission and Distribution, vol. 142, no. 4, pp. 372–380, 1995. View at Publisher · View at Google Scholar · View at Scopus
  38. L. D. S. Coelho and V. C. Mariani, “Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect,” IEEE Transactions on Power Systems, vol. 21, no. 2, pp. 989–996, 2006. View at Publisher · View at Google Scholar · View at Scopus
  39. L. D. S. Coelho and V. C. Mariani, “Erratum correction to “Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve point effect”,” IEEE Transactions on Power Systems, vol. 21, no. 3, p. 1465, 2006. View at Publisher · View at Google Scholar · View at Scopus
  40. S. K. Wang, J. P. Chiou, and C. W. Liu, “Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm,” IET Generation, Transmission and Distribution, vol. 1, no. 5, pp. 793–803, 2007. View at Publisher · View at Google Scholar · View at Scopus
  41. J. S. Alsumait, J. K. Sykulski, and A. K. Al-Othman, “A hybrid GA-PS-SQP method to solve power system valve-point economic dispatch problems,” Applied Energy, vol. 87, no. 5, pp. 1773–1781, 2010. View at Publisher · View at Google Scholar · View at Scopus
  42. H. Altun and T. Yalcinoz, “Implementing soft computing techniques to solve economic dispatch problem in power systems,” Expert Systems with Applications, vol. 35, no. 4, pp. 1668–1678, 2008. View at Publisher · View at Google Scholar · View at Scopus
  43. Z. W. Geem and Y. H. Cho, “Handling non-convex heat-power feasible region in combined heat and power economic dispatch,” International Journal of Electrical Power and Energy Systems, vol. 34, no. 1, pp. 171–173, 2012. View at Publisher · View at Google Scholar · View at Scopus
  44. M. H. Moradi and M. Abedini, “A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems,” International Journal of Electrical Power and Energy Systems, vol. 34, no. 1, pp. 66–74, 2012. View at Publisher · View at Google Scholar · View at Scopus
  45. A. Mahor and S. Rangnekar, “Short term generation scheduling of cascaded hydro electric system using novel self adaptive inertia weight PSO,” International Journal of Electrical Power and Energy Systems, vol. 34, no. 1, pp. 1–9, 2012. View at Publisher · View at Google Scholar · View at Scopus
  46. Z. W. Geem, “Size optimization for a hybrid photovoltaic—wind energy system,” International Journal of Electrical Power & Energy Systems, vol. 42, no. 1, pp. 448–451, 2012. View at Publisher · View at Google Scholar
  47. A. Bhattacharya and P. K. Chattopadhyay, “Solution of economic power dispatch problems using oppositional biogeography-based optimization,” Electric Power Components and Systems, vol. 38, no. 10, pp. 1139–1160, 2010. View at Publisher · View at Google Scholar · View at Scopus
  48. J. G. Vlachogiannis and K. Y. Lee, “Economic load dispatch—a comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO,” IEEE Transactions on Power Systems, vol. 24, no. 2, pp. 991–1001, 2009. View at Publisher · View at Google Scholar · View at Scopus
  49. K. T. Chaturvedi, M. Pandit, and L. Srivastava, “Self-organizing hierarchical particle swarm optimization for nonconvex economic dispatch,” IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1079–1087, 2008. View at Publisher · View at Google Scholar · View at Scopus
  50. B. K. Panigrahi, V. Ravikumar Pandi, and S. Das, “Adaptive particle swarm optimization approach for static and dynamic economic load dispatch,” Energy Conversion and Management, vol. 49, no. 6, pp. 1407–1415, 2008. View at Publisher · View at Google Scholar · View at Scopus
  51. C. C. Kuo, “A novel coding scheme for practical economic dispatch by modified particle swarm approach,” IEEE Transactions on Power Systems, vol. 23, no. 4, pp. 1825–1835, 2008. View at Publisher · View at Google Scholar · View at Scopus
