Araştırma Makalesi
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Doğadan Esinlenen Optimizasyon Algoritmaları ve Optimizasyon Algoritmalarının Optimizasyonu

Yıl 2016, Cilt: 4 Sayı: 1, 293 - 304, 30.01.2016

Öz

Matematiksel olarak Optimizasyon,  bir yada daha fazla bağımsız değişkene sahip olan bir fonksiyonun verilen kısıtlayıcı şartlar altındaki en iyi çözümünü arama işlemi olarak tanımlanabilir.  Optimizasyon problemlerini çözmek için sezgisel optimizasyon algoritmaları ve klasik çözüm yöntemleri mevcuttur. Ancak son yıllarda özellikle doğal süreçlerden esinlenilmiş birçok optimizasyon algoritması geliştirilmiştir. Doğadaki birçok canlı sahip oldukları kusursuz tasarımlarıyla var olan kaynakları minimum kullanarak, maksimum performans elde etmeyi başararak en zorlu şartlarda bile hayatta kalmayı başarmıştır. Canlıların koordineli hareket ederek özellikle yiyecek bulmada gösterdikleri zeka, “sürü zekası”(swarm intelligence) olarak adlandırılmaktadır. Bu çalışmada özellikle son yıllarda geliştirilen ve doğadan esinlenen optimizasyon algoritmaları, bu algoritmaların uygulama alanları ve performans analizleri incelenmiştir. 

