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A modified differential evolution based solution technique for economic dispatch problems
1. | Algoritmi R&D Centre, School of Engineering, University of Minho, 4710-057 Braga, Portugal, Portugal |
References:
[1] |
M. M. Ali, A recursive topographical differential evolution algorithm for potential energy minimization,, J. Ind. Manag. Optim., 6 (2010), 29.
doi: 10.3934/jimo.2010.6.29. |
[2] |
P. Attaviriyanupap, H. Kita, E. Tanaka and J. Hasegawa, A hybrid EP and SQP for dynamic economic dispatch with nonsmooth fuel cost function,, IEEE Trans. Power Syst., 17 (2002), 411.
doi: 10.1109/TPWRS.2002.1007911. |
[3] |
R. Balamurugan and S. Subramanian, Differential evolution-based dynamic economic dispatch of generating units with valve-point effects,, Electr. Power Compon. Syst., 36 (2008), 828.
doi: 10.1080/15325000801911427. |
[4] |
R. Balamurugan and S. Subramanian, An improved differential evolution based dynamic economic dispatch with nonsmooth fuel cost function,, J. Electr. Syst., 3 (2007), 151. Google Scholar |
[5] |
H.-G. Beyer and H.-P. Schwefel, Evolution strategies: A comprehensive introduction,, J. Nat. Comput., 1 (2002), 3.
doi: 10.1023/A:1015059928466. |
[6] |
P. Belotti, "Couenne: A User's Manual,", Available from: , (2009). Google Scholar |
[7] |
S. I. Birbil and S. C. Fang, An electromagnetism-like mechanism for global optimization,, J. Glob. Optim., 25 (2003), 263.
doi: 10.1023/A:1022452626305. |
[8] |
E. G. Birgin, C. A. Floudas and J. M. Martínez, Global minimization using an augmented Lagrangian method with variable lower-level constraints,, Math. Program. Ser. A, 125 (2010), 139.
doi: 10.1007/s10107-009-0264-y. |
[9] |
J. Brest, S. Greiner, B. Bošković, M. Mernik and V. Žumer, Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems,, IEEE Trans. Evol. Comput., 10 (2006), 646.
doi: 10.1109/TEVC.2006.872133. |
[10] |
A. Brooke, D. Kendrick, A. Meeraus and R. Raman, "GAMS: A User's Guide,", Release 2.25, (1992). Google Scholar |
[11] |
R. H. Byrd, J. Nocedal and R. A. Waltz, KNITRO: An integrated package for nonlinear optimization,, In, (2006), 35.
|
[12] |
C.-L. Chen, Non-convex economic dispatch: a direct search approach,, Energy Convers. Manage., 48 (2007), 219.
doi: 10.1016/j.enconman.2006.04.010. |
[13] |
P. H. Chen and H. C. Chang, Large-scale economic dispatch by genetic algorithm,, IEEE Trans. Power Syst., 10 (1995), 1919.
doi: 10.1109/59.476058. |
[14] |
J.-P. Chiou, Variable scaling hybrid differential evolution for large-scale economic dispatch problems,, Electr. Power Syst. Res., 77 (2007), 212.
doi: 10.1016/j.epsr.2006.02.013. |
[15] |
A. R. Conn, N. I. M. Gould and Ph. L. Toint, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds,, SIAM J. Numer. Anal., 28 (1991), 545.
doi: 10.1137/0728030. |
[16] |
D. B. Das and C. Patvardhan, Solution of economic load dispatch using real coded hybrid stochastic search,, Int. J. Electr. Power Energy Syst., 21 (1999), 165.
doi: 10.1016/S0142-0615(98)00036-2. |
[17] |
S. Das and P. N. Suganthan, Differential evolution: A survey of the state-of-the-art,, IEEE Trans. Evol. Comput., 15 (2011), 4.
