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Güncel metasezgisel optimizasyon algoritmalarının CEC2020 test fonksiyonları ile karşılaştırılması

Year 2021, Volume: 12 Issue: 5, 729 - 741, 31.12.2021

Elif Varol Altay Osman Altay

https://doi.org/10.24012/dumf.1051338
Cited By: 4

Abstract

Son yıllarda karmaşık, çok modlu, yüksek boyutlu ve doğrusal olmayan arama ve optimizasyon problemleri için birçok metasezgisel optimizasyon algoritması önerilmiştir. Doğada yer alan canlıların sürü davranışları, bitkilerin davranış biçimleri, insanların sosyal davranışları, matematiksel, fiziksel, kimyasal, biyolojik yasalar ve kurallardan ilham alan çok sayıda metasezgisel optimizasyon algoritması bulunmaktadır. Bu algoritmalar bazı problemlerde başarı ile sonuç üretirken bazı problemlerde yeterince başarılı sonuç üretememektedir. Önerilen bu algoritmaların performansları problemin yapısına göre değişiklik göstermektedir. Araştırmacılar da bundan dolayı her geçen gün yeni yöntemler önermektedir. Bu çalışmada son zamanlarda ortaya çıkan Cıvık Mantar Optimizasyon Algoritması, Balina Optimizasyon Algoritması, Gri Kurt Optimizasyonu, Harris Şahin Optimizasyonu ve Arşimet Optimizasyon Algoritması tanıtılmış ve bu yöntemlerin performansları 10 adet unimodal, multimodal, hibrit ve composition fonksiyonlarını içeren CEC2020 test fonksiyonlarında karşılaştırılmıştır.