  52. A. I. Selvakumar and K. Thanushkodi, “A new particle swarm optimization solution to nonconvex economic dispatch problems,” IEEE Transactions on Power Systems, vol. 22, no. 1, pp. 42–51, 2007. View at Publisher · View at Google Scholar · View at Scopus
  53. B. K. Panigrahi and V. Ravikumar Pandi, “Bacterial foraging optimisation: Nelder-Mead hybrid algorithm for economic load dispatch,” IET Generation, Transmission and Distribution, vol. 2, no. 4, pp. 556–565, 2008. View at Publisher · View at Google Scholar · View at Scopus
  54. L. D. S. Coelho and V. C. Mariani, “Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect,” IEEE Transactions on Power Systems, vol. 21, no. 2, pp. 989–996, 2006. View at Publisher · View at Google Scholar · View at Scopus
  55. A. I. Selvakumar and K. Thanushkodi, “Anti-predatory particle swarm optimization: solution to nonconvex economic dispatch problems,” Electric Power Systems Research, vol. 78, no. 1, pp. 2–10, 2008. View at Publisher · View at Google Scholar · View at Scopus
  56. S. K. Wang, J. P. Chiou, and C. W. Liu, “Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm,” IET Generation, Transmission and Distribution, vol. 1, no. 5, pp. 793–803, 2007. View at Publisher · View at Google Scholar · View at Scopus
  57. A. I. Selvakumar and K. Thanushkodi, “A new particle swarm optimization solution to nonconvex economic dispatch problems,” IEEE Transactions on Power Systems, vol. 22, no. 1, pp. 42–51, 2007. View at Publisher · View at Google Scholar · View at Scopus
  58. K. T. Chaturvedi, M. Pandit, and L. Srivastava, “Self-organizing hierarchical particle swarm optimization for nonconvex economic dispatch,” IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1079–1087, 2008. View at Publisher · View at Google Scholar · View at Scopus
  59. A. Bhattacharya and P. K. Chattopadhyay, “Solving complex economic load dispatch problems using biogeography-based optimization,” Expert Systems with Applications, vol. 37, no. 5, pp. 3605–3615, 2010. View at Publisher · View at Google Scholar · View at Scopus
  60. J. S. Alsumait, J. K. Sykulski, and A. K. Al-Othman, “A hybrid GA-PS-SQP method to solve power system valve-point economic dispatch problems,” Applied Energy, vol. 87, no. 5, pp. 1773–1781, 2010. View at Publisher · View at Google Scholar · View at Scopus
  61. B. K. Panigrahi and V. R. Pandi, “Bacterial foraging optimisation: Nelder-Mead hybrid algorithm for economic load dispatch,” IET Generation, Transmission and Distribution, vol. 2, no. 4, pp. 556–565, 2008. View at Publisher · View at Google Scholar · View at Scopus
  62. J. S. Al-Sumait, A. K. AL-Othman, and J. K. Sykulski, “Application of pattern search method to power system valve-point economic load dispatch,” International Journal of Electrical Power and Energy Systems, vol. 29, no. 10, pp. 720–730, 2007. View at Publisher · View at Google Scholar · View at Scopus
  63. F. Neri and C. Cotta, “Memetic algorithms and memetic computing optimization: a literature review,” Swarm and Evolutionary Computation, vol. 2, pp. 1–14, 2012. View at Publisher · View at Google Scholar · View at Scopus
  64. J. S. Al-Sumait, A. K. AL-Othman, and J. K. Sykulski, “Application of pattern search method to power system valve-point economic load dispatch,” International Journal of Electrical Power and Energy Systems, vol. 29, no. 10, pp. 720–730, 2007. View at Publisher · View at Google Scholar · View at Scopus
  65. G. Iacca, F. Neri, E. Mininno, Y. S. Ong, and M. H. Lim, “Ockham's Razor in memetic computing: three stage optimal memetic exploration,” Information Sciences, vol. 188, pp. 17–43, 2012. View at Publisher · View at Google Scholar · View at Scopus
  66. F. Caraffini, F. Neri, G. Iacca, and A. Mol, “Parallel memetic structures,” Information Sciences, vol. 227, pp. 60–82, 2013. View at Publisher · View at Google Scholar
