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Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X)

Yıl 2020, Cilt: 8 Sayı: 3, 1771 - 1793, 31.07.2020

Serdar Özyön Celal Yaşar Hasan Temurtaş

Öz

Optimizasyon problemlerinin çözümünde kullanılan sezgisel algoritmalar farklı tasarımlarından dolayı, her problem için en iyi sonuca kararlı bir şekilde ulaşamayabilir. Bu nedenle literatürde bu sezgisel algoritmalara bazı geliştirici yapıların eklendiği çalışmalara sıklıkla rastlanmaktadır. Benzer şekilde bu çalışmada sezgisel algoritmalardan biri olan yerçekimsel arama algoritmasının (GSA) performansının geliştirilmesine çalışılmıştır. Çalışmada algoritmanın yakınsama hızının artırılması amaçlanarak GSA’ya bazı kaotik haritalama metotları entegre edilerek, yeni bir algoritma ortaya çıkartılmıştır. Bu yeni algoritmaya Kaos tabanlı yerçekimsel arama algoritması (CbGSA-X) adı verilmiştir. Çalışmada CbGSA-X’deki ilk popülasyondaki ajanlar oluşturulurken ilk ajan arama uzayında rastgele konumlandırılırken, diğer ajanlar ise bu ajana bağlı olarak 5 farklı (X=1, 2, 3, 4, 5) kaotik haritalama yöntemi kullanılarak konumlandırılmıştır. Her haritalama metodu için performans değerlendirilmesi yapılabilmesi için literatürde GSA ile çözümü yer alan test fonksiyonları ele alınmış ve çözümü yapılarak sonuçlar değerlendirilmiştir.

Anahtar Kelimeler

Optimizasyon Sezgisel algoritmalar Yerçekimsel arama algoritması Kaotik haritalar Test fonksiyonları

Destekleyen Kurum

Kütahya Dumlupınar Üniversitesi

Proje Numarası

2016-65

Teşekkür

Bu çalışma Kütahya Dumlupınar Üniversitesi Bilimsel Araştırma Projeleri (BAP) komisyonu tarafından desteklenmiştir (Proje No: 2016-65).