Kaynakça

  • J.H Holland Adaptation in Natural and Artificial Systems University of Michigan Press, Ann Arbor, Michigan (1975)
  • D.E Goldberg Genetic Algorithms in Search, Optimization, and Machine Learning Addison-Wesley, Reading, MA (1989)
  • http://apps.webofknowladge.com/UA_GeneralSearch_input.do?product=UA&SID=N2j2zzcxZelCvVdCRdO&search_mode=GeneralSearch.( Son Erişim tarihi:03.01.2016)
  • S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi Optimization By Simulated Annealing Science 220( 4598) (1983) 671-680.
  • C. Blum Ant colony optimization: Introduction and recent trends Physics of Life Reviews 2(4)(2005) 353-373.
  • M. Dorigo Optimization Learning And Natural Algorithms Ph.D. Thesis, Politecnico Di Milano, Italy, (1992).
  • M. Dorigo, C. Blum, Ant colony optimization theory: A survey Theoretical Computer Science, 344(2–3)( 2005) 243-278.
  • K. Socha M. Dorigo Ant colony optimization for continuous domains European Journal of Operational Research 185(3)(2008)1155-1173.
  • J. Kennedy, R. Eberhart Particle swarm optimization IEEE Conference: 1995 IEEE International Conference on Neural Networks(ICNN95) , PROCEEDINGS, (1-6) ( 1942-1948 (1995)
  • D. Karaboga, B. Basturk On the Performance of Artificial Bee Colony (ABC) Algorithm, Applied Soft Computing 8 (1) (2008) 687–697.
  • C. Öztürk, E. Hançer, D. Karaboğa(2014) doi:http://dx.doi.org/10.17341/gummfd.00459
  • http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO_files/
  • Page422.htm. (Erişim Tarihi:04.01.2016)
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  • Y. Wenchao, Z.Yinzhi, G. Liang, L. Xinyu, M. Jianhui(2016) http://dx.doi.org/10.1016/j.eswa.2015.09.031.
  • A.N.K. Nasir, M.O. Tokhi, N.M.A. Ghani(2015) http://dx.doi.org/10.1016/j.eswa.2014.09.010.
  • M. Aziz, M. Tayarani (2014) http://dx.doi.org/10.1016/j.engappai.2014.07.021.
  • L. Wang, H. Ni, R. Yang, P. M. Pardalos, X. Du, M. Fei(2015) http://dx.doi.org/10.1016/j.ins.2015.05.022.
  • X. Geng, Z. Chen, W. Yang, D. Shi, K. Zhao (2011) http://dx.doi.org/10.1016/j.asoc.2011.01.039.
  • A. H. Karami, M. Hasanzadeh(2015) http://dx.doi.org/10.1016/j.compeleceng.2014.12.014.
  • M. K. Naik, R. P.(2016) http://dx.doi.org/10.1016/j.asoc.2015.10.039.
  • T. Zhang, T. Hu, X. Guo, Z. Chen, Y. Zheng (2013) http://dx.doi.org/10.1016/j.knosys.2013.07.015.
  • S. Sarafrazi, H. Nezamabadi-pour, S. Saryazdi (2011) http://dx.doi.org/10.1016/j.scient.2011.04.003.
  • Z. Li, W. Wang, Y. Yan, Z. Li (2015) http://dx.doi.org/10.1016/j.eswa.2015.07.043.
  • H. Garg (2016) http://dx.doi.org/10.1016/j.amc.2015.11.001.
  • M. Toksari(2016) http://dx.doi.org/10.1016/j.ijepes.2015.12.032.
  • S. Sarafrazi, H. Nezamabadi-pour, S. R. Seydnejad (2015) http://dx.doi.org/10.1016/j.jksuci.2014.10.003.
  • M. Metlicka, D. Davendra (2015) http://dx.doi.org/10.1016/j.swevo.2015.03.002.
  • M. Ghasemi, S. Ghavidel, E. Akbari, A.A. Vahed(2014) http://dx.doi.org/10.1016/j.energy.2014.06.026.
  • X. Yuan, J. Zhao, Y.Yang, Y. Wang (2014) http://dx.doi.org/10.1016/j.asoc.2013.12.016.
  • M. Pluhacek, R. Senkerik, D. Davendra (2015)http://dx.doi.org/10.1016/j.swevo.2015.10.008.
  • M. Mitić, N. Vuković, M. Petrović, Z. Miljković(2015) http://dx.doi.org/10.1016/j.knosys.2015.08.010.
  • A. Askarzadeh (2013) http://dx.doi.org/10.1016/j.solener.2013.08.014.
  • H. Aguiar, O. Junior, M. A. S. Machado(2015) http://dx.doi.org/10.1016/j.procs.2015.07.002.
  • E. Amiri, S. Mahmoudi(2015) http://dx.doi.org/10.1016/j.asoc.2015.12.008.
  • F. Gaxiola, P. Melin, F. Valdez, J. R. C., O. Castillo(2016) http://dx.doi.org/10.1016/j.asoc.2015.10.027.
  • S.Shadmand, B. Mashoufi (2016) http://dx.doi.org/10.1016/j.bspc.2015.10.008.
  • R.J. Kuo, W.L. Tseng, F.C. Tien, T. W. Liao(2012) http://dx.doi.org/10.1016/j.cie.2012.06.006.
