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Global optimization via differential evolution with automatic termination
1.  Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 6068501, Japan 
2.  Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 6068501 
References:
[1] 
S. Das and P. N. Suganthan, Differential evolution: A survey of the stateoftheart, IEEE Transactions on Evolutionary Computation, 15 (2011), 431. doi: 10.1109/TEVC.2010.2059031. 
[2] 
R. Gamperle, S. D. Muller and P. Koumoutsakos, A Parameter Study for Differential Evolution, in "Advances in intelligent systems, fuzzy systems, evolutionary computation" (eds. A. Grmela and N.E. Mastorakis), WSEAS Press, Interlaken, Switzerland, (2002), 293298. 
[3] 
M. S. Giggs, H. R. Maier, G. C. Dandy and J. B. Nixon, Minimum number of generations required for convergence of genetic algorithms, in "Proceedings of 2006 IEEE Congress on Evolutionary Computation," Vancouver, BC, Canada, (2006), 25802587. 
[4] 
N. Hansen, The CMA evolution strategy: a comparing review , in "Towards a New Evolutionary Computation. Advances on Estimation of Distribution Algorithms"(eds. J.A. Lozano, P. Larranaga, I. Inza and E. Bengoetxea), Springer, (2006), 75102. 
[5] 
A. R. Hedar and M. Fukushima, Minimizing multimodal functions by simplex coding genetic algorithm, Optimization Methods and Software, 18 (2003), 265282. 
[6] 
A. R. Hedar and M. Fukushima, Tabu search directed by direct search methods for nonlinear global optimization, European Journal of Operational Research, 170 (2006), 329349. doi: 10.1016/j.ejor.2004.05.033. 
[7] 
A. R. Hedar, B. T. Ong and M. Fukushima, Genetic algorithms with automatic accelerated termination, Technical report, Dept. of Applied Mathematics and Physics, Kyoto University, (2007). 
[8] 
B. J. Jain, H. Pohlheim and J. Wegener, On termination criteria of evolutionary algorithms, in "Proceedings of the Genetic and Evolutionary Computation Conference," Morgan Kaufmann Publishers, (2001), 768. 
[9] 
R. Joshi and A. C. Sanderson, Minimal representation multisensor fusion using differential evolution, IEEE Transactions on Systems, Man and Cybernetics (Part A), 29 (1999), 6376. doi: 10.1109/3468.736361. 
[10] 
C. T. Kelley, Detection and remediation of stagnation in the neldermead algorithm using a sufficient decrease condition, SIAM J. on Optimization, 10 (1999), 4355. doi: 10.1137/S1052623497315203. 
[11] 
N. M. Kwok, Q. P. Ha, D. K. Liu, G. Fang and K. C. Tan, Efficient particle swarm optimization: a termination condition based on the decisionmaking approach, in "Proceedings of the IEEE Congress on Evolutionary Computation," Singapore, (2007), 2528. doi: 10.1109/CEC.2007.4424905. 
[12] 
R. Mallipeddi, P. N. Suganthan, Q. K. Pan and M. F. Tasgetiren, Differential evolution algorithm with ensemble of parameters and mutation strategies, Applied Soft Computing, 11 (2011), 16791696. doi: 10.1016/j.asoc.2010.04.024. 
[13] 
P. McMinn, Searchbased software test data generation: A survey, Softw. Test. Verif. Reliab., 14 (2004), 105156. doi: 10.1002/stvr.294. 
[14] 
J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308313. 
[15] 
B. T. Ong and M. Fukushima, Genetic algorithm with automatic termination and search space rotation, Memetic Computing, 3 (2011), 111127. doi: 10.1007/s1229301100578. 
[16] 
M. O'Sullivan, S. Vssner and J. Wegener, Testing temporal correctness of realtime systems, in "EuroSTAR'98: Proceedings of the Sixth International Conference on Software Testing Analysis and Review," Munich, Germany, (1998). 
[17] 
K. V. Price, R. M. Storn and J. A. Lampinen, "Differential Evolution A Practical Approach to Global Optimization," Natural Computing Series, SpringerVerlag, Berlin, Germany, (2005). 
[18] 
A. K. Qin and P. N. Suganthan, Selfadaptive differential evolution algorithm for numerical optimization, in "The 2005 IEEE Congress on Evolutionary Computation," 2 (2005), 17851791. 
[19] 
R. Storn and K. Price, Differential evolution  a simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR95012, Online, (1995). 
[20] 
R. Storn and K. Price, Differential evolution  a simple and efficient heuristic for global optimization over continuous spaces, J. of Global Optimization, 11 (1997), 341359. doi: 10.1023/A:1008202821328. 
[21] 
P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. P. Chen, A. Auger and S. Tiwari, Problem definitions and evaluation criteria for the CEC 2005 special session on realparameter optimization , Technical report, Singapore: Nanyang Technol. Univ., (2005). 
[22] 
J. Zhang, V. Avasarala, A. C. Sanderson and T. Mullen, Differential evolution for discrete optimization: An experimental study on combinatorial auction problems, in "Proceedings of the 10th IEEE Congress on Evolutionary Computation CEC 2008 (IEEE World Congress on Computational Intelligence)," (2008), 27942800. doi: 10.1109/CEC.2008.4631173. 
show all references
References:
[1] 
S. Das and P. N. Suganthan, Differential evolution: A survey of the stateoftheart, IEEE Transactions on Evolutionary Computation, 15 (2011), 431. doi: 10.1109/TEVC.2010.2059031. 