Keywords

Metasezgisel yöntemler kalite test fonksiyonları global optimizasyon

References

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  • [5] B. Xing, W. J. Gao, “Central force optimization algorithm”, In Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms, Springer International Publishing, pp. 333-337, 2014.
  • [6] L. Xie, Y. Tan, J. Zeng, Z. Cui, “Artificial physics optimisation: a brief survey”, International Journal of Bio-Inspired Computation, vol. 2, no. 5, pp. 291-302, 2010.
  • [7] M. Kripka, R. M. L. Kripka, “Big crunch optimization method”, In International conference on engineering optimization. Brazil, 2008, pp. 1-5.
  • [8] H. Shah-Hosseini, “Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation”, Int. J. Computational Science and Engineering, vol. 6, pp. 132-140, 2011.
  • [9] H. Eskandar, A. Sadollah, A. Bahreininejad, M. Hamdi, “Water cycle algorithm–a novel metaheuristic optimization method for solving constrained engineering optimization problems”, Comput. Struct., vol. 110, pp. 151–166, 2012.
  • [10] B. Xing, W. J. Gao, “Charged system search algorithm”, In Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms, Springer International Publishing, 2014, pp. 339-346.
  • [11] E. Atashpaz-Gargari, C. Lucas, “Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition”, In 2007 IEEE Congress on Evolutionary Computation, 2007, pp. 4661-4667.
  • [12] R. V. Rao, V. Patel, “An improved teaching-learning-based optimization algorithm for solving unconstrained optimization problems”, Scientia Iranica, vol. 20, no. 3, pp. 710–720, 2013.
  • [13] A. Borji, M. Hamidi, “A new approach to global optimization motivated by parliamentary political competitions”, International Journal of Innovative Computing, Information and Control, vol. 5 no. 6, pp. 1643-1653, 2009.
  • [14] Z. Cui, Z. Shi, J. Zeng, “Using social emotional optimization algorithm to direct orbits of chaotic systems”, International Conference on Swarm, Evolutionary, and Memetic Computing, Springer, 2010, pp. 389-395
  • [15] Y. Shi, “Brain storm optimization algorithm”, In International Conference in Swarm Intelligence, Springer Berlin Heidelberg, 2011, pp. 303-309.
  • [16] A. Daskin, S. Kais, “Group leaders optimization algorithm”, Molecular Physics, vol. 109, no. 5, pp. 761-772, 2011.
  • [17] S. Balochian, H. Baloochian, “Social mimic optimization algorithm and engineering applications”, Expert Systems with Applications, vol. 134, pp. 178-191, 2019.
  • [18] F. Ramezani, S. Lotfi, “Social-based algorithm (SBA)”, Applied Soft Computing, vol. 13, no. 5, pp. 2837-2856, 2013.
  • [19] E. V. Altay, B. Alatas, “Performance comparisons of socially inspired metaheuristic algorithms on unconstrained global optimization”, In Advances in Computer Communication and Computational Sciences, Springer, Singapore, 2019, pp. 163-175.
  • [20] J. Kennedy, R. C. Eberhart, “Particle swarm optimization”, IEEE International Conference on Neural Networks, Piscataway, NJ. Nov/Dec 1995, pp. 1942-1948.
  • [21] M. Dorigo, T. Stützle, “Ant colony optimization”, MIT Press, Cambridge, 2004.
  • [22] D. Karaboga, B. Basturk, “A powerful and efficient algorithm for numerical function optimization: Artificial Bee Colony (ABC) algorithm”, J. Global Optim., vol. 39, pp. 459-171, 2007.
  • [23] A. Karcı, “A new metaheuristic algorithm based chemical process: Atom Algorithm”, 1st International Eurasian Conference on Mathematical Sciences and Applications, 2012, pp. 03-07.
  • [24] B. Alataş B., “ACROA: Artificial chemical reaction optimization algorithm for global optimization”, Expert Systems with Applications, vol. 38, no.10, pp. 13170–13180, 2011.
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  • [26] K. M. Passino, “Biomimicry of bacterial foraging for distributed optimization and control”, IEEE control systems magazine, vol. 22, no. 3, pp. 52–67, 2002.
  • [27] R. Storn, K. Price, “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces”, Journal of global optimization, vol. 11, no. 4, pp. 341–359, 1997.
  • [28] S. A. Salem, “BOA: A novel optimization algorithm”, IEEE 2012 International Conference on Engineering and Technology (ICET), 2012, pp. 1-5.
  • [29] S. Mirjalili, “SCA: A Sine cosine algorithm for solving optimization problems”, Knowledge-Based Systems, vol. 96, pp. 120-133, 2016.
  • [30] A. Karci, B. Alatas, “Thinking capability of saplings growing up algorithm”, In: Intelligent data engineering and automated learning—IDEAL 2006, Lecture notes in computer Science, Springer, Berlin, vol. 4224, pp. 386–393, 2006.
  • [31] F. Merrikh-Bayat, “The runner-root algorithm: a metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature”, Applied Soft Computing, vol. 33, pp. 292–303, 2015.
