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Minimax problems for setvalued mappings with set optimization
Essential issues on solving optimal power flow problems using softcomputing
1.  Department of Electrical and Computer Engineering, Curtin University, Perth, Australia, Australia 
2.  Business School, Central South University, Changsha, China 
3.  Department of Mathematics and Statistics, Curtin University, Perth, Australia 
References:
[1] 
A. G. Bakirtzis, P. N. Biskas, C. E. Zoumas and V. Petridis, Optimal power flow by enhanced genetic algorithm, IEEE Transactions on Power Systems, 17 (2002), 229236. 
[2] 
K. T. Chatuervedi, Manjaree Pandit and L. Srivastava, Selforganizing hierarchical particle swarm optimization for nonconvex economic dispatch, IEEE Transactions on Power Systems, 23 (2008), 10791087. 
[3] 
C. L. Chiang, Improved genetic algorithm for power economic dispatch of units with valvepoint effects and multiple fuels, IEEE Transactions on Power Systems, 24 (2005), 16901699. 
[4] 
M. Clerc and J. Kennedy, The particle swarm explosion, stability, and convergence in a multidimensional complex space, IEEE Transactions on Evolutionary Computations, 6 (2002), 5873. 
[5] 
D. Devaraj and B. Yegnanarayana, Geneticalgorithmbased optimal power flow for security enhancement, IEE Proceedings: Generation, Transmission and Distribution, 152 (2005), 899905. 
[6] 
R. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, in Proceedings 6th International Symposium on Micro Machine and Human Science, IEEE Service Center, Nagoya, 1995, 3943. 
[7] 
A. A. A. Esmin, G. L. Torres and A. C. Zamhroni, A hybrid particle swarm optimization applied to loss power minimization, IEEE Transactions on Power Systems, 20 (2005), 859866. 
[8] 
L. K. Kirchmayer, Economic Operation of Power Systems, Wiley, New York, 1958. 
[9] 
K. F. Man, K. S. Tang and S. Kwong, Genetic algorithm: concepts and applications, IEEE Transactions on Industrial Electronics, 43 (1996), 519534. 
[10] 
K. Meng, H. G. Wang, Z. Y. Dong and K. P. Wong, Quantum inspired particle swarm optimization for valve point economic load dispatch, IEEE Transactions on Power Systems, 25 (2010), 215222. 
[11] 
N. Mo, Z. Y. Zou, K. W. Chan and G. T. Y. Pong, Transient stability constrained optimal power flow using particle swarm optimization, IET Proceedings Generation, Transmission and Distribution, 1 (2007), 476483. 
[12] 
S. R. Paranjothi and K. Anburaja, Optimal power flow using refined genetic algorithm, Electric Power Components and Systems, 30 (2002), 10551063. 
[13] 
J. Pilgrim, F. Li and R. K. Aggarwal, Genetic algorithms for optimal reactive power compensation on the national grid system, Proceedings of IEEE Power Engineering Society Transmission and Distribution Conference 2000, 524529. 
[14] 
M. J. D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, Numerical Analysis, 630 (1977), 144157. 
[15] 
M. J. D. Powell, Algorithms for nonlinear constraints that use lagrangian functions, Mathematical Programming, 14 (1978), 224248. 
[16] 
M. J. D. Powell, The convergence of variable metric methods for nonlinearly constrained optimization calculations, In Proceedings of Nonlinear Programming 3 (1978), 2763. 
[17] 
C. R. Reeves, Genetic algorithms and neighbourhood search, Evolutionary Computing: AISB Workshop, 1994, 115130. 
[18] 
W. Y. Sun and Y. X. Yuan, Optimization Theory and Methods: Nonlinear Programming, Springer, 2006. 
[19] 
R. J. M. Vaessens, E. H. L. Aarts and J. K. Lenstra, A local search template, Proceedings of parallel problemsolving from nature, 2 (1992), 6574. 
[20] 
K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, New York: Longman Scientific & Technical, 1991. 
[21] 
M. Todorovski and D. Rajicic, An initialization procedure in solving optimal power flow by genetic algorithm, IEEE Transactions on Power Systems, 21 (2006), 480487. 
[22] 
R. J. M. Vaessens, E. H. L. Aarts and J. K. Lenstra, A local search template, Proceedings of Parallel ProblemSolving from Nature, 2 (1992), 6574. 
[23] 
A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, New York, John Wiley & Sons (2nd edition), 1996. 
[24] 
J. Yuryevich and K. P. Wong, Evolutionary programming based optimal power flow algorithm, IEEE Transactions on Power Systems, 14 (1999), 12451250. 
[25] 
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem, Journal of Industrial Management and Optimization, 8 (2012), 485491. doi: 10.3934/jimo.2012.8.485. 
