Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 47 Sayı: 3, 539 - 551, 01.06.2018

Öz

In the last two decades the eld evolutionary computation has become
a mainstream and several types of evolutionary algorithms are devel-
oped for solving optimization and search problems. Evolutionary algo-
rithms (EAs) are mainly inspired from the biological process of evolu-
tion. They do not demand for any concrete information such as conti-
nuity or dierentiability and other information related to the problems
to be solved. Due to population based nature, EAs provide a set of so-
lutions and share properties of adaptation through an iterative process.
The steepest descent methods and Broyden-Fletcher-Goldfarb-Shanno
(BFGS),Hill climbing local search are quite often used for exploitation
purposes in order to improve the performance of the existing EAs. In
this paper, We have employed the BFGS as an additional operator in
the framework of Genetic Algorithm. The idea of add-in BFGS is to
sharpen the search around local optima and to speeds up the search pro-
cess of the suggested algorithm. We have used 24 benchmark functions
which was designed for the special session of the 2005 IEEE-Congress
on Evolutionary Computation (IEEE-CEC 06) to examine the perfor-
mance of the suggested hybrid GA. The experimental results provided
by HGBA are much competitive and promising as compared to the
stand alone GA for dealing with most of the used test problems.

Kaynakça

  • S. Cagnoni, et al., Real-World Applications of Evolutionary Computing, Springer-Verlag Lecture Notes in Computer Science, Berlin, 2000.
  • R. Chiong, Th. Weise, Z. Michalewicz (Editors), Variants of Evolutionary Algorithms for Real-World Applications, Springer, 2012, ISBN 3642234232
  • Floudas, Christodoulos A., Panos M. Pardalos, Claire Adjiman, William R. Esposito, Zeynep H. Gums, Stephen T. Harding, John L. Klepeis, Cliord A. Meyer, and Carl A. Schweiger, Handbook of test problems in local and global optimization, Vol. 33. Springer Science & Business Media, 2013.
  • Wenyu Sun and Ya-Xiang Yua, Optimization Theory and Methods: Nonlinear Programming, Springer, ISBN 978-1441937650. pages, 541, 2010.
  • Rituparna Datta and Kalyanmoy Deb,Evolutionary Constrained Optimization,Infosys Sci- ence Foundation Series in Applied Sciences and Engineering,ISSN: 2363-4995, Springer, 2015.
  • S.H. Chen, J. Wu, and Y.D. Chen Interval optimization for uncertain structures, Finite Elements in Analysis and Design 40 (11), 1379-1398, 2004.
  • MarcoCavazzuti, Optimization Methods: From Theory to Design Scientic and Technolog- ical Aspects in Mechanics, Springer Berlin Heidelber,2013.
  • E. L. Lawler and D. E. Wood, Branch-and-Bound Methods: A Survey, Journal Operation Research, 14, 4, 699-719,Institute for Operations Research and the Management Sciences (INFORMS), Linthicum, Maryland, USA, 1996.
  • R. Vetschera, A general branch-and-bound algorithm for fair division problems, Journal Computers and Operations Research, 37(12), 2121-2130, December, 2010.
  • M. Veltman, Algebraic techniques, Computer Physics Communications, 3, 75-78, September, 1972.
  • J.A Nelder and R.Mead, A simplex method for function minimization, The computer jour- nal, 7(4), 308-313, 1965.
  • S. M. Goldfeld , R. E. Quandt andH. F. Trotter , Maximization by quadratic hill-climbing. Econometrica: Journal of the Econometric Society,34(3), 541-551, 1966.
  • S.Abbasbandy, Improving Newton-Raphson method for nonlinear equations by modied Adomian decomposition method, Applied Mathematics and Computation, 145(2), 887-893, 2003.
  • X. Geng, J. Xu, J. Xiao, and L. Pan, A simple simulated annealing algorithm for the maximum clique problem, Information Sciences, 177, 22, 5064-5071, 2007.
  • A. Eidehall and L. Petersson, Threat assessment for general road scenes using Monte Carlo sampling, IEEE Intelligent Transportation Systems Conference, 2006.