doi: 10.1109/TEVC.2010.2059031. |
[18] |
S. Das, A. Abraham, U. K. Chakraborty and A. Konar, Differential evolution using a neighborhood-based mutation operator,, IEEE Trans. Evol. Comput., 13 (2009), 526.
doi: 10.1109/TEVC.2008.2009457. |
[19] |
K. Deb, Scope of stationary multi-objective evolutionary optimization: A case study on a hydro-thermal power dispatch problem,, J. Glob. Optim., 41 (2008), 479.
doi: 10.1007/s10898-007-9261-y. |
[20] |
K. Deb, An efficient constraint handling method for genetic algorithms,, Comput. Meth. Appl. Mech. Eng., 186 (2000), 311.
doi: 10.1016/S0045-7825(99)00389-8. |
[21] |
V. N. Dieu and W. Ongsakul, Augmented lagrange hopfield network for large scale economic dispatch,, Proc. Int. Symp. Electr. Electron. Eng., (2007), 19. Google Scholar |
[22] |
M. Dorigo, V. Maniezzo and A. Colorni, The ant system: optimization by a colony of cooperating agents,, IEEE Trans. Syst. Man Cybern., 26 (1996), 29.
doi: 10.1109/3477.484436. |
[23] |
A. Drud, "CONOPT: Solver Manual,", ARKI Consulting and Development. Available from: , (). Google Scholar |
[24] |
D. E. Finkel and C. T. Kelley, Additive scaling and the DIRECT algorithm,, J. Glob. Optim., 36 (2006), 597.
doi: 10.1007/s10898-006-9029-9. |
[25] |
R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function,, Math. Program., 91 (2002), 239.
doi: 10.1007/s101070100244. |
[26] |
R. Fourer, D. M. Gay and B. W. Kernighan, "AMPL: A Modeling Language for Mathematical Programming,", Boyd & Fraser Publishing Co., (1993). Google Scholar |
[27] |
Z.-L Gaing, Particle swarm optimization to solving the economic dispatch considering the generators constraints,, IEEE Trans. Power Syst., 18 (2003), 1187.
doi: 10.1109/TPWRS.2003.814889. |
[28] |
Z. W. Geem, J.-H. Kim and G. V. Loganathan, A new heuristic optimization algorithm: harmony search,, Simulation, 76 (2001), 60.
doi: 10.1177/003754970107600201. |
[29] |
Ph. E. Gill, W. Murray and M. A. Saunders, SNOPT: An SQP algorithm for large-scale constrained optimization,, SIAM Rev., 47 (2005), 99.
doi: 10.1137/S0036144504446096. |
[30] |
F. Glover and M. Laguna, "Tabu Search,", Kluwer Academic Publishers, (1997).
|
[31] |
G. P. Granelli and M. Montagna, Security-constrained economic dispatch using dual quadratic programming,, Electr. Power Syst. Res., 56 (2000), 71.
doi: 10.1016/S0378-7796(00)00097-3. |
[32] |
D. He, F. Wang and Z. Mao, A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valve-point effect,, Electr. Power Energy Syst., 30 (2008), 31.
doi: 10.1016/j.ijepes.2007.06.023. |
[33] |
K. S. Hindi and A. R. Ab-Ghani, Dynamic economic dispatch for large-scale power systems: a Lagrangian relaxation approach,, Electr. Power Syst. Res., 13 (1991), 51.
doi: 10.1016/0142-0615(91)90018-Q. |
[34] |
J. H. Holland, "Adaptation in Natural and Artificial Systems,", University of Michigan Press, (1997).
|
[35] |
W. Huyer and A. Neumaier, Global optimization by multilevel coordinate search,, J. Glob. Optim., 14 (1999), 331.
doi: 10.1023/A:1008382309369. |
[36] |
R. A. Jabr, A. H. Coonick and B. J. Cory, A homogeneous linear programming algorithm for the security constrained economic dispatch problem,, IEEE Trans. Power Syst., 15 (2000), 930.
