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A modified differential evolution based solution technique for economic dispatch problems
State transition algorithm
1.  School of Information Science and Engineering, Central South University, Changsha, 410083, China 
References:
[1] 
G. Albeanu, A monte carlo approach for control search, Mathematics and Computers in Simulation, 43 (1997), 223228. doi: 10.1016/S03784754(96)000699. 
[2] 
H. A. Abbass, A. M. Bagirov and J. Zhang, The discrete gradient evolutionary strategy method for global optimization, in "Proceedings of IEEE Congress on Evolutionary Computation," 1 (2003), 435442. 
[3] 
D. D. Burgess, Rotation in simplex optimization, Analytica Chimica Acta, 181 (1986), 97106. doi: 10.1016/S00032670(00)852241. 
[4] 
F. V. Berth and A. P. Engelbrecht, A study of particle swarm optimization particle trajectories, Information Sciences, 176 (2006), 937971. doi: 10.1016/j.ins.2005.02.003. 
[5] 
P. Collet and J. P. Rennard, "Stochastic Optimization Algorithms," Handbook of Research on Nature Inspired Computing for Economics and Management, 2006. 
[6] 
K. Deb and R. B. Agrawal, Simulated binary crossover for continuous search space, Complex Systems, 9 (1995), 115148. 
[7] 
R. C. Eberhart and Y. H. Shi, Comparison between genetic algorithms and particle swarm optimization, in "Annual Conference on Evolutionary Programming," San Diego, (1998), 611616. 
[8] 
D. E. Goldberg, "Genetic Algorithms in Search, Optimization, and Machine Learning," Reading: AddisonWesley, 1989. 
[9] 
C. Hamzacebi and F. Kutay, A heuristic approach for finding the global minimum: Adaptive random search technique, Applied Mathematics and Computation, 173 (2006), 13231333. doi: 10.1016/j.amc.2005.05.002. 
[10] 
C. Hamzacebi and F. Kutay, Continous functions minimization by dynamic random search technique, Applied Mathematical Modeling, 31 (2007), 21892198. doi: 10.1016/j.apm.2006.08.015. 
[11] 
R. Hooke and T. A. Jeeves, Direct search solution of numerical and statistical problems, Journal of the Association for Computing Machinery(ACM), 8 (1961), 212229. 
[12] 
J. Kennedy and R. C. Eberhart, Particle swarm optimization, in "Proceedings of IEEE International Conference on Neural Networks," IEEE Service Center, Piscataway, NJ, (1995), 19421948. 
[13] 
J. C. Lagarias, J. A. Reeds, M. H. Wright and P. E. Wright, Convergence properties of the NelderMead simplex method in low dimensions, SIAM J. OPTIM., 9 (1998), 112147. 
[14] 
J. J. Liang, A. K. Qin, P. N. Suganthan and S. Baskar, Comprehensive learning particle swarm optimizer for global optimization of multimodal functions, IEEE Transaction on Evolutionary Computation, 10 (2006), 281295. 
[15] 
J. Y. Li and R. R. Rhinehart, Heuristic random optimization, Computers and Chemical Engineering, 22 (1998), 427444. 
[16] 
T. W. Leung, C. K. Chan and M. D. Troutt, A mixed simulated annealinggenetic algorithm approach to the multibuyer multiitem joint replenishment problem: advantages of metaheuristics, Journal of Industrial and Management Optimization, 4 (2008), 5366. 
[17] 
J. Matyas, Random optimization, Automation and Remote Control, 26 (1965), 246253. 
[18] 
Z. Michalewicz, A modified genetic algorithm for optimal control problems, Computers Math. Applic, 23 (1992), 8394. doi: 10.1016/08981221(92)90094X. 
[19] 
J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308313. 
[20] 
A. K. Qin, V. L. Huang, and P. N. Suganthan, Differential evolution algorithm with strategy adaptation for global numerical optimization, IEEE Transactions on Evolutionary Computation, 13 (2009), 398417. 
[21] 
G. Rudolph, Convergence analysis of canonical genetic algorithms, IEEE Transactions on Neural Networks, 5 (1994), 96101. 
[22] 
D. W. Stroock, "An Introduction to Markov Processes," Beijing: World Publishing Corporation, 2009. 
[23] 
F. J. Solis and R. J. B. Wets, Minimization by random search techniques, Mathematics of Operations Research, 6 (1981), 1930. 