  • [32] Y. Zhou, Y. Wang, X. Chen, L. Zhang, K. Wu, “A Novel path planning algorithm based on plant growth mechanism”, Soft Computing, vol. 21 no. 2, pp. 435-445, 2017.
  • [33] Y. Labbi, D. B. Attous, H. A. Gabbar, B. Mahdad, A. Zidan, “A new rooted tree optimization algorithm for economic dispatch with valve-point effect”, International Journal of Electrical Power & Energy Systems, vol. 79, pp. 298–311, 2016.
  • [34] A. A. Kamarudin, Z. A. Othman, H. M. Sarim, “Water flow algorithm decision support tool for travelling salesman problem”, In Proceedings of the International Conference on Applied Science and Technology 2016 (ICAST’16), AIP Publishing, 2016, vol. 1761, no. 1.
  • [35] A. Sadollah, H. Eskandar, A. Bahreininejad, J. H. Kim, “Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems”, Applied Soft Computing, vol. 30, pp. 58–71, 2015.
  • [36] A. Kaveh, T. Bakhshpoori, “Water evaporation optimization: A novel physically inspired optimization algorithm”, Computers & Structures, vol. 167, pp. 69-85, 2016.
  • [37] A. Ibrahim, S. Rahnamayan, M. V. Martin, “Simulated raindrop algorithm for global optimization”, IEEE 27th Canadian Conference Electrical and Computer Engineering (CCECE), 2014, pp. 1-8.
  • [38] A. H. Kashan, “League Championship Algorithm: A new algorithm for numerical function optimization”, In 2009 international conference of soft computing and pattern recognition, 2009, pp. 43-48.
  • [39] E. Khaji, “Soccer League Optimization: A heuristic Algorithm Inspired by the Football System in European Countries”, 2014, arXiv preprint arXiv:1406.4462.
  • [40] H. D. Purnomo, H. M. Wee, “Soccer game optimization: an innovative integration of evolutionary algorithm and swarm intelligence algorithm”, Meta-Heuristics optimization algorithms in engineering, business, economics, and finance. IGI Global, Pennsylvania, pp. 386-420, 2013.
  • [41] N. Moosavian and B. K. Roodsari, “Soccer league competition algorithm, a new method for solving systems of nonlinear equations”, International Journal of Intelligence Science, vol. 4, no. 1, pp. 7, 2013.
  • [42] E. Osaba, F. Diaz, E. Onieva, “A novel meta-heuristic based on soccer concepts to solve routing problems”, In Proceedings of the 15th annual conference companion on Genetic and evolutionary computation, ACM, pp. 1743-1744, 2013.
  • [43] Z. W. Geem, J. H. Kim, G. V. Loganathan, “A new heuristic optimization algorithm: harmony search”, Simulation, vol. 76, no. 2, pp. 60-68, 2001.
  • [44] S. M. Ashrafi, A. B. Dariane, “A novel and effective algorithm for numerical optimization: melody search (MS)”, In 2011 11th international conference on hybrid intelligent systems (HIS), IEEE, 2011, pp. 109-114.
  • [45] R. A. Mora-Gutiérrez, J. Ramírez-Rodríguez, E. A. Rincón-García, A. Ponsich, O. Herrera, & P. Lara-Velázquez, “Adaptation of the musical composition method for solving constrained optimization problems”, Soft Computing, vol. 18, no. 10, pp. 1931-1948, 2014.
  • [46] E. V. Altay, B. Alatas, “Randomness as source for inspiring solution search methods: Music based approaches”, Physica A: Statistical Mechanics and its Applications, vol. 537, no. 122650, 2020.
  • [47] E. V. Altay, B. Alatas, “Music based metaheuristic methods for constrained optimization”, In 2018 6th International Symposium on Digital Forensic and Security (ISDFS), IEEE, 2018, pp. 1-6.
  • [48] Y. C. Ho, D. L. Pepyne, “Simple explanation of the no-free-lunch theorem and its implications”, Journal of optimization theory and applications, vol. 115, no. 3, pp. 549-570, 2002.
  • [49] S. Li, H. Chen, M. Wang, A. A. Heidari, S. Mirjalili, “Slime mould algorithm: A new method for stochastic optimization”, Future Generation Computer Systems, vol. 111, pp. 300-323, 2020.
  • [50] S. Mirjalili, A. Lewis, “The whale optimization algorithm”, Advances in engineering software, vol. 95, pp. 51-67, 2016.
  • [51] S. Mirjalili, S. M. Mirjalili, A. Lewis, “Grey wolf optimizer”, Advances in engineering software, vol. 69, pp. 46-61, 2014.
  • [52] A. A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, H. Chen, “Harris hawks optimization: Algorithm and applications”, Future generation computer systems, vol. 97, pp. 849-872, 2019.
  • [53] F. A. Hashim, K. Hussain, E. H. Houssein, M. S. Mabrouk, W. Al-Atabany, “Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems”, Applied Intelligence, vol. 51, no. 3, pp. 1531-1551, 2021.
  • [54] A.W. Mohamed, A.A. Hadi, A. K. Mohamed, N.H. Awad, “Evaluating the performance of adaptive gainingsharing knowledge based algorithm on CEC 2020 benchmark problems”, In: 2020 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2020, pp. 1–8.
  • [55] O. Altay, “Chaotic slime mould optimization algorithm for global optimization”, Artificial Intelligence Review, pp. 1-62, 2021.