doi: 10.1109/59.871715. |
[37] |
P. Kaelo and M. M. Ali, A numerical study of some modified differential evolution algorithms,, Eur. J. Oper. Res., 169 (2006), 1176.
doi: 10.1016/j.ejor.2004.08.047. |
[38] |
D. Karaboga and B. Basturk, A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm,, J. Glob. Optim., 39 (2007), 459.
doi: 10.1007/s10898-007-9149-x. |
[39] |
A. A. El-Keib, H. Ma and J. L. Hart, Environmentally constrained economic dispatch using the Lagrangian relaxation method,, IEEE Trans. Power Syst., 9 (1994), 1723.
doi: 10.1109/59.331423. |
[40] |
J. Kennedy, R. C. Eberhart and Y. Shi, "Swarm Intelligence,", Morgan Kaufmann, (2001). Google Scholar |
[41] |
S. Kirkpatrick, C. D. Gelatt Jr. and M. P. Vecchi, Optimization by simulated annealing,, Science, 220 (1983), 671.
doi: 10.1126/science.220.4598.671. |
[42] |
J. J. Liang, T. P. Runarsson, E. Mezura-Montes, M. Clerc, P. N. Suganthan, C. A. Coello Coello and K. Deb, "Problem Definitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization,", Technical Report, (2006). Google Scholar |
[43] |
, "LINDOGlobal: Solver Manual,", Lindo Systems, (2007). Google Scholar |
[44] |
J. Liu and J. Lampinen, A fuzzy adaptive differential evolution algorithm,, Soft Comput., 9 (2005), 448.
doi: 10.1007/s00500-004-0363-x. |
[45] |
R. Mallipeddi, P. N. Suganthan, Q. K. Pan and M. F. Tasgetiren, Differential evolution algorithm with ensemble of parameters and mutation strategies,, Appl. Soft Comput., 11 (2011), 1679.
doi: 10.1016/j.asoc.2010.04.024. |
[46] |
R. Mallipeddi and P. N. Suganthan, Ensemble of constraint handling techniques,, IEEE Trans. Evol. Comput., 14 (2010), 561.
doi: 10.1109/TEVC.2009.2033582. |
[47] |
B. A. Murtagh and M. A. Saunders, "MINOS 5.5 User's Guide, Report SOL 83-20R,", Dept. of Operations Research, (1998). Google Scholar |
[48] |
C. K. Panigrahi, P. K. Chattopadhyay, R. N. Chakrabarti and M. Basu, Simulated annealing technique for dynamic economic dispatch,, Electr. Power Compon. Syst., 34 (2006), 577.
doi: 10.1080/15325000500360843. |
[49] |
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 Trans. Power Syst., 20 (2005), 34.
doi: 10.1109/TPWRS.2004.831275. |
[50] |
Y.-M. Park, J. R. Won and J. B. Park, New approach to economic load dispatch based on improved evolutionary programming,, Eng. Intell. Syst. Electr. Eng. Commun., 6 (1998), 103. Google Scholar |
[51] |
A. K. Qin, V. L. Huang and P. N. Suganthan, Differential evolution algorithm with strategy adaptation for global numerical optimization,, IEEE Trans. Evol. Comput., 13 (2009), 398.
doi: 10.1109/TEVC.2008.927706. |
[52] |
T. P. Runarsson and X. Yao, Constrained evolutionary optimization-the penalty function approach,, in, (2003), 87.
|
[53] |
N. Sinha, R. Chakrabarti and P. K. Chattopadhyay, Evolutionary programming techniques for economic load dispatch,, IEEE Trans. Evol. Comput., 7 (2003), 83.
