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A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization
1. | School of Science, Information, Technology and Engineering, University of Ballarat, Mt Helen, 3350, Victoria |
2. | School of Built Environment, Curtin University, Perth 4845, WA, Australia |
References:
[1] |
A. M. Bagirov and A. N. Ganjehlou, A quasisecant method for minimizing nonsmooth functions,, Optimization Methods & Software, 25 (2010), 3.
doi: 10.1080/10556780903151565. |
[2] |
M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithm (Third Edition),, Wiley Online Library, (2006).
doi: 10.1002/0471787779. |
[3] |
S. Ben Hamida and M. Schoenauer, Aschea: New results using adaptive segregational constraint handling,, in Evolutionary Computation, 1 (2002), 884. Google Scholar |
[4] |
Z. Cai and Y. Wang, A multiobjective optimization-based evolutionary algorithm for constrained optimization,, Evolutionary Computation, 10 (2006), 658.
doi: 10.1109/TEVC.2006.872344. |
[5] |
G. Camp, Inequality-constrained stationary-value problems,, Journal of the Operations Research Society of America, 3 (1955), 548.
doi: 10.1287/opre.3.4.548a. |
[6] |
C. Carroll and A. Fiacco, The created response surface technique for optimizing nonlinear restrained systems,, Operations Research, 9 (1961), 169.
doi: 10.1287/opre.9.2.169. |
[7] |
R. Chelouah and P. Siarry, A hybrid method combining continuous tabu search and nelder-mead simplex algorithms for the global optimization of multiminima functions,, European Journal of Operational Research, 161 (2005), 636.
doi: 10.1016/j.ejor.2003.08.053. |
[8] |
Z. Chen, S. Qiu and Y. Jiao, A penalty-free method for equality constrained optimization,, Journal of Industrial and Management Optimization, 9 (2013), 391.
doi: 10.3934/jimo.2013.9.391. |
[9] |
F. E. Curtis and M. L. Overton, A sequential quadratic programming algorithm for nonconvex, nonsmooth constrained optimization,, SIAM Journal on Optimization, 22 (2012), 474.
doi: 10.1137/090780201. |
[10] |
N. Durand and J. Alliot, A combined nelder-mead simplex and genetic algorithm,, in Proceedings of the Genetic and Evolutionary Computation Conference GECCO, 99 (1999), 1. Google Scholar |
[11] |
R. Fletcher, An ideal penalty function for constrained optimization,, IMA Journal of Applied Mathematics, 15 (1975), 319.
doi: 10.1093/imamat/15.3.319. |
[12] |
D. E. Goldberg, Genetic algorithms in search,, optimization, (). Google Scholar |
[13] |
H. Greenberg, The generalized penalty-function/surrogate model,, Operations Research, 21 (1973), 162.
doi: 10.1287/opre.21.1.162. |
[14] |
A. Hedar, Global optimization methods and codes,, , (). Google Scholar |
[15] |
A. Hedar and M. Fukushima, Hybrid simulated annealing and direct search method for nonlinear global optimization,, Department of Applied Mathematics & Physics Kyoto University, 17 (2002), 891.
doi: 10.1080/1055678021000030084. |
[16] |
A. Hedar and M. Fukushima, Derivative-free filter simulated annealing method for constrained continuous global optimization,, Journal of Global Optimization, 35 (2006), 521.
doi: 10.1007/s10898-005-3693-z. |
[17] |
E. Karas, A. Ribeiro, C. Sagastizábal and M. Solodov, A bundle-filter method for nonsmooth convex constrained optimization,, Mathematical Programming, 116 (2009), 297.
doi: 10.1007/s10107-007-0123-7. |
[18] |
N. Karmitsa, A. Bagirov and M. Mäkelä, Comparing different nonsmooth minimization methods and software,, Optimization Methods and Software, 27 (2012), 131.
doi: 10.1080/10556788.2010.526116. |
[19] |
S. Koziel and Z. Michalewicz, Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization,, Evolutionary computation, 7 (1999), 19.
doi: 10.1162/evco.1999.7.1.19. |
[20] |
O. Kramer, A review of constraint-handling techniques for evolution strategies,, Applied Computational Intelligence and Soft Computing, 2010 ().
doi: 10.1155/2010/185063. |
[21] |
Y. Liu, An exterior point linear programming method based on inclusive nornal cone,, Journal of Industrial and Management Optimization, 6 (2010), 825.