Kaynakça

  • [1] E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, “GSA: A gravitational search algorithm,” Information Sciences, c. 179, s. 13, ss. 2232-2248, 2009.
  • [2] U. Güvenç, F. Katırcıoğlu, “En İyi Ajana Özel Davranış: Geliştirilmiş Yerçekimi Arama Algoritması,” El-Cezeri Jounal of Science and Engineering, c. 3, s. 1, ss. 143-153, 2016.
  • [3] A. Kaveh, VR. Mahdavi, “Colliding bodies optimization: A novel meta‐heuristic method,” Computers and Structures, c. 139, ss. 18-27, 2014.
  • [4] OK. Erol, I. Eksin, “A new optimization method: Big Bang–Big Crunch,” Advances in Engineering Software, c. 37, s. 2, ss. 106-111, 2006.
  • [5] A. Hatamlou, “Black hole: A new heuristic optimization approach for data clustering,” Information Sciences, c. 222, ss. 175-184, 2013.
  • [6] S. Kirkpatrick, CD. Gelatt, MP. Vecchi, “Optimisation by simulated annealing,” Science, c. 220, ss. 671-680, 1983.
  • [7] DE. Goldberg, “Genetic Algorithms in Search, Optimization, and Machine Learning,” Addison-Wesley Publishing Company, Inc.,1989.
  • [8] R. Storn, K. Price, “Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, c. 11, ss. 341-359, 1997.
  • [9] Aİ. Çanakoğlu, AG. Yetgin, H. Temurtaş, M. Turan, “Induction motor parameter estimation using metaheuristic methods,” Turkish Journal of Electrical Engineering & Computer Sciences, c. 22, ss. 1177-1192, 2014.
  • [10] J. Kennedy, R. Eberhart, “Particle Swarm Optimization,” Proceedings of IEEE International Conference on Neural Networks, c. 4, ss. 1942-1948, 1995.
  • [11] ZW. Geem, JH. Kim, GV. Loganathan, “A new heuristic optimization algorithm: Harmony search,” Simulation, c. 76, s. 2, ss. 60-68, 2001.
  • [12] D. Karaboğa, B. Baştürk, “A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm,” Journal of Global Optimization, c. 39, s. 3, ss. 459-471, 2007.
  • [13] A. Kaveh, S. Talahatari, “A novel heuristic optimization method: Charged system search,” Acta Mechanica, c. 213, s. 3-4, ss. 267-289, 2010.
  • [14] YJ. Zheng, “Water wave optimization: A new nature-inspired metaheuristic,” Computers and Operations Research, c. 55, ss. 1-11, 2015.
  • [15] S. Mirjalili, A. Lewis, “The whale optimization algorithm,” Advances in Engineering Software, c. 95, ss. 51-67, 2016.
  • [16] R. Rajabioun, “Cuckoo optimization algorithm,” Applied Soft Computing, c. 11, ss. 5508-5518, 2011.
  • [17] A. Askarzadeh, “A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm,” Computers and Structures, c. 169, ss. 1-12, 2016.
  • [18] AH. Kashan, “A new metaheuristic for optimization: Optics inspired optimization (OIO),” Computers and Operations Research, c. 55, ss. 99-125, 2015.
  • [19] S. Mirjalili, SM. Mirjalili, A. Lewis, “Grey wolf optimizer,” Advances in Engineering Software, c. 69, ss. 46-61, 2014.
  • [20] B. Doğan, T. Ölmez, “A new metaheuristic for numerical function optimization: Vortex search algorithm,” Information Sciences, c. 293, ss. 125-145, 2015.
  • [21] S. Saremi, S. Mirjalili, A. Lewis, “Biogeography-based optimisation with chaos,” Neural Computing and Applications, c. 25, ss. 1077-1097, 2014.
  • [22] B. Nouhi, S. Talatahari, H. Kheiri, C. Cattani, “Chaotic charged system search with a feasible-based method for constraint optimization problems,” Mathematical Problems in Engineering, c. 2013, ss. 1-8, 2013.
  • [23] M. Mitic, N. Vukovic, M. Petrovic, Z. Miljkovic, “Chaotic fruit fly optimization algorithm,” Knowledge-Based Systems, c. 89, ss. 446-458, 2015.
  • [24] AH. Gandomi, XS. Yang, “Chaotic bat algorithm,” Journal of Computational Science, c. 5, ss. 224-232, 2014.
  • [25] GG. Wang, L. Guo, AH. Gandomi, GS. Hao, H. Wang, “Chaotic krill herd algorithm,” Information Sciences, c. 274, ss. 17-34, 2014.
  • [26] B. Alataş, “Chaotic harmony search algorithms,” Applied Mathematics and Computation, c. 216, ss. 2687-2699, 2016.
  • [27] B. Alataş, E. Akın, O. Bedri, “Chaos embedded particle swarm optimization algorithms,” Chaos, Solitons and Fractals, c. 40, s. 4, ss. 1715-1734, 2009.
  • [28] B. Alataş, “Chaotic bee colony algorithms for global numerical optimization,” Expert Systems with Applications, c. 37, s. 8, ss. 5682-5687, 2010.
  • [29] H. Peitgen, H. Jurgens, D. Saupe, “Chaos and Fractals: New frontiers of science.” Springer-Verlag, Berlin, 1992.
  • [30] A. Törn, A. Zilinskas, “Global Optimization.” Springer-Verlag, Berlin, 1989.
  • [31] X. Yao, Y. Liu, G. Lin, “Evolutionary programming made faster,” IEEE Transactions on Evolutionary Computation, c. 3, s. 2, ss. 82-102, 1999.
  • [32] VI. Arnold, A. Avez, “Ergodic problems in classical mechanics,” Benjamin, New York, 1968.
  • [33] F. Ge, L. Tan, Y. Wang, “Traffic modeling with Bernoulli Shift Map,” 2009 Fifth International Joint Conference on INC, IMS and IDC, Seoul, ss. 449-452, 2009.
  • [34] B. Stoyanov, “Pseudo-random bit generation algorithm based on Chebyshev Polynomial and Tinkerbell Map,” Applied Mathematical Sciences, c. 8, s. 125, ss. 6205-6210, 2014.
  • [35] B. Stoyanov, K. Kordov, “Novel image encryption scheme based on Chebyshev Polynomial and Duffing Map,” The Scientific World Journal, c. 2014, ss. 1-11, 2014.
  • [36] WM. Zheng, “Kneading plane of the circle map,” Chaos, Solitons and Fractals, c. 4, s. 7, ss. 1221-1233, 1994.
  • [37] R. Caponetto, L. Fortuna, S. Fazzino, MG. Xibilia, “Chaotic sequences to improve the performance of evolutionary algorithms,” IEEE Transactions on Evolutionary Computation, c. 7, s. 3, ss. 289-304, 2003.
  • [38] H. Lu, X. Wang, Z. Fei, M. Qiu, “The effects of using chaotic map on improving the performance of multiobjective evolutionary algorithms,” Mathematical Problems in Engineering, c. 2014, ss. 1-16, 2014.
  • [39] S. García, D. Molina, M. Lozano, F. Herrera, “A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization,” Journal of Heuristics, c. 15, ss. 617-644, 2009.