[26] 
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems, Journal of Industrial Management and Optimization, 6 (2010), 895910. doi: 10.3934/jimo.2010.6.895. 
show all references
References:
[1] 
A. G. Bakirtzis, P. N. Biskas, C. E. Zoumas and V. Petridis, Optimal power flow by enhanced genetic algorithm, IEEE Transactions on Power Systems, 17 (2002), 229236. 
[2] 
K. T. Chatuervedi, Manjaree Pandit and L. Srivastava, Selforganizing hierarchical particle swarm optimization for nonconvex economic dispatch, IEEE Transactions on Power Systems, 23 (2008), 10791087. 
[3] 
C. L. Chiang, Improved genetic algorithm for power economic dispatch of units with valvepoint effects and multiple fuels, IEEE Transactions on Power Systems, 24 (2005), 16901699. 
[4] 
M. Clerc and J. Kennedy, The particle swarm explosion, stability, and convergence in a multidimensional complex space, IEEE Transactions on Evolutionary Computations, 6 (2002), 5873. 
[5] 
D. Devaraj and B. Yegnanarayana, Geneticalgorithmbased optimal power flow for security enhancement, IEE Proceedings: Generation, Transmission and Distribution, 152 (2005), 899905. 
[6] 
R. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, in Proceedings 6th International Symposium on Micro Machine and Human Science, IEEE Service Center, Nagoya, 1995, 3943. 
[7] 
A. A. A. Esmin, G. L. Torres and A. C. Zamhroni, A hybrid particle swarm optimization applied to loss power minimization, IEEE Transactions on Power Systems, 20 (2005), 859866. 
[8] 
L. K. Kirchmayer, Economic Operation of Power Systems, Wiley, New York, 1958. 
[9] 
K. F. Man, K. S. Tang and S. Kwong, Genetic algorithm: concepts and applications, IEEE Transactions on Industrial Electronics, 43 (1996), 519534. 
[10] 
K. Meng, H. G. Wang, Z. Y. Dong and K. P. Wong, Quantum inspired particle swarm optimization for valve point economic load dispatch, IEEE Transactions on Power Systems, 25 (2010), 215222. 
[11] 
N. Mo, Z. Y. Zou, K. W. Chan and G. T. Y. Pong, Transient stability constrained optimal power flow using particle swarm optimization, IET Proceedings Generation, Transmission and Distribution, 1 (2007), 476483. 
[12] 
S. R. Paranjothi and K. Anburaja, Optimal power flow using refined genetic algorithm, Electric Power Components and Systems, 30 (2002), 10551063. 
[13] 
J. Pilgrim, F. Li and R. K. Aggarwal, Genetic algorithms for optimal reactive power compensation on the national grid system, Proceedings of IEEE Power Engineering Society Transmission and Distribution Conference 2000, 524529. 
[14] 
M. J. D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, Numerical Analysis, 630 (1977), 144157. 
[15] 
M. J. D. Powell, Algorithms for nonlinear constraints that use lagrangian functions, Mathematical Programming, 14 (1978), 224248. 
[16] 
M. J. D. Powell, The convergence of variable metric methods for nonlinearly constrained optimization calculations, In Proceedings of Nonlinear Programming 3 (1978), 2763. 
[17] 
C. R. Reeves, Genetic algorithms and neighbourhood search, Evolutionary Computing: AISB Workshop, 1994, 115130. 
[18] 
W. Y. Sun and Y. X. Yuan, Optimization Theory and Methods: Nonlinear Programming, Springer, 2006. 
[19] 
R. J. M. Vaessens, E. H. L. Aarts and J. K. Lenstra, A local search template, Proceedings of parallel problemsolving from nature, 2 (1992), 6574. 
[20] 
K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, New York: Longman Scientific & Technical, 1991. 
[21] 
M. Todorovski and D. Rajicic, An initialization procedure in solving optimal power flow by genetic algorithm, IEEE Transactions on Power Systems, 21 (2006), 480487. 
[22] 
R. J. M. Vaessens, E. H. L. Aarts and J. K. Lenstra, A local search template, Proceedings of Parallel ProblemSolving from Nature, 2 (1992), 6574. 
[23] 
A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, New York, John Wiley & Sons (2nd edition), 1996. 
[24] 
J. Yuryevich and K. P. Wong, Evolutionary programming based optimal power flow algorithm, IEEE Transactions on Power Systems, 14 (1999), 12451250. 
[25] 
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem, Journal of Industrial Management and Optimization, 8 (2012), 485491. doi: 10.3934/jimo.2012.8.485. 
[26] 
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems, Journal of Industrial Management and Optimization, 6 (2010), 895910. doi: 10.3934/jimo.2010.6.895. 
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