[24] 
R. Storn and K. V. Price, Differential evolutionaryA simple and efficient heuristic for global optimization over continous spaces, Journal of Global Optimization, 11 (1997), 341359. doi: 10.1023/A:1008202821328. 
[25] 
Y. H. Shi and R. C. Eberhart, Empirical study of particle swarm optimization, in "Proceedings of the IEEE Congress on Evolutionary Computation," IEEE Press, Seoul, Korea, (2001), 19451950. 
[26] 
T. D. Tran and G. G. Jin, Realcoded genetic algorithm benchmarked on noiseless blackbox optimization testbed, in "Workshop Proceedings of the Genetic and Evolutionary Computation Conference," (2010), 17311738. 
[27] 
A. H. Wright, Genetic algorithms for real parameter optimization, in "Foundations of Genetic Algorithms" (Ed. G. J. E. Rawlins), (1991), 205220. 
[28] 
D. H. Wolpert and W. G. Macready, No free lunch theorems for optimization, IEEE Transactions on Evolutionary Computation, 1 (1997), 6782. 
[29] 
K. F. C. Yiu, Y. Liu and K. L. Teo, A hybrid descent method for global optimization, Journal of Global Optimization, 28 (2004), 229238. doi: 10.1023/B:JOGO.0000015313.93974.b0. 
[30] 
X. S. Yang, "Engineering Optimization: An Introduction with Metaheuristic Applications," Wiley, 2010. 
[31] 
Y. X. Yuan, "Nonlinear Optimization Calculation Method," Beijing: Science press, 2008. 
[32] 
T. Zhang, Y. J. Zhang, Q. P. Zheng and P. M. Pardalos, A hybrid particle swarm optimization and tabu search algorithm for order planning problems of steel factories on the maketostock and maketoorder management architecture, Journal of Industrial and Management Optimization, 7 (2011), 3151. 
[33] 
X. J. Zhou, C. H. Yang and W. H. Gui, Initial version of state transition algorithm, in "the 2nd International Conference on Digital Manufacturing and Automation(ICDMA)," (2011), 644647. 
[34] 
X. J. Zhou, C. H. Yang and W. H. Gui, A new transformation into state transition algorithm for finding the global minimum, in "the 2nd International Conference on Intelligent Control and Information Processing," (2011), 674678. 
show all references
References:
[1] 
G. Albeanu, A monte carlo approach for control search, Mathematics and Computers in Simulation, 43 (1997), 223228. doi: 10.1016/S03784754(96)000699. 
[2] 
H. A. Abbass, A. M. Bagirov and J. Zhang, The discrete gradient evolutionary strategy method for global optimization, in "Proceedings of IEEE Congress on Evolutionary Computation," 1 (2003), 435442. 
[3] 
D. D. Burgess, Rotation in simplex optimization, Analytica Chimica Acta, 181 (1986), 97106. doi: 10.1016/S00032670(00)852241. 
[4] 
F. V. Berth and A. P. Engelbrecht, A study of particle swarm optimization particle trajectories, Information Sciences, 176 (2006), 937971. doi: 10.1016/j.ins.2005.02.003. 
[5] 
P. Collet and J. P. Rennard, "Stochastic Optimization Algorithms," Handbook of Research on Nature Inspired Computing for Economics and Management, 2006. 
[6] 
K. Deb and R. B. Agrawal, Simulated binary crossover for continuous search space, Complex Systems, 9 (1995), 115148. 
[7] 
R. C. Eberhart and Y. H. Shi, Comparison between genetic algorithms and particle swarm optimization, in "Annual Conference on Evolutionary Programming," San Diego, (1998), 611616. 
[8] 
D. E. Goldberg, "Genetic Algorithms in Search, Optimization, and Machine Learning," Reading: AddisonWesley, 1989. 
[9] 
C. Hamzacebi and F. Kutay, A heuristic approach for finding the global minimum: Adaptive random search technique, Applied Mathematics and Computation, 173 (2006), 13231333. doi: 10.1016/j.amc.2005.05.002. 
[10] 
C. Hamzacebi and F. Kutay, Continous functions minimization by dynamic random search technique, Applied Mathematical Modeling, 31 (2007), 21892198. doi: 10.1016/j.apm.2006.08.015. 
[11] 
R. Hooke and T. A. Jeeves, Direct search solution of numerical and statistical problems, Journal of the Association for Computing Machinery(ACM), 8 (1961), 212229. 