Chaos Based Gravitational Search Algorithms (CbGSA-X) for Benchmark Functions

Yıl 2020, Cilt: 8 Sayı: 3, 1771 - 1793, 31.07.2020

Serdar Özyön Celal Yaşar Hasan Temurtaş

Öz

The heuristic algorithms used in the solution of optimization problems may not be able to reach the best result for each problem resolutely due to their different designs. As a consequence, literature denotes some developing structures which are added to these heuristic algorithms. Within this scope, we evaluated the performance of gravitational search algorithm (GSA), which is one of the most prominent heuristic algorithm. In the study, aiming to increase the convergence speed of the algorithm, a new algorithm has been created by integrating some chaotic mapping methods to GSA. This new algorithm has been called chaos-based gravitational search algorithm (CbGSA-X). In order to make a performance evaluation for each mapping method, we utilized test functions which were solved with GSA in literature. Finally we introduce our solutions and performed evaluations.

Anahtar Kelimeler

Optimization Meta-heuristic algorithms Gravitational search algorithm Chaotic maps Benchmark functions

Proje Numarası

2016-65

Kaynakça

  • [1] E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, “GSA: A gravitational search algorithm,” Information Sciences, c. 179, s. 13, ss. 2232-2248, 2009.
  • [2] U. Güvenç, F. Katırcıoğlu, “En İyi Ajana Özel Davranış: Geliştirilmiş Yerçekimi Arama Algoritması,” El-Cezeri Jounal of Science and Engineering, c. 3, s. 1, ss. 143-153, 2016.
  • [3] A. Kaveh, VR. Mahdavi, “Colliding bodies optimization: A novel meta‐heuristic method,” Computers and Structures, c. 139, ss. 18-27, 2014.
  • [4] OK. Erol, I. Eksin, “A new optimization method: Big Bang–Big Crunch,” Advances in Engineering Software, c. 37, s. 2, ss. 106-111, 2006.
  • [5] A. Hatamlou, “Black hole: A new heuristic optimization approach for data clustering,” Information Sciences, c. 222, ss. 175-184, 2013.
  • [6] S. Kirkpatrick, CD. Gelatt, MP. Vecchi, “Optimisation by simulated annealing,” Science, c. 220, ss. 671-680, 1983.
  • [7] DE. Goldberg, “Genetic Algorithms in Search, Optimization, and Machine Learning,” Addison-Wesley Publishing Company, Inc.,1989.
  • [8] R. Storn, K. Price, “Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, c. 11, ss. 341-359, 1997.
  • [9] Aİ. Çanakoğlu, AG. Yetgin, H. Temurtaş, M. Turan, “Induction motor parameter estimation using metaheuristic methods,” Turkish Journal of Electrical Engineering & Computer Sciences, c. 22, ss. 1177-1192, 2014.
  • [10] J. Kennedy, R. Eberhart, “Particle Swarm Optimization,” Proceedings of IEEE International Conference on Neural Networks, c. 4, ss. 1942-1948, 1995.
  • [11] ZW. Geem, JH. Kim, GV. Loganathan, “A new heuristic optimization algorithm: Harmony search,” Simulation, c. 76, s. 2, ss. 60-68, 2001.
  • [12] D. Karaboğa, B. Baştürk, “A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm,” Journal of Global Optimization, c. 39, s. 3, ss. 459-471, 2007.
  • [13] A. Kaveh, S. Talahatari, “A novel heuristic optimization method: Charged system search,” Acta Mechanica, c. 213, s. 3-4, ss. 267-289, 2010.
  • [14] YJ. Zheng, “Water wave optimization: A new nature-inspired metaheuristic,” Computers and Operations Research, c. 55, ss. 1-11, 2015.
  • [15] S. Mirjalili, A. Lewis, “The whale optimization algorithm,” Advances in Engineering Software, c. 95, ss. 51-67, 2016.
  • [16] R. Rajabioun, “Cuckoo optimization algorithm,” Applied Soft Computing, c. 11, ss. 5508-5518, 2011.