doi: 10.1109/TEVC.2002.806788. |
[54] |
R. Storn and K. Price, Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces,, J. Glob. Optim., 11 (1997), 341.
doi: 10.1023/A:1008202821328. |
[55] |
C.-T. Su and W.-T. Tyen, A genetic algorithm approach employing floating point representation for economic dispatch of electric power systems,, Proc. Int. Congr. Model. Simul., (1997), 1444. Google Scholar |
[56] |
S. Takriti and B. Krasenbrink, A decomposition approach for the fuel-constrained economic power-dispatch problem,, Eur. J. Oper. Res., 112 (1999), 460.
doi: 10.1016/S0377-2217(98)00131-3. |
[57] |
M. Tawarmalani and N. Sahinidis, "Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming,", Kluwer Academic Publishers, (2002).
|
[58] |
R. J. Vanderbei and D. F. Shanno, An interior-point algorithm for nonconvex nonlinear programming,, Comput. Optim. Appl., 13 (1999), 231.
doi: 10.1023/A:1008677427361. |
[59] |
T. A. A. Victorie and A. E. Jeyakumar, Hybrid PSO-SQP for economic dispatch with valve-point effect,, Electr. Power Syst. Res., 71 (2004), 51.
doi: 10.1016/j.epsr.2003.12.017. |
[60] |
A. Wächter and L. T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming,, Math. Program., 106 (2006), 25.
doi: 10.1007/s10107-004-0559-y. |
[61] |
D. C. Walters and G. B. Sheble, Genetic algorithm solution of economic dispatch with valve-point loadings,, IEEE Trans. Power Syst., 8 (1993), 1325.
doi: 10.1109/59.260861. |
[62] |
K. P. Wong and Y. W. Wong, Genetic and genetic/simulated-annealing approaches to economic dispatch,, IEE Proc. Gener. Transm. Distrib., 141 (1994), 507.
doi: 10.1049/ip-gtd:19941354. |
[63] |
K. P. Wong and C. C. Fung, Simulated annealing based economic dispatch algorithm,, IEE Proc. Gener. Transm. Distrib., 140 (1993), 509. Google Scholar |
[64] |
H.-T. Yang, P.-C. Yang and C.-L. Huang, Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions,, IEEE Trans. Power Syst., 11 (1996), 112.
doi: 10.1109/59.485992. |
[65] |
J. Zhang and A. C. Sanderson, JADE: Adaptive differential evolution with optional external archive,, IEEE Trans. Evol. Comput., 13 (2009), 945.
doi: 10.1109/TEVC.2009.2014613. |
show all references
References:
[1] |
M. M. Ali, A recursive topographical differential evolution algorithm for potential energy minimization,, J. Ind. Manag. Optim., 6 (2010), 29.
doi: 10.3934/jimo.2010.6.29. |
[2] |
P. Attaviriyanupap, H. Kita, E. Tanaka and J. Hasegawa, A hybrid EP and SQP for dynamic economic dispatch with nonsmooth fuel cost function,, IEEE Trans. Power Syst., 17 (2002), 411.
doi: 10.1109/TPWRS.2002.1007911. |
[3] |
R. Balamurugan and S. Subramanian, Differential evolution-based dynamic economic dispatch of generating units with valve-point effects,, Electr. Power Compon. Syst., 36 (2008), 828.
doi: 10.1080/15325000801911427. |
[4] |
R. Balamurugan and S. Subramanian, An improved differential evolution based dynamic economic dispatch with nonsmooth fuel cost function,, J. Electr. Syst., 3 (2007), 151. Google Scholar |
[5] |
H.-G. Beyer and H.-P. Schwefel, Evolution strategies: A comprehensive introduction,, J. Nat. Comput., 1 (2002), 3.
doi: 10.1023/A:1015059928466. |
[6] |
P. Belotti, "Couenne: A User's Manual,", Available from: , (2009). Google Scholar |
[7] |
S. I. Birbil and S. C. Fang, An electromagnetism-like mechanism for global optimization,, J. Glob. Optim., 25 (2003), 263.