  • Z. Izakian, M. S. Mesgari, A. Abraham(2016) http://dx.doi.org/10.1016/j.compenvurbsys.2015.10.009.
  • H. Li, H. He, Y. Wen(2015) http://dx.doi.org/10.1016/j.ijleo.2015.09.127.
  • C. Ozturk, E. Hancer, D. Karaboga(2015) http://dx.doi.org/10.1016/j.asoc.2014.11.040.
  • B. Jiang, F. Qiu, L. Wang, Z. Zhang(2013) http://dx.doi.org/10.1016/j.ipm.2015.11.003.
  • J. Tvrdík, I. Křivý,(2015) http://dx.doi.org/10.1016/j.asoc.2015.06.032.
  • Y. Ding, X. Fu(2015) http://dx.doi.org/10.1016/j.neucom.2015.01.106.
  • S. Alam, G. Dobbie, S.U. Rehman(2015) http://dx.doi.org/10.1016/j.swevo.2015.10.003.
  • T.O. Ting, J. Ma, K. S. Kim, K. Huang(2016) http://dx.doi.org/10.1016/j.asoc.2015.10.054.
  • C. Wang, D. Mu, F. Zhao, J. W. Sutherland(2015) http://dx.doi.org/10.1016/j.cie.2015.02.005.
  • P. Cai, Y. Cai, I. Chandrasekaran, J. Zheng(2016) http://dx.doi.org/10.1016/j.autcon.2015.09.007.
  • E. Rashedi, H. Nezamabadi-pour, S. Saryazdi(2009) http://dx.doi.org/10.1016/j.ins.2009.03.004.
  • M. Abdechiri, M. R. Meybodi, H. Bahrami(2013) http://dx.doi.org/10.1016/j.asoc.2012.03.068.
  • V. K. Patel, V. J. Savsani(2015) http://dx.doi.org/10.1016/j.ins.2015.06.044.
  • H. Abedinpourshotorban, S. M. Shamsuddin, Z. Beheshti, D. N.A. Jawawi (2015) http://dx.doi.org/10.1016/j.swevo.2015.07.002.
  • A. H. Kashan(2015) http://dx.doi.org/10.1016/j.cor.2014.10.011.
  • A. Baykasoğlu, Ş. Akpinar(2015) http://dx.doi.org/10.1016/j.asoc.2015.10.036.
  • A. Baykasoğlu, Ş. Akpinar(2015) http://dx.doi.org/10.1016/j.asoc.2015.08.052.
  • M.Ghaemi, M.R.Feizi-Derakhshi(2014) http://dx.doi.org/10.1016/j.eswa.2014.05.009.
  • I. Rbouh, A. Ameur El Imrani(2014) http://dx.doi.org/10.1016/j.aasri.2014.05.005.
  • H. Shah-Hosseini(2012) http://dx.doi.org/10.1016/j.sbspro.2012.01.033.
  • A. Hatamlou(2013) http://dx.doi.org/10.1016/j.ins.2012.08.023.
  • H. Eskandar, A. Sadollah, A. Bahreininejad, M. Hamdi(2012) http://dx.doi.org/10.1016/j.compstruc.2012.07.010.
  • H. Shareef, A. Asrul Ibrahim, A. Hussein Mutlag(2015) http://dx.doi.org/10.1016/j.asoc.2015.07.028.
  • M. Dorigo, V. Maniezzo, A Colorni(1996) doi: 10.1109/3477.484436
  • T. Stutzle, H.H. Hoos MAX–MIN Ant System Future Generation Computer Systems 16(8)(2000) 889–914.
  • M. Clerc, M; Kennedy, J. (2002) doi: 10.1109/4235.985692
  • D. Karaboga, B. Basturk A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm JOURNAL OF GLOBAL OPTIMIZATION 39(3)(2007)
  • W. Pan (2012) http://dx.doi.org/10.1016/j.knosys.2011.07.001.
  • X. S. Yang, S. Deb (2009) doi: 10.1109/NABIC.2009.5393690
  • A. H. Gandomi, A. H. Alavi (2012) doi:10.1016/j.cnsns.2012.05.010
  • K.M. Passino(2002) doi: 10.1109/MCS.2002.1004010
  • X. S. Yang A New Metaheuristic Bat-Inspired Algorithm International Workshop on Nature Inspired Cooperative Strategies for Optimization (NICSO 2008)Location: Tenerife, SPAIN Date: 2008
  • X.S. Yang, Firefly Algorithms for Multimodal Optimization, Lecture Notes in Computer Science 5792(2009) 169-178
  • B.R. Rajakumar, The Lion's Algorithm: A New Nature-Inspired Search Algorithm, Procedia Technology 6(2012) 126-135
  • S. Mirjalili, S. M. Mirjalili, A. Lewis (2014)http://dx.doi.org/10.1016/j.advengsoft.2013.12.007.
  • A. Kaveh, N. Farhoudi(2013) http://dx.doi.org/10.1016/j.advengsoft.2013.03.004.
  • A.R. Mehrabian, C. Lucas(2006) http://dx.doi.org/10.1016/j.ecoinf.2006.07.003.
  • S.A. Uymaz, G. Tezel, E. Yel(2015) http://dx.doi.org/10.1016/j.asoc.2015.03.003.
  • M. D. Li, H. Zhao, X. W. Weng, T. Han(2016) http://dx.doi.org/10.1016/j.advengsoft.2015.11.004.
  • O. Abedinia, N. Amjady,A.Ghasemi(2014) DOI: 10.1002/cplx.21634
  • J. J.Q. Yu, V. O.K. Li(2015) http://dx.doi.org/10.1016/j.asoc.2015.02.014
  • L. Wang, H. Ni, R. Yang, P. M. Pardalos, X. Du, M. Fei(2015) http://dx.doi.org/10.1016/j.ins.2015.05.022.