  • M. Lin and J. Wawrzynek,Improving FPGA placement with dynamically adaptive stochas- tic tunneling, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 29, 12, 1858-1869, 2010.
  • J. Machta, Strengths and weaknesses of parallel tempering, Physical Review E- Statistical, Nonlinear, and Soft Matter Physics, 80, 5, 2009.
  • A. Engelbrecht, Computational Intelligence- An Introduction2ndedition, Wiley, 2007.
  • C. Pan, C. Xu, and G. Li, Dierential evolutionary strategies for global optimization, Shen- zhen Daxue Xuebao (Ligong Ban), Journal of Shenzhen University Science and Engineering, 25, 2, 211-215, 2008.
  • B. Blaha and D. Wunsch, Evolutionary programming to optimize an assembly program, Proceedings of the 2002 Congress on Evolutionary Computation. CEC-02, 2, 1901-1903.
  • Fogel, L.J., Owens, A.J., Walsh, M.J., Articial Intelligence through Simulated Evolution, John Wiley, 1966.
  • Fogel, L.J., Intelligence through Simulated Evolution: Forty Years of Evolutionary Pro- gramming, John Wiley, 1999.
  • J. Kennedy and R. Eberhart, Particle swarm optimization, in Proceedings of the IEEE International Conference on Neural Networks, 4, 1942-1948,1995.
  • J. Yu, L. Xi and S.Wang, An improved particle swarm optimization for evolving feedforward articial neural networks, Neural Processing Letters, vol. 26, no. 3, pp. 217-231, 2007.
  • C.Wu, Ant colony multilevel path optimize tactic based on information consistence optimize, 2010 International Conference on Computer Application and System Modeling (ICCASM 2010), 1, 533-536, November, 2010.
  • R. Storn and K. Price,Dierential Evolution: A Simple and Ecient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, 11(4), 341-359, 1997.
  • Ajith Abraham, Crina Grosan and Hisao Ishibuchi,Hybrid Evolutionary Algorithms, Studies in Computational Intelligence, Springer, 2007.
  • X. Li, M. R.Bonyadi, Z.Michalewicz and L. Barone, A Hybrid Evolutionary Algorithm for Wheat Blending Problem, The Scientic World Journal, 2014.
  • L.Zhang, L.Liu, XS Yang and Y.Dai, A novel hybrid rey algorithm for global optimization, PloS one,11(9), 2016.
  • Roger Fletcher, Practical methods of optimization, New York: John Wiley & Sons, 1987.
  • P.Venkataraman, Applied Optimization with Matlab programming, John Wiley & Sons, New York, 2002.
  • P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y.-P. Chen, A. Auger and S. Tiwari, Problem Denitions and Evaluation Criteria for the CEC 2005 Special Session on Real- Parameter Optimization, Technical Report, Nanyang Technological University, Singapore and KanGAL Report No:2005005, IIT Kanpur, India.
  • J. Holland, Adaptation in Natural and Articial Systems: The University of Michigan, 1975.
  • K. De Jong, An analysis of the behavior of a class of genetic adaptive systems, Doctoral Dissertation. Ann Arbor: The University of Michigan, 1975.
  • Wang G-G, Guo L, Gandomi AH, Hao G-S, Wang H, Chaotic krill herd algorithm, Infor- mation Science, 274, 17-34, 2014.
  • Wang G-G, Gandomi AH, Alavi AH, Stud krill herd algorithm, Neurocomputing, 128, 363- 370, 2014.
  • Wang G, Guo L, Wang H, Duan H, Liu L, Li J, Incorporating mutation scheme into krill herd algorithm for global numerical optimization, Neural Comput Appl 24(3-4):853-871, 2014.
  • Wang G-G, Deb S, Cui Z, Monarch buttery optimization, Neural Comput Applcation, 2015.
  • Wang G-G, Deb S, Coelho LdS, Earthworm optimization algorithm: a bio-inspired meta- heuristic algorithm for global optimization problems, Int J of Bio-Inspired Computation, 2015.
  • Sulaiman, Muhammad, Salhi, Abdellah, Mashwani, Wali Khan, and Rashidi, Muhammad M, A Novel Plant Propagation Algorithm: Modications and Implementation, Science International, 28 (1), 201-209, 2016.
  • Sulaiman, Muhammad, and Salhi, Abdellah, A Seed-based Plant Propagation Algorithm: The Feeding Station Model, The Scientic World Journal, 1-16, 2015
  • Sulaiman, Muhammad, Salhi, Abdellah, Selamoglu, Birsen Irem, Bahaaldin Kirikchi, Omar, A Plant Propagation Algorithm for Constrained Engineering Optimisation Problems, Math- ematical problems in engineering, 1-10, 2014.