[2] 
R. Gamperle, S. D. Muller and P. Koumoutsakos, A Parameter Study for Differential Evolution, in "Advances in intelligent systems, fuzzy systems, evolutionary computation" (eds. A. Grmela and N.E. Mastorakis), WSEAS Press, Interlaken, Switzerland, (2002), 293298. 
[3] 
M. S. Giggs, H. R. Maier, G. C. Dandy and J. B. Nixon, Minimum number of generations required for convergence of genetic algorithms, in "Proceedings of 2006 IEEE Congress on Evolutionary Computation," Vancouver, BC, Canada, (2006), 25802587. 
[4] 
N. Hansen, The CMA evolution strategy: a comparing review , in "Towards a New Evolutionary Computation. Advances on Estimation of Distribution Algorithms"(eds. J.A. Lozano, P. Larranaga, I. Inza and E. Bengoetxea), Springer, (2006), 75102. 
[5] 
A. R. Hedar and M. Fukushima, Minimizing multimodal functions by simplex coding genetic algorithm, Optimization Methods and Software, 18 (2003), 265282. 
[6] 
A. R. Hedar and M. Fukushima, Tabu search directed by direct search methods for nonlinear global optimization, European Journal of Operational Research, 170 (2006), 329349. doi: 10.1016/j.ejor.2004.05.033. 
[7] 
A. R. Hedar, B. T. Ong and M. Fukushima, Genetic algorithms with automatic accelerated termination, Technical report, Dept. of Applied Mathematics and Physics, Kyoto University, (2007). 
[8] 
B. J. Jain, H. Pohlheim and J. Wegener, On termination criteria of evolutionary algorithms, in "Proceedings of the Genetic and Evolutionary Computation Conference," Morgan Kaufmann Publishers, (2001), 768. 
[9] 
R. Joshi and A. C. Sanderson, Minimal representation multisensor fusion using differential evolution, IEEE Transactions on Systems, Man and Cybernetics (Part A), 29 (1999), 6376. doi: 10.1109/3468.736361. 
[10] 
C. T. Kelley, Detection and remediation of stagnation in the neldermead algorithm using a sufficient decrease condition, SIAM J. on Optimization, 10 (1999), 4355. doi: 10.1137/S1052623497315203. 
[11] 
N. M. Kwok, Q. P. Ha, D. K. Liu, G. Fang and K. C. Tan, Efficient particle swarm optimization: a termination condition based on the decisionmaking approach, in "Proceedings of the IEEE Congress on Evolutionary Computation," Singapore, (2007), 2528. doi: 10.1109/CEC.2007.4424905. 
[12] 
R. Mallipeddi, P. N. Suganthan, Q. K. Pan and M. F. Tasgetiren, Differential evolution algorithm with ensemble of parameters and mutation strategies, Applied Soft Computing, 11 (2011), 16791696. doi: 10.1016/j.asoc.2010.04.024. 
[13] 
P. McMinn, Searchbased software test data generation: A survey, Softw. Test. Verif. Reliab., 14 (2004), 105156. doi: 10.1002/stvr.294. 
[14] 
J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308313. 
[15] 
B. T. Ong and M. Fukushima, Genetic algorithm with automatic termination and search space rotation, Memetic Computing, 3 (2011), 111127. doi: 10.1007/s1229301100578. 
[16] 
M. O'Sullivan, S. Vssner and J. Wegener, Testing temporal correctness of realtime systems, in "EuroSTAR'98: Proceedings of the Sixth International Conference on Software Testing Analysis and Review," Munich, Germany, (1998). 
[17] 
K. V. Price, R. M. Storn and J. A. Lampinen, "Differential Evolution A Practical Approach to Global Optimization," Natural Computing Series, SpringerVerlag, Berlin, Germany, (2005). 
[18] 
A. K. Qin and P. N. Suganthan, Selfadaptive differential evolution algorithm for numerical optimization, in "The 2005 IEEE Congress on Evolutionary Computation," 2 (2005), 17851791. 
[19] 
R. Storn and K. Price, Differential evolution  a simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR95012, Online, (1995). 
[20] 
R. Storn and K. Price, Differential evolution  a simple and efficient heuristic for global optimization over continuous spaces, J. of Global Optimization, 11 (1997), 341359. doi: 10.1023/A:1008202821328. 
[21] 
P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. P. Chen, A. Auger and S. Tiwari, Problem definitions and evaluation criteria for the CEC 2005 special session on realparameter optimization , Technical report, Singapore: Nanyang Technol. Univ., (2005). 
[22] 
J. Zhang, V. Avasarala, A. C. Sanderson and T. Mullen, Differential evolution for discrete optimization: An experimental study on combinatorial auction problems, in "Proceedings of the 10th IEEE Congress on Evolutionary Computation CEC 2008 (IEEE World Congress on Computational Intelligence)," (2008), 27942800. doi: 10.1109/CEC.2008.4631173. 
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