Nature Inspired Optimization Algorithms and Optimization of the Optimization Algorithms

Yıl 2016, Cilt: 4 Sayı: 1, 293 - 304, 30.01.2016

Öz

Optimization is defined as a process of searching the best solution of a function which has one or more variable under some constraints. There are classical solution methods and heuristic optimization algorithms in order to solve optimization problems. Recently, it has been developed a lot of optimization algorithms inspired from nature. Most of the living being in the nature has been successful to survive perfect designs accomplishing to take maximum performance from minimum resource. The cooperative behavior of animals for finding foods is called swarm intelligence. In this study, recently developed optimization algorithms especially inspired from nature have been researched. It has been shown that for these algorithms in order to give optimum results is dependendent to the parameters used in the algorithms. 

Kaynakça

  • J.H Holland Adaptation in Natural and Artificial Systems University of Michigan Press, Ann Arbor, Michigan (1975)
  • D.E Goldberg Genetic Algorithms in Search, Optimization, and Machine Learning Addison-Wesley, Reading, MA (1989)
  • http://apps.webofknowladge.com/UA_GeneralSearch_input.do?product=UA&SID=N2j2zzcxZelCvVdCRdO&search_mode=GeneralSearch.( Son Erişim tarihi:03.01.2016)
  • S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi Optimization By Simulated Annealing Science 220( 4598) (1983) 671-680.
  • C. Blum Ant colony optimization: Introduction and recent trends Physics of Life Reviews 2(4)(2005) 353-373.
  • M. Dorigo Optimization Learning And Natural Algorithms Ph.D. Thesis, Politecnico Di Milano, Italy, (1992).
  • M. Dorigo, C. Blum, Ant colony optimization theory: A survey Theoretical Computer Science, 344(2–3)( 2005) 243-278.
  • K. Socha M. Dorigo Ant colony optimization for continuous domains European Journal of Operational Research 185(3)(2008)1155-1173.
  • J. Kennedy, R. Eberhart Particle swarm optimization IEEE Conference: 1995 IEEE International Conference on Neural Networks(ICNN95) , PROCEEDINGS, (1-6) ( 1942-1948 (1995)
  • D. Karaboga, B. Basturk On the Performance of Artificial Bee Colony (ABC) Algorithm, Applied Soft Computing 8 (1) (2008) 687–697.
  • C. Öztürk, E. Hançer, D. Karaboğa(2014) doi:http://dx.doi.org/10.17341/gummfd.00459
  • http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO_files/
  • Page422.htm. (Erişim Tarihi:04.01.2016)
  • A. Yurtkuran, E. Emel(2015) http://dx.doi.org/10.1016/j.amc.2015.09.064.
  • Y. Wenchao, Z.Yinzhi, G. Liang, L. Xinyu, M. Jianhui(2016) http://dx.doi.org/10.1016/j.eswa.2015.09.031.
  • A.N.K. Nasir, M.O. Tokhi, N.M.A. Ghani(2015) http://dx.doi.org/10.1016/j.eswa.2014.09.010.
  • M. Aziz, M. Tayarani (2014) http://dx.doi.org/10.1016/j.engappai.2014.07.021.
  • L. Wang, H. Ni, R. Yang, P. M. Pardalos, X. Du, M. Fei(2015) http://dx.doi.org/10.1016/j.ins.2015.05.022.
  • X. Geng, Z. Chen, W. Yang, D. Shi, K. Zhao (2011) http://dx.doi.org/10.1016/j.asoc.2011.01.039.
  • A. H. Karami, M. Hasanzadeh(2015) http://dx.doi.org/10.1016/j.compeleceng.2014.12.014.
  • M. K. Naik, R. P.(2016) http://dx.doi.org/10.1016/j.asoc.2015.10.039.
  • T. Zhang, T. Hu, X. Guo, Z. Chen, Y. Zheng (2013) http://dx.doi.org/10.1016/j.knosys.2013.07.015.
  • S. Sarafrazi, H. Nezamabadi-pour, S. Saryazdi (2011) http://dx.doi.org/10.1016/j.scient.2011.04.003.
  • Z. Li, W. Wang, Y. Yan, Z. Li (2015) http://dx.doi.org/10.1016/j.eswa.2015.07.043.
  • H. Garg (2016) http://dx.doi.org/10.1016/j.amc.2015.11.001.
  • M. Toksari(2016) http://dx.doi.org/10.1016/j.ijepes.2015.12.032.
  • S. Sarafrazi, H. Nezamabadi-pour, S. R. Seydnejad (2015) http://dx.doi.org/10.1016/j.jksuci.2014.10.003.
  • M. Metlicka, D. Davendra (2015) http://dx.doi.org/10.1016/j.swevo.2015.03.002.
  • M. Ghasemi, S. Ghavidel, E. Akbari, A.A. Vahed(2014) http://dx.doi.org/10.1016/j.energy.2014.06.026.
  • X. Yuan, J. Zhao, Y.Yang, Y. Wang (2014) http://dx.doi.org/10.1016/j.asoc.2013.12.016.
  • M. Pluhacek, R. Senkerik, D. Davendra (2015)http://dx.doi.org/10.1016/j.swevo.2015.10.008.
  • M. Mitić, N. Vuković, M. Petrović, Z. Miljković(2015) http://dx.doi.org/10.1016/j.knosys.2015.08.010.
  • A. Askarzadeh (2013) http://dx.doi.org/10.1016/j.solener.2013.08.014.