doi: 10.1023/A:1022452626305. |
[8] |
E. G. Birgin, C. A. Floudas and J. M. Martínez, Global minimization using an augmented Lagrangian method with variable lower-level constraints,, Math. Program. Ser. A, 125 (2010), 139.
doi: 10.1007/s10107-009-0264-y. |
[9] |
J. Brest, S. Greiner, B. Bošković, M. Mernik and V. Žumer, Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems,, IEEE Trans. Evol. Comput., 10 (2006), 646.
doi: 10.1109/TEVC.2006.872133. |
[10] |
A. Brooke, D. Kendrick, A. Meeraus and R. Raman, "GAMS: A User's Guide,", Release 2.25, (1992). Google Scholar |
[11] |
R. H. Byrd, J. Nocedal and R. A. Waltz, KNITRO: An integrated package for nonlinear optimization,, In, (2006), 35.
|
[12] |
C.-L. Chen, Non-convex economic dispatch: a direct search approach,, Energy Convers. Manage., 48 (2007), 219.
doi: 10.1016/j.enconman.2006.04.010. |
[13] |
P. H. Chen and H. C. Chang, Large-scale economic dispatch by genetic algorithm,, IEEE Trans. Power Syst., 10 (1995), 1919.
doi: 10.1109/59.476058. |
[14] |
J.-P. Chiou, Variable scaling hybrid differential evolution for large-scale economic dispatch problems,, Electr. Power Syst. Res., 77 (2007), 212.
doi: 10.1016/j.epsr.2006.02.013. |
[15] |
A. R. Conn, N. I. M. Gould and Ph. L. Toint, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds,, SIAM J. Numer. Anal., 28 (1991), 545.
doi: 10.1137/0728030. |
[16] |
D. B. Das and C. Patvardhan, Solution of economic load dispatch using real coded hybrid stochastic search,, Int. J. Electr. Power Energy Syst., 21 (1999), 165.
doi: 10.1016/S0142-0615(98)00036-2. |
[17] |
S. Das and P. N. Suganthan, Differential evolution: A survey of the state-of-the-art,, IEEE Trans. Evol. Comput., 15 (2011), 4.
doi: 10.1109/TEVC.2010.2059031. |
[18] |
S. Das, A. Abraham, U. K. Chakraborty and A. Konar, Differential evolution using a neighborhood-based mutation operator,, IEEE Trans. Evol. Comput., 13 (2009), 526.
doi: 10.1109/TEVC.2008.2009457. |
[19] |
K. Deb, Scope of stationary multi-objective evolutionary optimization: A case study on a hydro-thermal power dispatch problem,, J. Glob. Optim., 41 (2008), 479.
doi: 10.1007/s10898-007-9261-y. |
[20] |
K. Deb, An efficient constraint handling method for genetic algorithms,, Comput. Meth. Appl. Mech. Eng., 186 (2000), 311.
doi: 10.1016/S0045-7825(99)00389-8. |
[21] |
V. N. Dieu and W. Ongsakul, Augmented lagrange hopfield network for large scale economic dispatch,, Proc. Int. Symp. Electr. Electron. Eng., (2007), 19. Google Scholar |
[22] |
M. Dorigo, V. Maniezzo and A. Colorni, The ant system: optimization by a colony of cooperating agents,, IEEE Trans. Syst. Man Cybern., 26 (1996), 29.
doi: 10.1109/3477.484436. |
[23] |
A. Drud, "CONOPT: Solver Manual,", ARKI Consulting and Development. Available from: , (). Google Scholar |
[24] |
D. E. Finkel and C. T. Kelley, Additive scaling and the DIRECT algorithm,, J. Glob. Optim., 36 (2006), 597.
doi: 10.1007/s10898-006-9029-9. |
[25] |
R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function,, Math. Program., 91 (2002), 239.