  • Abdellah Salhi and Eric S. Fraga, Nature-Inspired Optimisation Approaches and the New Plant Propagation Algorithm, Proceedings of the ICeMATH2011, K2-1 to K2-8.
  • A.E. Eiben and J.E. Smith, Introduction to Evolutionary Computing, Springer, Natural Computing Series, 2003.
  • Wang G-G, Gandomi AH, Alavi AH, Hao G-S, Hybrid krill herd algorithm with dierential evolution for global numerical optimization, Neural Comput Appl, 25(2):297-308, 2014.
  • Wang G-G, Gandomi AH, Zhao X, Chu HE, Hybridizing harmony search algorithm with cuckoo search for global numerical optimization, Soft Computing, 20(1):273-285, 2016.
  • Muhammad Asim, Wali Khan Mashwani and M.A.Jan, Hybrid Genetic Firey Algorithm for Global Optimization Problems, Sindh University Research Journal, 49(3), 2017.
  • Muhammad Asim, Wali Khan Mashwani, Muhammad Asif Jan and Javed Ali, Derivative Based Hybrid Genetic Algorithm: A Preliminary Experimental Results, Punjab University Journal of Mathematics, Vol. 49(2) (2017) pp. 89-99.
  • Khug Alam,Wali Khan Mashwani and Muhammad Asim, Hybrid Biography Based Opti- mization Algorithm for Optimization Problems, Gomal University Journal of Research, Vol 33, issue1, pp:134-142, 2017.
  • Hamza Wazir, Muhammad Asif Jan, Wali Khan Mashwani and Tayyaba Shah, A Penalty Function Based Dierential Evolution Algorithm for Constrained Optimization, The Nu- cleus Journal , Vol 53, No. 1 (2016) 155-161.
  • Habib Shah, Nasser Tairan, Wali Khan Mashwani, Abdulrahman Ahmad Al-Sewari, Muhammad Asif Jan, Gran Badshah, Hybrid Global Crossover Bees Algorithm for Solving Boolean Function Classication Task, International Conference on Intelligent Computing ICIC (3) 2017: 467-478
  • D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning: Addison-Wesley, 1989.
  • J. H. Holland, Adaptation in Natural and Articial Systems: an Introductory analysis with Applications to Biology, Control, and Articial Intelligence, MIT Press, 1992.
  • Melanie Mitchell, An Introduction to Genetic Algorithms, MIT Press Cambridge, MA, USA, 1998.
  • Jyoti Sharma and Ravi Shankar Singhal,Genetic Algorithm and Hybrid Genetic Algorithm for Space Allocation Problems-A Review, International Journal of Computer Applications, 95(4), 2014.
  • Tarek A. El-Mihoub, Adrian A. Hopgood, Lars Nolle and Alan Battersby, Hybrid Genetic Algorithms: A Review, Engineering Letters, 13(2), 124-137, 2006.
  • Rashida Adeeb Khanum, Nasser Mansoor Tairan, Muhammad Asif Janan d Wali Khan Mashwani, Hybridization of Adaptive Dierential Evolution with an Expensive Local Search Method, Journal of Optimization, Volume 2016 (2016), Article ID 3260940, 14 pages
  • R. Farmani and J. A. Wright,Self-Adaptive Fitness Formulation for Constrained Optimiza- tion, IEEE Transactions on Evolutionary Computation,7, 445-455, 2003.
  • Homaifar, A., Lai, S.H.Y. and Qi, X , Constrained optimization via genetic algorithms, Simulation, 62, 242-254, 1994.
  • H. Liu, Z. Cai, and Y. Wang, Hybridizing particle swarm optimization with dierential evolution for constrained numerical and engineering optimization, Applied Soft Computing, 10(2), 629-640, 2010.
  • Tayaba Shah, Muhammad Asif Jan, Wali Kahan Mashwani and Hamza Wazir, Adaptive dierential evalution for constrained optimization problems, Science Int.(Lahore), 3(28) 4104-4108, 2016.
  • Wali Khan Mashwani, Abdellah Salhi, Muhammad Asif. Jan, Muhammad Sulaiman, R.A. Khanum and Abdulmohsen Algarni,Evolutionary Algorithms Based on Decomposition and Indicator Functions: State-of-the-art Survey, International Journal of Advanced Computer Science and Applications, 7(2), 583-593, 2016
  • J. J. Liang, T. P. Runarsson, E. Mezura-Montes, M. Clerc, P. N. Suganthan1, C. A. Coello Coello and K. Deb, Problem denitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization, Technical Report, Nanyang Technolog- ical University, Singapore, 2006.