Year 2021, Volume: 12 Issue: 5, 729 - 741, 31.12.2021

Elif Varol Altay Osman Altay

https://doi.org/10.24012/dumf.1051338
Cited By: 4

Abstract

References

  • [1] B. Bunday, Basic Optimization Methods, London: Edward Arnold Ltd, 1984.
  • [2] E. V. Altay, B. Alatas, “Bird swarm algorithms with chaotic mapping”, Artificial Intelligence Review, vol. 53 no. 2, pp. 1373-1414, 2020. [3] E. Varol, B. Alataş, “Sürü zekâsında yeni bir yaklaşım: Kuş sürüsü algoritması”, Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi, vol. 8, no. 1, pp. 133-146, 2017.
  • [4] S. İ. Birbil, S. C. Fang, “An electromagnetism-like mechanism for global optimization”, Journal of global optimization, vol. 25, no. 3, pp. 263-282, 2003.
  • [5] B. Xing, W. J. Gao, “Central force optimization algorithm”, In Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms, Springer International Publishing, pp. 333-337, 2014.
  • [6] L. Xie, Y. Tan, J. Zeng, Z. Cui, “Artificial physics optimisation: a brief survey”, International Journal of Bio-Inspired Computation, vol. 2, no. 5, pp. 291-302, 2010.
  • [7] M. Kripka, R. M. L. Kripka, “Big crunch optimization method”, In International conference on engineering optimization. Brazil, 2008, pp. 1-5.
  • [8] H. Shah-Hosseini, “Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation”, Int. J. Computational Science and Engineering, vol. 6, pp. 132-140, 2011.
  • [9] H. Eskandar, A. Sadollah, A. Bahreininejad, M. Hamdi, “Water cycle algorithm–a novel metaheuristic optimization method for solving constrained engineering optimization problems”, Comput. Struct., vol. 110, pp. 151–166, 2012.
  • [10] B. Xing, W. J. Gao, “Charged system search algorithm”, In Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms, Springer International Publishing, 2014, pp. 339-346.
  • [11] E. Atashpaz-Gargari, C. Lucas, “Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition”, In 2007 IEEE Congress on Evolutionary Computation, 2007, pp. 4661-4667.
  • [12] R. V. Rao, V. Patel, “An improved teaching-learning-based optimization algorithm for solving unconstrained optimization problems”, Scientia Iranica, vol. 20, no. 3, pp. 710–720, 2013.
  • [13] A. Borji, M. Hamidi, “A new approach to global optimization motivated by parliamentary political competitions”, International Journal of Innovative Computing, Information and Control, vol. 5 no. 6, pp. 1643-1653, 2009.
  • [14] Z. Cui, Z. Shi, J. Zeng, “Using social emotional optimization algorithm to direct orbits of chaotic systems”, International Conference on Swarm, Evolutionary, and Memetic Computing, Springer, 2010, pp. 389-395
  • [15] Y. Shi, “Brain storm optimization algorithm”, In International Conference in Swarm Intelligence, Springer Berlin Heidelberg, 2011, pp. 303-309.
  • [16] A. Daskin, S. Kais, “Group leaders optimization algorithm”, Molecular Physics, vol. 109, no. 5, pp. 761-772, 2011.
  • [17] S. Balochian, H. Baloochian, “Social mimic optimization algorithm and engineering applications”, Expert Systems with Applications, vol. 134, pp. 178-191, 2019.
  • [18] F. Ramezani, S. Lotfi, “Social-based algorithm (SBA)”, Applied Soft Computing, vol. 13, no. 5, pp. 2837-2856, 2013.
  • [19] E. V. Altay, B. Alatas, “Performance comparisons of socially inspired metaheuristic algorithms on unconstrained global optimization”, In Advances in Computer Communication and Computational Sciences, Springer, Singapore, 2019, pp. 163-175.
  • [20] J. Kennedy, R. C. Eberhart, “Particle swarm optimization”, IEEE International Conference on Neural Networks, Piscataway, NJ. Nov/Dec 1995, pp. 1942-1948.