[12] 
J. Kennedy and R. C. Eberhart, Particle swarm optimization, in "Proceedings of IEEE International Conference on Neural Networks," IEEE Service Center, Piscataway, NJ, (1995), 19421948. 
[13] 
J. C. Lagarias, J. A. Reeds, M. H. Wright and P. E. Wright, Convergence properties of the NelderMead simplex method in low dimensions, SIAM J. OPTIM., 9 (1998), 112147. 
[14] 
J. J. Liang, A. K. Qin, P. N. Suganthan and S. Baskar, Comprehensive learning particle swarm optimizer for global optimization of multimodal functions, IEEE Transaction on Evolutionary Computation, 10 (2006), 281295. 
[15] 
J. Y. Li and R. R. Rhinehart, Heuristic random optimization, Computers and Chemical Engineering, 22 (1998), 427444. 
[16] 
T. W. Leung, C. K. Chan and M. D. Troutt, A mixed simulated annealinggenetic algorithm approach to the multibuyer multiitem joint replenishment problem: advantages of metaheuristics, Journal of Industrial and Management Optimization, 4 (2008), 5366. 
[17] 
J. Matyas, Random optimization, Automation and Remote Control, 26 (1965), 246253. 
[18] 
Z. Michalewicz, A modified genetic algorithm for optimal control problems, Computers Math. Applic, 23 (1992), 8394. doi: 10.1016/08981221(92)90094X. 
[19] 
J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308313. 
[20] 
A. K. Qin, V. L. Huang, and P. N. Suganthan, Differential evolution algorithm with strategy adaptation for global numerical optimization, IEEE Transactions on Evolutionary Computation, 13 (2009), 398417. 
[21] 
G. Rudolph, Convergence analysis of canonical genetic algorithms, IEEE Transactions on Neural Networks, 5 (1994), 96101. 
[22] 
D. W. Stroock, "An Introduction to Markov Processes," Beijing: World Publishing Corporation, 2009. 
[23] 
F. J. Solis and R. J. B. Wets, Minimization by random search techniques, Mathematics of Operations Research, 6 (1981), 1930. 
[24] 
R. Storn and K. V. Price, Differential evolutionaryA simple and efficient heuristic for global optimization over continous spaces, Journal of Global Optimization, 11 (1997), 341359. doi: 10.1023/A:1008202821328. 
[25] 
Y. H. Shi and R. C. Eberhart, Empirical study of particle swarm optimization, in "Proceedings of the IEEE Congress on Evolutionary Computation," IEEE Press, Seoul, Korea, (2001), 19451950. 
[26] 
T. D. Tran and G. G. Jin, Realcoded genetic algorithm benchmarked on noiseless blackbox optimization testbed, in "Workshop Proceedings of the Genetic and Evolutionary Computation Conference," (2010), 17311738. 
[27] 
A. H. Wright, Genetic algorithms for real parameter optimization, in "Foundations of Genetic Algorithms" (Ed. G. J. E. Rawlins), (1991), 205220. 
[28] 
D. H. Wolpert and W. G. Macready, No free lunch theorems for optimization, IEEE Transactions on Evolutionary Computation, 1 (1997), 6782. 
[29] 
K. F. C. Yiu, Y. Liu and K. L. Teo, A hybrid descent method for global optimization, Journal of Global Optimization, 28 (2004), 229238. doi: 10.1023/B:JOGO.0000015313.93974.b0. 
[30] 
X. S. Yang, "Engineering Optimization: An Introduction with Metaheuristic Applications," Wiley, 2010. 
[31] 
Y. X. Yuan, "Nonlinear Optimization Calculation Method," Beijing: Science press, 2008. 
[32] 
T. Zhang, Y. J. Zhang, Q. P. Zheng and P. M. Pardalos, A hybrid particle swarm optimization and tabu search algorithm for order planning problems of steel factories on the maketostock and maketoorder management architecture, Journal of Industrial and Management Optimization, 7 (2011), 3151. 
[33] 
X. J. Zhou, C. H. Yang and W. H. Gui, Initial version of state transition algorithm, in "the 2nd International Conference on Digital Manufacturing and Automation(ICDMA)," (2011), 644647. 
[34] 
X. J. Zhou, C. H. Yang and W. H. Gui, A new transformation into state transition algorithm for finding the global minimum, in "the 2nd International Conference on Intelligent Control and Information Processing," (2011), 674678. 
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