doi: 10.1007/s101070100244. |
[26] |
R. Fourer, D. M. Gay and B. W. Kernighan, "AMPL: A Modeling Language for Mathematical Programming,", Boyd & Fraser Publishing Co., (1993). Google Scholar |
[27] |
Z.-L Gaing, Particle swarm optimization to solving the economic dispatch considering the generators constraints,, IEEE Trans. Power Syst., 18 (2003), 1187.
doi: 10.1109/TPWRS.2003.814889. |
[28] |
Z. W. Geem, J.-H. Kim and G. V. Loganathan, A new heuristic optimization algorithm: harmony search,, Simulation, 76 (2001), 60.
doi: 10.1177/003754970107600201. |
[29] |
Ph. E. Gill, W. Murray and M. A. Saunders, SNOPT: An SQP algorithm for large-scale constrained optimization,, SIAM Rev., 47 (2005), 99.
doi: 10.1137/S0036144504446096. |
[30] |
F. Glover and M. Laguna, "Tabu Search,", Kluwer Academic Publishers, (1997).
|
[31] |
G. P. Granelli and M. Montagna, Security-constrained economic dispatch using dual quadratic programming,, Electr. Power Syst. Res., 56 (2000), 71.
doi: 10.1016/S0378-7796(00)00097-3. |
[32] |
D. He, F. Wang and Z. Mao, A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valve-point effect,, Electr. Power Energy Syst., 30 (2008), 31.
doi: 10.1016/j.ijepes.2007.06.023. |
[33] |
K. S. Hindi and A. R. Ab-Ghani, Dynamic economic dispatch for large-scale power systems: a Lagrangian relaxation approach,, Electr. Power Syst. Res., 13 (1991), 51.
doi: 10.1016/0142-0615(91)90018-Q. |
[34] |
J. H. Holland, "Adaptation in Natural and Artificial Systems,", University of Michigan Press, (1997).
|
[35] |
W. Huyer and A. Neumaier, Global optimization by multilevel coordinate search,, J. Glob. Optim., 14 (1999), 331.
doi: 10.1023/A:1008382309369. |
[36] |
R. A. Jabr, A. H. Coonick and B. J. Cory, A homogeneous linear programming algorithm for the security constrained economic dispatch problem,, IEEE Trans. Power Syst., 15 (2000), 930.
doi: 10.1109/59.871715. |
[37] |
P. Kaelo and M. M. Ali, A numerical study of some modified differential evolution algorithms,, Eur. J. Oper. Res., 169 (2006), 1176.
doi: 10.1016/j.ejor.2004.08.047. |
[38] |
D. Karaboga and B. Basturk, A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm,, J. Glob. Optim., 39 (2007), 459.
doi: 10.1007/s10898-007-9149-x. |
[39] |
A. A. El-Keib, H. Ma and J. L. Hart, Environmentally constrained economic dispatch using the Lagrangian relaxation method,, IEEE Trans. Power Syst., 9 (1994), 1723.
doi: 10.1109/59.331423. |
[40] |
J. Kennedy, R. C. Eberhart and Y. Shi, "Swarm Intelligence,", Morgan Kaufmann, (2001). Google Scholar |
[41] |
S. Kirkpatrick, C. D. Gelatt Jr. and M. P. Vecchi, Optimization by simulated annealing,, Science, 220 (1983), 671.
doi: 10.1126/science.220.4598.671. |
[42] |
J. J. Liang, T. P. Runarsson, E. Mezura-Montes, M. Clerc, P. N. Suganthan, C. A. Coello Coello and K. Deb, "Problem Definitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization,", Technical Report, (2006). Google Scholar |
[43] |
, "LINDOGlobal: Solver Manual,", Lindo Systems, (2007). Google Scholar |
[44] |
J. Liu and J. Lampinen, A fuzzy adaptive differential evolution algorithm,, Soft Comput., 9 (2005), 448.
doi: 10.1007/s00500-004-0363-x. |
[45] |
R. Mallipeddi, P. N. Suganthan, Q. K. Pan and M. F. Tasgetiren, Differential evolution algorithm with ensemble of parameters and mutation strategies,, Appl. Soft Comput., 11 (2011), 1679.