doi: 10.3934/jimo.2010.6.825. |
[22] |
D. Luenberger, Introduction to linear, and nonlinear programming., (). Google Scholar |
[23] |
R. Mallipeddi and P. N. Suganthan, Ensemble of constraint handling techniques,, Evolutionary Computation, 14 (2010), 561.
doi: 10.1109/TEVC.2009.2033582. |
[24] |
E. Mezura-Montes and C. C. Coello, A simple multimembered evolution strategy to solve constrained optimization problems,, Evolutionary Computation, 9 (2005), 1.
doi: 10.1109/TEVC.2004.836819. |
[25] |
W. Nakamura, Y. Narushima and H. Yabe, Nonlinear conjugrte gradient methods with sufficient descent properties for uniconstrained optimization,, Journal of Industrial and Management Optimization, 9 (2013), 595.
doi: 10.3934/jimo.2013.9.595. |
[26] |
W. Pierskalla, Mathematical programming with increasing constraint functions,, Management Science, 15 (): 416.
|
[27] |
T. P. Runarsson and X. Yao, Stochastic ranking for constrained evolutionary optimization,, Evolutionary Computation, 4 (2000), 284.
doi: 10.1109/4235.873238. |
[28] |
J. Vasconcelos, J. Ramirez, R. Takahashi and R. Saldanha, Improvements in genetic algorithms,, Magnetics, 37 (2001), 3414.
doi: 10.1109/20.952626. |
[29] |
Y. Wang, Z. Cai, Y. Zhou and Z. Fan, Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique,, Structural and Multidisciplinary Optimization, 37 (2009), 395.
doi: 10.1007/s00158-008-0238-3. |
[30] |
C. Yu, K. L. Teo, L. Zhang and Y. Bai, A new exact penalty function method for continuous inequality constrained optimization problems,, Journal of Industrial and Management Optimization, 6 (2010).
doi: 10.3934/jimo.2010.6.895. |
[31] |
Q. H. Zhiqiang Meng and C. Dang, A penalty function algorithm with objective parameters for nonlinear mathematical programming,, Journal of Industrial and Management Optimization, 5 (2009), 585.
doi: 10.3934/jimo.2009.5.585. |
show all references
References:
[1] |
A. M. Bagirov and A. N. Ganjehlou, A quasisecant method for minimizing nonsmooth functions,, Optimization Methods & Software, 25 (2010), 3.
doi: 10.1080/10556780903151565. |
[2] |
M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithm (Third Edition),, Wiley Online Library, (2006).
doi: 10.1002/0471787779. |
[3] |
S. Ben Hamida and M. Schoenauer, Aschea: New results using adaptive segregational constraint handling,, in Evolutionary Computation, 1 (2002), 884. Google Scholar |
[4] |
Z. Cai and Y. Wang, A multiobjective optimization-based evolutionary algorithm for constrained optimization,, Evolutionary Computation, 10 (2006), 658.
doi: 10.1109/TEVC.2006.872344. |
[5] |
G. Camp, Inequality-constrained stationary-value problems,, Journal of the Operations Research Society of America, 3 (1955), 548.
doi: 10.1287/opre.3.4.548a. |
[6] |
C. Carroll and A. Fiacco, The created response surface technique for optimizing nonlinear restrained systems,, Operations Research, 9 (1961), 169.
doi: 10.1287/opre.9.2.169. |
[7] |
R. Chelouah and P. Siarry, A hybrid method combining continuous tabu search and nelder-mead simplex algorithms for the global optimization of multiminima functions,, European Journal of Operational Research, 161 (2005), 636.
doi: 10.1016/j.ejor.2003.08.053. |
[8] |
Z. Chen, S. Qiu and Y. Jiao, A penalty-free method for equality constrained optimization,, Journal of Industrial and Management Optimization, 9 (2013), 391.
doi: 10.3934/jimo.2013.9.391. |
[9] |
F. E. Curtis and M. L. Overton, A sequential quadratic programming algorithm for nonconvex, nonsmooth constrained optimization,, SIAM Journal on Optimization, 22 (2012), 474.