  • [17] A. Askarzadeh, “A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm,” Computers and Structures, c. 169, ss. 1-12, 2016.
  • [18] AH. Kashan, “A new metaheuristic for optimization: Optics inspired optimization (OIO),” Computers and Operations Research, c. 55, ss. 99-125, 2015.
  • [19] S. Mirjalili, SM. Mirjalili, A. Lewis, “Grey wolf optimizer,” Advances in Engineering Software, c. 69, ss. 46-61, 2014.
  • [20] B. Doğan, T. Ölmez, “A new metaheuristic for numerical function optimization: Vortex search algorithm,” Information Sciences, c. 293, ss. 125-145, 2015.
  • [21] S. Saremi, S. Mirjalili, A. Lewis, “Biogeography-based optimisation with chaos,” Neural Computing and Applications, c. 25, ss. 1077-1097, 2014.
  • [22] B. Nouhi, S. Talatahari, H. Kheiri, C. Cattani, “Chaotic charged system search with a feasible-based method for constraint optimization problems,” Mathematical Problems in Engineering, c. 2013, ss. 1-8, 2013.
  • [23] M. Mitic, N. Vukovic, M. Petrovic, Z. Miljkovic, “Chaotic fruit fly optimization algorithm,” Knowledge-Based Systems, c. 89, ss. 446-458, 2015.
  • [24] AH. Gandomi, XS. Yang, “Chaotic bat algorithm,” Journal of Computational Science, c. 5, ss. 224-232, 2014.
  • [25] GG. Wang, L. Guo, AH. Gandomi, GS. Hao, H. Wang, “Chaotic krill herd algorithm,” Information Sciences, c. 274, ss. 17-34, 2014.
  • [26] B. Alataş, “Chaotic harmony search algorithms,” Applied Mathematics and Computation, c. 216, ss. 2687-2699, 2016.
  • [27] B. Alataş, E. Akın, O. Bedri, “Chaos embedded particle swarm optimization algorithms,” Chaos, Solitons and Fractals, c. 40, s. 4, ss. 1715-1734, 2009.
  • [28] B. Alataş, “Chaotic bee colony algorithms for global numerical optimization,” Expert Systems with Applications, c. 37, s. 8, ss. 5682-5687, 2010.
  • [29] H. Peitgen, H. Jurgens, D. Saupe, “Chaos and Fractals: New frontiers of science.” Springer-Verlag, Berlin, 1992.
  • [30] A. Törn, A. Zilinskas, “Global Optimization.” Springer-Verlag, Berlin, 1989.
  • [31] X. Yao, Y. Liu, G. Lin, “Evolutionary programming made faster,” IEEE Transactions on Evolutionary Computation, c. 3, s. 2, ss. 82-102, 1999.
  • [32] VI. Arnold, A. Avez, “Ergodic problems in classical mechanics,” Benjamin, New York, 1968.
  • [33] F. Ge, L. Tan, Y. Wang, “Traffic modeling with Bernoulli Shift Map,” 2009 Fifth International Joint Conference on INC, IMS and IDC, Seoul, ss. 449-452, 2009.
  • [34] B. Stoyanov, “Pseudo-random bit generation algorithm based on Chebyshev Polynomial and Tinkerbell Map,” Applied Mathematical Sciences, c. 8, s. 125, ss. 6205-6210, 2014.
  • [35] B. Stoyanov, K. Kordov, “Novel image encryption scheme based on Chebyshev Polynomial and Duffing Map,” The Scientific World Journal, c. 2014, ss. 1-11, 2014.
  • [36] WM. Zheng, “Kneading plane of the circle map,” Chaos, Solitons and Fractals, c. 4, s. 7, ss. 1221-1233, 1994.
  • [37] R. Caponetto, L. Fortuna, S. Fazzino, MG. Xibilia, “Chaotic sequences to improve the performance of evolutionary algorithms,” IEEE Transactions on Evolutionary Computation, c. 7, s. 3, ss. 289-304, 2003.
  • [38] H. Lu, X. Wang, Z. Fei, M. Qiu, “The effects of using chaotic map on improving the performance of multiobjective evolutionary algorithms,” Mathematical Problems in Engineering, c. 2014, ss. 1-16, 2014.
  • [39] S. García, D. Molina, M. Lozano, F. Herrera, “A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization,” Journal of Heuristics, c. 15, ss. 617-644, 2009.
Toplam 39 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Serdar Özyön 0000-0002-4469-3908