doi: 10.1016/j.asoc.2010.04.024. |
[46] |
R. Mallipeddi and P. N. Suganthan, Ensemble of constraint handling techniques,, IEEE Trans. Evol. Comput., 14 (2010), 561.
doi: 10.1109/TEVC.2009.2033582. |
[47] |
B. A. Murtagh and M. A. Saunders, "MINOS 5.5 User's Guide, Report SOL 83-20R,", Dept. of Operations Research, (1998). Google Scholar |
[48] |
C. K. Panigrahi, P. K. Chattopadhyay, R. N. Chakrabarti and M. Basu, Simulated annealing technique for dynamic economic dispatch,, Electr. Power Compon. Syst., 34 (2006), 577.
doi: 10.1080/15325000500360843. |
[49] |
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 Trans. Power Syst., 20 (2005), 34.
doi: 10.1109/TPWRS.2004.831275. |
[50] |
Y.-M. Park, J. R. Won and J. B. Park, New approach to economic load dispatch based on improved evolutionary programming,, Eng. Intell. Syst. Electr. Eng. Commun., 6 (1998), 103. Google Scholar |
[51] |
A. K. Qin, V. L. Huang and P. N. Suganthan, Differential evolution algorithm with strategy adaptation for global numerical optimization,, IEEE Trans. Evol. Comput., 13 (2009), 398.
doi: 10.1109/TEVC.2008.927706. |
[52] |
T. P. Runarsson and X. Yao, Constrained evolutionary optimization-the penalty function approach,, in, (2003), 87.
|
[53] |
N. Sinha, R. Chakrabarti and P. K. Chattopadhyay, Evolutionary programming techniques for economic load dispatch,, IEEE Trans. Evol. Comput., 7 (2003), 83.
doi: 10.1109/TEVC.2002.806788. |
[54] |
R. Storn and K. Price, Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces,, J. Glob. Optim., 11 (1997), 341.
doi: 10.1023/A:1008202821328. |
[55] |
C.-T. Su and W.-T. Tyen, A genetic algorithm approach employing floating point representation for economic dispatch of electric power systems,, Proc. Int. Congr. Model. Simul., (1997), 1444. Google Scholar |
[56] |
S. Takriti and B. Krasenbrink, A decomposition approach for the fuel-constrained economic power-dispatch problem,, Eur. J. Oper. Res., 112 (1999), 460.
doi: 10.1016/S0377-2217(98)00131-3. |
[57] |
M. Tawarmalani and N. Sahinidis, "Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming,", Kluwer Academic Publishers, (2002).
|
[58] |
R. J. Vanderbei and D. F. Shanno, An interior-point algorithm for nonconvex nonlinear programming,, Comput. Optim. Appl., 13 (1999), 231.
doi: 10.1023/A:1008677427361. |
[59] |
T. A. A. Victorie and A. E. Jeyakumar, Hybrid PSO-SQP for economic dispatch with valve-point effect,, Electr. Power Syst. Res., 71 (2004), 51.
doi: 10.1016/j.epsr.2003.12.017. |
[60] |
A. Wächter and L. T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming,, Math. Program., 106 (2006), 25.
doi: 10.1007/s10107-004-0559-y. |
[61] |
D. C. Walters and G. B. Sheble, Genetic algorithm solution of economic dispatch with valve-point loadings,, IEEE Trans. Power Syst., 8 (1993), 1325.
doi: 10.1109/59.260861. |
[62] |
K. P. Wong and Y. W. Wong, Genetic and genetic/simulated-annealing approaches to economic dispatch,, IEE Proc. Gener. Transm. Distrib., 141 (1994), 507.
doi: 10.1049/ip-gtd:19941354. |
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