Hybrid genetic algorithms for global optimization problems

Yıl 2018, Cilt: 47 Sayı: 3, 539 - 551, 01.06.2018

Öz

In the last two decades the field evolutionary computation has become a mainstream and several types of evolutionary algorithms are developed for solving optimization and search problems. Evolutionary algorithms (EAs) are mainly inspired from the biological process of evolution. They do not demand for any concrete information such as continuity or differentiability and other information related to the problems to be solved. Due to population based nature, EAs provide a set of solutions and share properties of adaptation through an iterative process. The steepest descent methods and Broyden-Fletcher-Goldfarb-Shanno (BFGS),Hill climbing local search are quite often used for exploitation purposes in order to improve the performance of the existing EAs. In this paper, We have employed the BFGS as an additional operator in the framework of Genetic Algorithm. The idea of add-in BFGS is to sharpen the search around local optima and to speeds up the search process of the suggested algorithm. We have used 24 benchmark functions which was designed for the special session of the 2005 IEEE-Congress on Evolutionary Computation (IEEE-CEC 06) to examine the performance of the suggested hybrid GA. The experimental results provided by HGBA are much competitive and promising as compared to the stand alone GA for dealing with most of the used test problems.

Kaynakça

  • S. Cagnoni, et al., Real-World Applications of Evolutionary Computing, Springer-Verlag Lecture Notes in Computer Science, Berlin, 2000.
  • R. Chiong, Th. Weise, Z. Michalewicz (Editors), Variants of Evolutionary Algorithms for Real-World Applications, Springer, 2012, ISBN 3642234232
  • Floudas, Christodoulos A., Panos M. Pardalos, Claire Adjiman, William R. Esposito, Zeynep H. Gums, Stephen T. Harding, John L. Klepeis, Cliord A. Meyer, and Carl A. Schweiger, Handbook of test problems in local and global optimization, Vol. 33. Springer Science & Business Media, 2013.
  • Wenyu Sun and Ya-Xiang Yua, Optimization Theory and Methods: Nonlinear Programming, Springer, ISBN 978-1441937650. pages, 541, 2010.
  • Rituparna Datta and Kalyanmoy Deb,Evolutionary Constrained Optimization,Infosys Sci- ence Foundation Series in Applied Sciences and Engineering,ISSN: 2363-4995, Springer, 2015.
  • S.H. Chen, J. Wu, and Y.D. Chen Interval optimization for uncertain structures, Finite Elements in Analysis and Design 40 (11), 1379-1398, 2004.
  • MarcoCavazzuti, Optimization Methods: From Theory to Design Scientic and Technolog- ical Aspects in Mechanics, Springer Berlin Heidelber,2013.
  • E. L. Lawler and D. E. Wood, Branch-and-Bound Methods: A Survey, Journal Operation Research, 14, 4, 699-719,Institute for Operations Research and the Management Sciences (INFORMS), Linthicum, Maryland, USA, 1996.
  • R. Vetschera, A general branch-and-bound algorithm for fair division problems, Journal Computers and Operations Research, 37(12), 2121-2130, December, 2010.
  • M. Veltman, Algebraic techniques, Computer Physics Communications, 3, 75-78, September, 1972.
  • J.A Nelder and R.Mead, A simplex method for function minimization, The computer jour- nal, 7(4), 308-313, 1965.
  • S. M. Goldfeld , R. E. Quandt andH. F. Trotter , Maximization by quadratic hill-climbing. Econometrica: Journal of the Econometric Society,34(3), 541-551, 1966.
  • S.Abbasbandy, Improving Newton-Raphson method for nonlinear equations by modied Adomian decomposition method, Applied Mathematics and Computation, 145(2), 887-893, 2003.
  • X. Geng, J. Xu, J. Xiao, and L. Pan, A simple simulated annealing algorithm for the maximum clique problem, Information Sciences, 177, 22, 5064-5071, 2007.
  • A. Eidehall and L. Petersson, Threat assessment for general road scenes using Monte Carlo sampling, IEEE Intelligent Transportation Systems Conference, 2006.