  • H. Aguiar, O. Junior, M. A. S. Machado(2015) http://dx.doi.org/10.1016/j.procs.2015.07.002.
  • E. Amiri, S. Mahmoudi(2015) http://dx.doi.org/10.1016/j.asoc.2015.12.008.
  • F. Gaxiola, P. Melin, F. Valdez, J. R. C., O. Castillo(2016) http://dx.doi.org/10.1016/j.asoc.2015.10.027.
  • S.Shadmand, B. Mashoufi (2016) http://dx.doi.org/10.1016/j.bspc.2015.10.008.
  • R.J. Kuo, W.L. Tseng, F.C. Tien, T. W. Liao(2012) http://dx.doi.org/10.1016/j.cie.2012.06.006.
  • Z. Izakian, M. S. Mesgari, A. Abraham(2016) http://dx.doi.org/10.1016/j.compenvurbsys.2015.10.009.
  • H. Li, H. He, Y. Wen(2015) http://dx.doi.org/10.1016/j.ijleo.2015.09.127.
  • C. Ozturk, E. Hancer, D. Karaboga(2015) http://dx.doi.org/10.1016/j.asoc.2014.11.040.
  • B. Jiang, F. Qiu, L. Wang, Z. Zhang(2013) http://dx.doi.org/10.1016/j.ipm.2015.11.003.
  • J. Tvrdík, I. Křivý,(2015) http://dx.doi.org/10.1016/j.asoc.2015.06.032.
  • Y. Ding, X. Fu(2015) http://dx.doi.org/10.1016/j.neucom.2015.01.106.
  • S. Alam, G. Dobbie, S.U. Rehman(2015) http://dx.doi.org/10.1016/j.swevo.2015.10.003.
  • T.O. Ting, J. Ma, K. S. Kim, K. Huang(2016) http://dx.doi.org/10.1016/j.asoc.2015.10.054.
  • C. Wang, D. Mu, F. Zhao, J. W. Sutherland(2015) http://dx.doi.org/10.1016/j.cie.2015.02.005.
  • P. Cai, Y. Cai, I. Chandrasekaran, J. Zheng(2016) http://dx.doi.org/10.1016/j.autcon.2015.09.007.
  • E. Rashedi, H. Nezamabadi-pour, S. Saryazdi(2009) http://dx.doi.org/10.1016/j.ins.2009.03.004.
  • M. Abdechiri, M. R. Meybodi, H. Bahrami(2013) http://dx.doi.org/10.1016/j.asoc.2012.03.068.
  • V. K. Patel, V. J. Savsani(2015) http://dx.doi.org/10.1016/j.ins.2015.06.044.
  • H. Abedinpourshotorban, S. M. Shamsuddin, Z. Beheshti, D. N.A. Jawawi (2015) http://dx.doi.org/10.1016/j.swevo.2015.07.002.
  • A. H. Kashan(2015) http://dx.doi.org/10.1016/j.cor.2014.10.011.
  • A. Baykasoğlu, Ş. Akpinar(2015) http://dx.doi.org/10.1016/j.asoc.2015.10.036.
  • A. Baykasoğlu, Ş. Akpinar(2015) http://dx.doi.org/10.1016/j.asoc.2015.08.052.
  • M.Ghaemi, M.R.Feizi-Derakhshi(2014) http://dx.doi.org/10.1016/j.eswa.2014.05.009.
  • I. Rbouh, A. Ameur El Imrani(2014) http://dx.doi.org/10.1016/j.aasri.2014.05.005.
  • H. Shah-Hosseini(2012) http://dx.doi.org/10.1016/j.sbspro.2012.01.033.
  • A. Hatamlou(2013) http://dx.doi.org/10.1016/j.ins.2012.08.023.
  • H. Eskandar, A. Sadollah, A. Bahreininejad, M. Hamdi(2012) http://dx.doi.org/10.1016/j.compstruc.2012.07.010.
  • H. Shareef, A. Asrul Ibrahim, A. Hussein Mutlag(2015) http://dx.doi.org/10.1016/j.asoc.2015.07.028.
  • M. Dorigo, V. Maniezzo, A Colorni(1996) doi: 10.1109/3477.484436
  • T. Stutzle, H.H. Hoos MAX–MIN Ant System Future Generation Computer Systems 16(8)(2000) 889–914.
  • M. Clerc, M; Kennedy, J. (2002) doi: 10.1109/4235.985692
  • D. Karaboga, B. Basturk A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm JOURNAL OF GLOBAL OPTIMIZATION 39(3)(2007)
  • W. Pan (2012) http://dx.doi.org/10.1016/j.knosys.2011.07.001.
  • X. S. Yang, S. Deb (2009) doi: 10.1109/NABIC.2009.5393690
  • A. H. Gandomi, A. H. Alavi (2012) doi:10.1016/j.cnsns.2012.05.010
  • K.M. Passino(2002) doi: 10.1109/MCS.2002.1004010
  • X. S. Yang A New Metaheuristic Bat-Inspired Algorithm International Workshop on Nature Inspired Cooperative Strategies for Optimization (NICSO 2008)Location: Tenerife, SPAIN Date: 2008
  • X.S. Yang, Firefly Algorithms for Multimodal Optimization, Lecture Notes in Computer Science 5792(2009) 169-178
  • B.R. Rajakumar, The Lion's Algorithm: A New Nature-Inspired Search Algorithm, Procedia Technology 6(2012) 126-135
  • S. Mirjalili, S. M. Mirjalili, A. Lewis (2014)http://dx.doi.org/10.1016/j.advengsoft.2013.12.007.
  • A. Kaveh, N. Farhoudi(2013) http://dx.doi.org/10.1016/j.advengsoft.2013.03.004.
  • A.R. Mehrabian, C. Lucas(2006) http://dx.doi.org/10.1016/j.ecoinf.2006.07.003.
  • S.A. Uymaz, G. Tezel, E. Yel(2015) http://dx.doi.org/10.1016/j.asoc.2015.03.003.
  • M. D. Li, H. Zhao, X. W. Weng, T. Han(2016) http://dx.doi.org/10.1016/j.advengsoft.2015.11.004.
  • O. Abedinia, N. Amjady,A.Ghasemi(2014) DOI: 10.1002/cplx.21634
  • J. J.Q. Yu, V. O.K. Li(2015) http://dx.doi.org/10.1016/j.asoc.2015.02.014
  • L. Wang, H. Ni, R. Yang, P. M. Pardalos, X. Du, M. Fei(2015) http://dx.doi.org/10.1016/j.ins.2015.05.022.
Toplam 80 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Pakize Erdoğmuş