  • [21] M. Dorigo, T. Stützle, “Ant colony optimization”, MIT Press, Cambridge, 2004.
  • [22] D. Karaboga, B. Basturk, “A powerful and efficient algorithm for numerical function optimization: Artificial Bee Colony (ABC) algorithm”, J. Global Optim., vol. 39, pp. 459-171, 2007.
  • [23] A. Karcı, “A new metaheuristic algorithm based chemical process: Atom Algorithm”, 1st International Eurasian Conference on Mathematical Sciences and Applications, 2012, pp. 03-07.
  • [24] B. Alataş B., “ACROA: Artificial chemical reaction optimization algorithm for global optimization”, Expert Systems with Applications, vol. 38, no.10, pp. 13170–13180, 2011.
  • [25] D. E. Goldberg, “Genetic algorithm in search: optimization and machine learning”, Kluwer Academic Publishers, Boston, USA, 1989.
  • [26] K. M. Passino, “Biomimicry of bacterial foraging for distributed optimization and control”, IEEE control systems magazine, vol. 22, no. 3, pp. 52–67, 2002.
  • [27] R. Storn, K. Price, “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces”, Journal of global optimization, vol. 11, no. 4, pp. 341–359, 1997.
  • [28] S. A. Salem, “BOA: A novel optimization algorithm”, IEEE 2012 International Conference on Engineering and Technology (ICET), 2012, pp. 1-5.
  • [29] S. Mirjalili, “SCA: A Sine cosine algorithm for solving optimization problems”, Knowledge-Based Systems, vol. 96, pp. 120-133, 2016.
  • [30] A. Karci, B. Alatas, “Thinking capability of saplings growing up algorithm”, In: Intelligent data engineering and automated learning—IDEAL 2006, Lecture notes in computer Science, Springer, Berlin, vol. 4224, pp. 386–393, 2006.
  • [31] F. Merrikh-Bayat, “The runner-root algorithm: a metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature”, Applied Soft Computing, vol. 33, pp. 292–303, 2015.
  • [32] Y. Zhou, Y. Wang, X. Chen, L. Zhang, K. Wu, “A Novel path planning algorithm based on plant growth mechanism”, Soft Computing, vol. 21 no. 2, pp. 435-445, 2017.
  • [33] Y. Labbi, D. B. Attous, H. A. Gabbar, B. Mahdad, A. Zidan, “A new rooted tree optimization algorithm for economic dispatch with valve-point effect”, International Journal of Electrical Power & Energy Systems, vol. 79, pp. 298–311, 2016.
  • [34] A. A. Kamarudin, Z. A. Othman, H. M. Sarim, “Water flow algorithm decision support tool for travelling salesman problem”, In Proceedings of the International Conference on Applied Science and Technology 2016 (ICAST’16), AIP Publishing, 2016, vol. 1761, no. 1.
  • [35] A. Sadollah, H. Eskandar, A. Bahreininejad, J. H. Kim, “Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems”, Applied Soft Computing, vol. 30, pp. 58–71, 2015.
  • [36] A. Kaveh, T. Bakhshpoori, “Water evaporation optimization: A novel physically inspired optimization algorithm”, Computers & Structures, vol. 167, pp. 69-85, 2016.
  • [37] A. Ibrahim, S. Rahnamayan, M. V. Martin, “Simulated raindrop algorithm for global optimization”, IEEE 27th Canadian Conference Electrical and Computer Engineering (CCECE), 2014, pp. 1-8.
  • [38] A. H. Kashan, “League Championship Algorithm: A new algorithm for numerical function optimization”, In 2009 international conference of soft computing and pattern recognition, 2009, pp. 43-48.
  • [39] E. Khaji, “Soccer League Optimization: A heuristic Algorithm Inspired by the Football System in European Countries”, 2014, arXiv preprint arXiv:1406.4462.
  • [40] H. D. Purnomo, H. M. Wee, “Soccer game optimization: an innovative integration of evolutionary algorithm and swarm intelligence algorithm”, Meta-Heuristics optimization algorithms in engineering, business, economics, and finance. IGI Global, Pennsylvania, pp. 386-420, 2013.