  • M. Lin and J. Wawrzynek,Improving FPGA placement with dynamically adaptive stochas- tic tunneling, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 29, 12, 1858-1869, 2010.
  • J. Machta, Strengths and weaknesses of parallel tempering, Physical Review E- Statistical, Nonlinear, and Soft Matter Physics, 80, 5, 2009.
  • A. Engelbrecht, Computational Intelligence- An Introduction2ndedition, Wiley, 2007.
  • C. Pan, C. Xu, and G. Li, Dierential evolutionary strategies for global optimization, Shen- zhen Daxue Xuebao (Ligong Ban), Journal of Shenzhen University Science and Engineering, 25, 2, 211-215, 2008.
  • B. Blaha and D. Wunsch, Evolutionary programming to optimize an assembly program, Proceedings of the 2002 Congress on Evolutionary Computation. CEC-02, 2, 1901-1903.
  • Fogel, L.J., Owens, A.J., Walsh, M.J., Articial Intelligence through Simulated Evolution, John Wiley, 1966.
  • Fogel, L.J., Intelligence through Simulated Evolution: Forty Years of Evolutionary Pro- gramming, John Wiley, 1999.
  • J. Kennedy and R. Eberhart, Particle swarm optimization, in Proceedings of the IEEE International Conference on Neural Networks, 4, 1942-1948,1995.
  • J. Yu, L. Xi and S.Wang, An improved particle swarm optimization for evolving feedforward articial neural networks, Neural Processing Letters, vol. 26, no. 3, pp. 217-231, 2007.
  • C.Wu, Ant colony multilevel path optimize tactic based on information consistence optimize, 2010 International Conference on Computer Application and System Modeling (ICCASM 2010), 1, 533-536, November, 2010.
  • R. Storn and K. Price,Dierential Evolution: A Simple and Ecient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, 11(4), 341-359, 1997.
  • Ajith Abraham, Crina Grosan and Hisao Ishibuchi,Hybrid Evolutionary Algorithms, Studies in Computational Intelligence, Springer, 2007.
  • X. Li, M. R.Bonyadi, Z.Michalewicz and L. Barone, A Hybrid Evolutionary Algorithm for Wheat Blending Problem, The Scientic World Journal, 2014.
  • L.Zhang, L.Liu, XS Yang and Y.Dai, A novel hybrid rey algorithm for global optimization, PloS one,11(9), 2016.
  • Roger Fletcher, Practical methods of optimization, New York: John Wiley & Sons, 1987.
  • P.Venkataraman, Applied Optimization with Matlab programming, John Wiley & Sons, New York, 2002.
  • P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y.-P. Chen, A. Auger and S. Tiwari, Problem Denitions and Evaluation Criteria for the CEC 2005 Special Session on Real- Parameter Optimization, Technical Report, Nanyang Technological University, Singapore and KanGAL Report No:2005005, IIT Kanpur, India.
  • J. Holland, Adaptation in Natural and Articial Systems: The University of Michigan, 1975.
  • K. De Jong, An analysis of the behavior of a class of genetic adaptive systems, Doctoral Dissertation. Ann Arbor: The University of Michigan, 1975.
  • Wang G-G, Guo L, Gandomi AH, Hao G-S, Wang H, Chaotic krill herd algorithm, Infor- mation Science, 274, 17-34, 2014.
  • Wang G-G, Gandomi AH, Alavi AH, Stud krill herd algorithm, Neurocomputing, 128, 363- 370, 2014.
  • Wang G, Guo L, Wang H, Duan H, Liu L, Li J, Incorporating mutation scheme into krill herd algorithm for global numerical optimization, Neural Comput Appl 24(3-4):853-871, 2014.
  • Wang G-G, Deb S, Cui Z, Monarch buttery optimization, Neural Comput Applcation, 2015.
  • Wang G-G, Deb S, Coelho LdS, Earthworm optimization algorithm: a bio-inspired meta- heuristic algorithm for global optimization problems, Int J of Bio-Inspired Computation, 2015.
  • Sulaiman, Muhammad, Salhi, Abdellah, Mashwani, Wali Khan, and Rashidi, Muhammad M, A Novel Plant Propagation Algorithm: Modications and Implementation, Science International, 28 (1), 201-209, 2016.
  • Sulaiman, Muhammad, and Salhi, Abdellah, A Seed-based Plant Propagation Algorithm: The Feeding Station Model, The Scientic World Journal, 1-16, 2015
  • Sulaiman, Muhammad, Salhi, Abdellah, Selamoglu, Birsen Irem, Bahaaldin Kirikchi, Omar, A Plant Propagation Algorithm for Constrained Engineering Optimisation Problems, Math- ematical problems in engineering, 1-10, 2014.