doi: 10.1137/090780201. |
[10] |
N. Durand and J. Alliot, A combined nelder-mead simplex and genetic algorithm,, in Proceedings of the Genetic and Evolutionary Computation Conference GECCO, 99 (1999), 1. Google Scholar |
[11] |
R. Fletcher, An ideal penalty function for constrained optimization,, IMA Journal of Applied Mathematics, 15 (1975), 319.
doi: 10.1093/imamat/15.3.319. |
[12] |
D. E. Goldberg, Genetic algorithms in search,, optimization, (). Google Scholar |
[13] |
H. Greenberg, The generalized penalty-function/surrogate model,, Operations Research, 21 (1973), 162.
doi: 10.1287/opre.21.1.162. |
[14] |
A. Hedar, Global optimization methods and codes,, , (). Google Scholar |
[15] |
A. Hedar and M. Fukushima, Hybrid simulated annealing and direct search method for nonlinear global optimization,, Department of Applied Mathematics & Physics Kyoto University, 17 (2002), 891.
doi: 10.1080/1055678021000030084. |
[16] |
A. Hedar and M. Fukushima, Derivative-free filter simulated annealing method for constrained continuous global optimization,, Journal of Global Optimization, 35 (2006), 521.
doi: 10.1007/s10898-005-3693-z. |
[17] |
E. Karas, A. Ribeiro, C. Sagastizábal and M. Solodov, A bundle-filter method for nonsmooth convex constrained optimization,, Mathematical Programming, 116 (2009), 297.
doi: 10.1007/s10107-007-0123-7. |
[18] |
N. Karmitsa, A. Bagirov and M. Mäkelä, Comparing different nonsmooth minimization methods and software,, Optimization Methods and Software, 27 (2012), 131.
doi: 10.1080/10556788.2010.526116. |
[19] |
S. Koziel and Z. Michalewicz, Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization,, Evolutionary computation, 7 (1999), 19.
doi: 10.1162/evco.1999.7.1.19. |
[20] |
O. Kramer, A review of constraint-handling techniques for evolution strategies,, Applied Computational Intelligence and Soft Computing, 2010 ().
doi: 10.1155/2010/185063. |
[21] |
Y. Liu, An exterior point linear programming method based on inclusive nornal cone,, Journal of Industrial and Management Optimization, 6 (2010), 825.
doi: 10.3934/jimo.2010.6.825. |
[22] |
D. Luenberger, Introduction to linear, and nonlinear programming., (). Google Scholar |
[23] |
R. Mallipeddi and P. N. Suganthan, Ensemble of constraint handling techniques,, Evolutionary Computation, 14 (2010), 561.
doi: 10.1109/TEVC.2009.2033582. |
[24] |
E. Mezura-Montes and C. C. Coello, A simple multimembered evolution strategy to solve constrained optimization problems,, Evolutionary Computation, 9 (2005), 1.
doi: 10.1109/TEVC.2004.836819. |
[25] |
W. Nakamura, Y. Narushima and H. Yabe, Nonlinear conjugrte gradient methods with sufficient descent properties for uniconstrained optimization,, Journal of Industrial and Management Optimization, 9 (2013), 595.
doi: 10.3934/jimo.2013.9.595. |
[26] |
W. Pierskalla, Mathematical programming with increasing constraint functions,, Management Science, 15 (): 416.
|
[27] |
T. P. Runarsson and X. Yao, Stochastic ranking for constrained evolutionary optimization,, Evolutionary Computation, 4 (2000), 284.
doi: 10.1109/4235.873238. |
[28] |
J. Vasconcelos, J. Ramirez, R. Takahashi and R. Saldanha, Improvements in genetic algorithms,, Magnetics, 37 (2001), 3414.
doi: 10.1109/20.952626. |
[29] |
Y. Wang, Z. Cai, Y. Zhou and Z. Fan, Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique,, Structural and Multidisciplinary Optimization, 37 (2009), 395.
doi: 10.1007/s00158-008-0238-3. |
[30] |
C. Yu, K. L. Teo, L. Zhang and Y. Bai, A new exact penalty function method for continuous inequality constrained optimization problems,, Journal of Industrial and Management Optimization, 6 (2010).
doi: 10.3934/jimo.2010.6.895. |
[31] |
Q. H. Zhiqiang Meng and C. Dang, A penalty function algorithm with objective parameters for nonlinear mathematical programming,, Journal of Industrial and Management Optimization, 5 (2009), 585.
doi: 10.3934/jimo.2009.5.585. |
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