Yayımlanma Tarihi 30 Ocak 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

APA Erdoğmuş, P. (2016). Doğadan Esinlenen Optimizasyon Algoritmaları ve Optimizasyon Algoritmalarının Optimizasyonu. Duzce University Journal of Science and Technology, 4(1), 293-304.
AMA Erdoğmuş P. Doğadan Esinlenen Optimizasyon Algoritmaları ve Optimizasyon Algoritmalarının Optimizasyonu. DÜBİTED. Ocak 2016;4(1):293-304.
Chicago Erdoğmuş, Pakize. “Doğadan Esinlenen Optimizasyon Algoritmaları Ve Optimizasyon Algoritmalarının Optimizasyonu”. Duzce University Journal of Science and Technology 4, sy. 1 (Ocak 2016): 293-304.
EndNote Erdoğmuş P (01 Ocak 2016) Doğadan Esinlenen Optimizasyon Algoritmaları ve Optimizasyon Algoritmalarının Optimizasyonu. Duzce University Journal of Science and Technology 4 1 293–304.
IEEE P. Erdoğmuş, “Doğadan Esinlenen Optimizasyon Algoritmaları ve Optimizasyon Algoritmalarının Optimizasyonu”, DÜBİTED, c. 4, sy. 1, ss. 293–304, 2016.
ISNAD Erdoğmuş, Pakize. “Doğadan Esinlenen Optimizasyon Algoritmaları Ve Optimizasyon Algoritmalarının Optimizasyonu”. Duzce University Journal of Science and Technology 4/1 (Ocak 2016), 293-304.
JAMA Erdoğmuş P. Doğadan Esinlenen Optimizasyon Algoritmaları ve Optimizasyon Algoritmalarının Optimizasyonu. DÜBİTED. 2016;4:293–304.
MLA Erdoğmuş, Pakize. “Doğadan Esinlenen Optimizasyon Algoritmaları Ve Optimizasyon Algoritmalarının Optimizasyonu”. Duzce University Journal of Science and Technology, c. 4, sy. 1, 2016, ss. 293-04.
Vancouver Erdoğmuş P. Doğadan Esinlenen Optimizasyon Algoritmaları ve Optimizasyon Algoritmalarının Optimizasyonu. DÜBİTED. 2016;4(1):293-304.