  • Abdellah Salhi and Eric S. Fraga, Nature-Inspired Optimisation Approaches and the New Plant Propagation Algorithm, Proceedings of the ICeMATH2011, K2-1 to K2-8.
  • A.E. Eiben and J.E. Smith, Introduction to Evolutionary Computing, Springer, Natural Computing Series, 2003.
  • Wang G-G, Gandomi AH, Alavi AH, Hao G-S, Hybrid krill herd algorithm with dierential evolution for global numerical optimization, Neural Comput Appl, 25(2):297-308, 2014.
  • Wang G-G, Gandomi AH, Zhao X, Chu HE, Hybridizing harmony search algorithm with cuckoo search for global numerical optimization, Soft Computing, 20(1):273-285, 2016.
  • Muhammad Asim, Wali Khan Mashwani and M.A.Jan, Hybrid Genetic Firey Algorithm for Global Optimization Problems, Sindh University Research Journal, 49(3), 2017.
  • Muhammad Asim, Wali Khan Mashwani, Muhammad Asif Jan and Javed Ali, Derivative Based Hybrid Genetic Algorithm: A Preliminary Experimental Results, Punjab University Journal of Mathematics, Vol. 49(2) (2017) pp. 89-99.
  • Khug Alam,Wali Khan Mashwani and Muhammad Asim, Hybrid Biography Based Opti- mization Algorithm for Optimization Problems, Gomal University Journal of Research, Vol 33, issue1, pp:134-142, 2017.
  • Hamza Wazir, Muhammad Asif Jan, Wali Khan Mashwani and Tayyaba Shah, A Penalty Function Based Dierential Evolution Algorithm for Constrained Optimization, The Nu- cleus Journal , Vol 53, No. 1 (2016) 155-161.
  • Habib Shah, Nasser Tairan, Wali Khan Mashwani, Abdulrahman Ahmad Al-Sewari, Muhammad Asif Jan, Gran Badshah, Hybrid Global Crossover Bees Algorithm for Solving Boolean Function Classication Task, International Conference on Intelligent Computing ICIC (3) 2017: 467-478
  • D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning: Addison-Wesley, 1989.
  • J. H. Holland, Adaptation in Natural and Articial Systems: an Introductory analysis with Applications to Biology, Control, and Articial Intelligence, MIT Press, 1992.
  • Melanie Mitchell, An Introduction to Genetic Algorithms, MIT Press Cambridge, MA, USA, 1998.
  • Jyoti Sharma and Ravi Shankar Singhal,Genetic Algorithm and Hybrid Genetic Algorithm for Space Allocation Problems-A Review, International Journal of Computer Applications, 95(4), 2014.
  • Tarek A. El-Mihoub, Adrian A. Hopgood, Lars Nolle and Alan Battersby, Hybrid Genetic Algorithms: A Review, Engineering Letters, 13(2), 124-137, 2006.
  • Rashida Adeeb Khanum, Nasser Mansoor Tairan, Muhammad Asif Janan d Wali Khan Mashwani, Hybridization of Adaptive Dierential Evolution with an Expensive Local Search Method, Journal of Optimization, Volume 2016 (2016), Article ID 3260940, 14 pages
  • R. Farmani and J. A. Wright,Self-Adaptive Fitness Formulation for Constrained Optimiza- tion, IEEE Transactions on Evolutionary Computation,7, 445-455, 2003.
  • Homaifar, A., Lai, S.H.Y. and Qi, X , Constrained optimization via genetic algorithms, Simulation, 62, 242-254, 1994.
  • H. Liu, Z. Cai, and Y. Wang, Hybridizing particle swarm optimization with dierential evolution for constrained numerical and engineering optimization, Applied Soft Computing, 10(2), 629-640, 2010.
  • Tayaba Shah, Muhammad Asif Jan, Wali Kahan Mashwani and Hamza Wazir, Adaptive dierential evalution for constrained optimization problems, Science Int.(Lahore), 3(28) 4104-4108, 2016.
  • Wali Khan Mashwani, Abdellah Salhi, Muhammad Asif. Jan, Muhammad Sulaiman, R.A. Khanum and Abdulmohsen Algarni,Evolutionary Algorithms Based on Decomposition and Indicator Functions: State-of-the-art Survey, International Journal of Advanced Computer Science and Applications, 7(2), 583-593, 2016
  • J. J. Liang, T. P. Runarsson, E. Mezura-Montes, M. Clerc, P. N. Suganthan1, C. A. Coello Coello and K. Deb, Problem denitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization, Technical Report, Nanyang Technolog- ical University, Singapore, 2006.
Toplam 63 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Muhammad Asim Bu kişi benim