Celal Yaşar

Hasan Temurtaş 0000-0001-6738-3024

Proje Numarası 2016-65
Yayımlanma Tarihi 31 Temmuz 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 3

Kaynak Göster

APA Özyön, S., Yaşar, C., & Temurtaş, H. (2020). Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X). Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, 8(3), 1771-1793.
AMA Özyön S, Yaşar C, Temurtaş H. Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X). DÜBİTED. Temmuz 2020;8(3):1771-1793.
Chicago Özyön, Serdar, Celal Yaşar, ve Hasan Temurtaş. “Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X)”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi 8, sy. 3 (Temmuz 2020): 1771-93.
EndNote Özyön S, Yaşar C, Temurtaş H (01 Temmuz 2020) Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X). Düzce Üniversitesi Bilim ve Teknoloji Dergisi 8 3 1771–1793.
IEEE S. Özyön, C. Yaşar, ve H. Temurtaş, “Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X)”, DÜBİTED, c. 8, sy. 3, ss. 1771–1793, 2020.
ISNAD Özyön, Serdar vd. “Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X)”. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 8/3 (Temmuz 2020), 1771-1793.
JAMA Özyön S, Yaşar C, Temurtaş H. Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X). DÜBİTED. 2020;8:1771–1793.
MLA Özyön, Serdar vd. “Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X)”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, c. 8, sy. 3, 2020, ss. 1771-93.
Vancouver Özyön S, Yaşar C, Temurtaş H. Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X). DÜBİTED. 2020;8(3):1771-93.