  • [41] N. Moosavian and B. K. Roodsari, “Soccer league competition algorithm, a new method for solving systems of nonlinear equations”, International Journal of Intelligence Science, vol. 4, no. 1, pp. 7, 2013.
  • [42] E. Osaba, F. Diaz, E. Onieva, “A novel meta-heuristic based on soccer concepts to solve routing problems”, In Proceedings of the 15th annual conference companion on Genetic and evolutionary computation, ACM, pp. 1743-1744, 2013.
  • [43] Z. W. Geem, J. H. Kim, G. V. Loganathan, “A new heuristic optimization algorithm: harmony search”, Simulation, vol. 76, no. 2, pp. 60-68, 2001.
  • [44] S. M. Ashrafi, A. B. Dariane, “A novel and effective algorithm for numerical optimization: melody search (MS)”, In 2011 11th international conference on hybrid intelligent systems (HIS), IEEE, 2011, pp. 109-114.
  • [45] R. A. Mora-Gutiérrez, J. Ramírez-Rodríguez, E. A. Rincón-García, A. Ponsich, O. Herrera, & P. Lara-Velázquez, “Adaptation of the musical composition method for solving constrained optimization problems”, Soft Computing, vol. 18, no. 10, pp. 1931-1948, 2014.
  • [46] E. V. Altay, B. Alatas, “Randomness as source for inspiring solution search methods: Music based approaches”, Physica A: Statistical Mechanics and its Applications, vol. 537, no. 122650, 2020.
  • [47] E. V. Altay, B. Alatas, “Music based metaheuristic methods for constrained optimization”, In 2018 6th International Symposium on Digital Forensic and Security (ISDFS), IEEE, 2018, pp. 1-6.
  • [48] Y. C. Ho, D. L. Pepyne, “Simple explanation of the no-free-lunch theorem and its implications”, Journal of optimization theory and applications, vol. 115, no. 3, pp. 549-570, 2002.
  • [49] S. Li, H. Chen, M. Wang, A. A. Heidari, S. Mirjalili, “Slime mould algorithm: A new method for stochastic optimization”, Future Generation Computer Systems, vol. 111, pp. 300-323, 2020.
  • [50] S. Mirjalili, A. Lewis, “The whale optimization algorithm”, Advances in engineering software, vol. 95, pp. 51-67, 2016.
  • [51] S. Mirjalili, S. M. Mirjalili, A. Lewis, “Grey wolf optimizer”, Advances in engineering software, vol. 69, pp. 46-61, 2014.
  • [52] A. A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, H. Chen, “Harris hawks optimization: Algorithm and applications”, Future generation computer systems, vol. 97, pp. 849-872, 2019.
  • [53] F. A. Hashim, K. Hussain, E. H. Houssein, M. S. Mabrouk, W. Al-Atabany, “Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems”, Applied Intelligence, vol. 51, no. 3, pp. 1531-1551, 2021.
  • [54] A.W. Mohamed, A.A. Hadi, A. K. Mohamed, N.H. Awad, “Evaluating the performance of adaptive gainingsharing knowledge based algorithm on CEC 2020 benchmark problems”, In: 2020 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2020, pp. 1–8.
  • [55] O. Altay, “Chaotic slime mould optimization algorithm for global optimization”, Artificial Intelligence Review, pp. 1-62, 2021.
There are 54 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Elif Varol Altay This is me 0000-0001-8087-2754

Osman Altay This is me 0000-0003-3989-2432

Publication Date December 31, 2021
Submission Date October 8, 2021
Published in Issue Year 2021 Volume: 12 Issue: 5

Cite

IEEE E. Varol Altay and O. Altay, “Güncel metasezgisel optimizasyon algoritmalarının CEC2020 test fonksiyonları ile karşılaştırılması”, DUJE, vol. 12, no. 5, pp. 729–741, 2021, doi: 10.24012/dumf.1051338.

Cited By

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