Wali Mashwani Khan

Özgür Yeniay Bu kişi benim

Muhammad Asif Jan Bu kişi benim

Nasser Tairan Bu kişi benim

H. Hussian Bu kişi benim

Gai-ge Wang Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 47 Sayı: 3

Kaynak Göster

APA Asim, M., Khan, W. M., Yeniay, Ö., Jan, M. A., vd. (2018). Hybrid genetic algorithms for global optimization problems. Hacettepe Journal of Mathematics and Statistics, 47(3), 539-551.
AMA Asim M, Khan WM, Yeniay Ö, Jan MA, Tairan N, Hussian H, Wang Gg. Hybrid genetic algorithms for global optimization problems. Hacettepe Journal of Mathematics and Statistics. Haziran 2018;47(3):539-551.
Chicago Asim, Muhammad, Wali Mashwani Khan, Özgür Yeniay, Muhammad Asif Jan, Nasser Tairan, H. Hussian, ve Gai-ge Wang. “Hybrid Genetic Algorithms for Global Optimization Problems”. Hacettepe Journal of Mathematics and Statistics 47, sy. 3 (Haziran 2018): 539-51.
EndNote Asim M, Khan WM, Yeniay Ö, Jan MA, Tairan N, Hussian H, Wang G-g (01 Haziran 2018) Hybrid genetic algorithms for global optimization problems. Hacettepe Journal of Mathematics and Statistics 47 3 539–551.
IEEE M. Asim, “Hybrid genetic algorithms for global optimization problems”, Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 3, ss. 539–551, 2018.
ISNAD Asim, Muhammad vd. “Hybrid Genetic Algorithms for Global Optimization Problems”. Hacettepe Journal of Mathematics and Statistics 47/3 (Haziran 2018), 539-551.
JAMA Asim M, Khan WM, Yeniay Ö, Jan MA, Tairan N, Hussian H, Wang G-g. Hybrid genetic algorithms for global optimization problems. Hacettepe Journal of Mathematics and Statistics. 2018;47:539–551.
MLA Asim, Muhammad vd. “Hybrid Genetic Algorithms for Global Optimization Problems”. Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 3, 2018, ss. 539-51.
Vancouver Asim M, Khan WM, Yeniay Ö, Jan MA, Tairan N, Hussian H, Wang G-g. Hybrid genetic algorithms for global optimization problems. Hacettepe Journal of Mathematics and Statistics. 2018;47(3):539-51.