  67. H. Ishibuchi, T. Yoshida, and T. Murata, “Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling,” IEEE Transactions on Evolutionary Computation, vol. 7, no. 2, pp. 204–223, 2003. View at Publisher · View at Google Scholar · View at Scopus
  68. K. C. Tan, S. C. Chiam, A. A. Mamun, and C. K. Goh, “Balancing exploration and exploitation with adaptive variation for evolutionary multi-objective optimization,” European Journal of Operational Research, vol. 197, no. 2, pp. 701–713, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  69. H. A. Abbass, “An evolutionary artificial neural networks approach for breast cancer diagnosis,” Artificial Intelligence in Medicine, vol. 25, no. 3, pp. 265–281, 2002. View at Publisher · View at Google Scholar · View at Scopus
  70. J. Tang, M. H. Lim, and Y. S. Ong, “Diversity-adaptive parallel memetic algorithm for solving large scale combinatorial optimization problems,” Soft Computing, vol. 11, no. 9, pp. 873–888, 2007. View at Publisher · View at Google Scholar · View at Scopus
  71. S. M. K. Hasan, R. Sarker, D. Essam, and D. Cornforth, “Memetic algorithms for solving job-shop scheduling problems,” Memetic Computing, vol. 1, no. 1, pp. 69–83, 2009. View at Publisher · View at Google Scholar · View at Scopus
  72. K. K. Lim, Y. S. Ong, M. H. Lim, X. Chen, and A. Agarwal, “Hybrid ant colony algorithms for path planning in sparse graphs,” Soft Computing, vol. 12, no. 10, pp. 981–994, 2008. View at Publisher · View at Google Scholar · View at Scopus
  73. K. C. Tan, C. Y. Cheong, and C. K. Goh, “Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation,” European Journal of Operational Research, vol. 177, no. 2, pp. 813–839, 2006. View at Publisher · View at Google Scholar · View at Scopus
  74. A. Caponio, G. L. Cascella, F. Neri, N. Salvatore, and M. Sumner, “A fast adaptive memetic algorithm for online and offline control design of PMSM drives,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 37, no. 1, pp. 28–41, 2007. View at Publisher · View at Google Scholar · View at Scopus
  75. F. Neri and E. Mininno, “Memetic compact differential evolution for cartesian robot control,” IEEE Computational Intelligence Magazine, vol. 5, no. 2, pp. 54–65, 2010. View at Publisher · View at Google Scholar · View at Scopus
  76. T. Rogalsky and R. W. Derksen, “Hybridization of differential evolution for aerodynamic design,” in Proceedings of the 8th Annual Conference of the Computational Fluid Dynamics Society of Canada, pp. 729–736, 2000.
  77. Z. W. Geem, “Parameter estimation for the nonlinear Muskingum model using the BFGS technique,” Journal of Irrigation and Drainage Engineering, vol. 132, no. 5, pp. 474–478, 2006. View at Publisher · View at Google Scholar · View at Scopus
  78. Z. W. Geem, “Parameter estimation of the nonlinear muskingum model using parameter-setting-free harmony search,” Journal of Hydrologic Engineering, vol. 16, no. 8, pp. 684–688, 2011. View at Publisher · View at Google Scholar · View at Scopus
  79. H. Karahan, G. Gurarslan, and Z. W. Geem, “Parameter estimation of the nonlinear Muskingum flood routing model using a hybrid harmony search algorithm,” ASCE Journal of Hydrologic Engineering, vol. 18, no. 3, pp. 352–260, 2013. View at Publisher · View at Google Scholar
  80. F. Gao and L. Han, “Implementing the Nelder-Mead simplex algorithm with adaptive parameters,” Computational Optimization and Applications, vol. 51, no. 1, pp. 259–277, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  81. E. Afzalan and M. Joorabian, “Emission, reserve and economic load dispatch problem with non-smooth and non-convex cost functions using epsilon-multi-objective genetic algorithm variable,” International Journal of Electrical Power and Energy Systems, vol. 52, pp. 55–67, 2013. View at Publisher · View at Google Scholar