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Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması

Yıl 2020, Cilt: 8 Sayı: 4, 2566 - 2582, 29.10.2020

Fetiye Sultan Özpehlivan Ay Pakize Erdoğmuş

https://doi.org/10.29130/dubited.765012

Öz

Temel anlamda optimizasyon, bir veya birden fazla problemin belirli koşullar altındaki en iyi çözümlerini bulma işlemidir. Günümüzde bu problemlerin çözümü için klasik yöntemler ve sezgisel yöntemler kullanılmaktadır. Sezgisel yöntemlerden biri olan Rüzgar Güdümlü Optimizasyon algoritması, rüzgarın atmosfer içerisindeki hareketini temel alarak atmosferik dinamik eşitlikten yararlanan tek amaçlı optimizasyon problemlerine çözüm arayan bir algoritmadır.

Bu çalışmada çok-amaçlı optimizasyon problemlerinin çözümü için Rüzgar Güdümlü Optimizasyon algoritması yeniden düzenlenmiştir. Çok-amaçlı optimizasyon problemlerinde elde edilen sonuçların gerçek sonuçlara ne kadar yakınsadığı ve bu sonuçların ne kadar çeşitli olduğu kullanılan yöntemlerin performansı hakkında bilgi vermektedir. Baskın olmayan sıralama, ağırlıklı toplam, normal sınır kesişimi gibi metotlar çok-amaçlı optimizasyon problemlerinde sıklıkla kullanılan yaklaşımlardır. Bu yaklaşımlardan bazıları çeşitlilik açısından ön plana çıkarken bazılarının ise en iyi sonuca daha iyi yakınsadığı gözlenmiştir. Bu çalışmanın temel amacı elde edilen çözümleri hem çeşitlilik hem de yakınsama açısından en iyi hale getirmektir.

Bu amaç kapsamında baskın olmayan sıralama ve adaptif ızgara yaklaşımları bir arada kullanılarak yeni bir hibrit yaklaşım geliştirilmiştir. Daha iyi bir yakınsama için baskın olmayan sıralama, çeşitlilik için adaptif ızgara yaklaşımı bir arada kullanılmıştır. Geliştirilen bu hibrit yaklaşım test problemleri ve doğrusal olmayan denklem sistemlerinde test edilerek sonuçları literatürde iyi bilinen Baskın Olmayan Sıralamalı Genetik Algoritma (NSGA-II) ve Çok-Amaçlı Parçacık Sürü Optimizasyonu (MOPSO) algoritmaları ile karşılaştırılmıştır. Deneysel sonuçlar incelendiğinde çeşitlilik ve yakınsama performansı açısından geliştirilen hibrit yaklaşımın kabul edilebilir olduğu gözlenmiştir.

Anahtar Kelimeler

Optimizasyon Çok-Amaçlı Optimizasyon Rüzgar Güdümlü Optimizasyon Algoritması

Kaynakça

  • [1] P. Erdoğmuş, “Doğadan esinlenen optimizasyon algoritmaları ve optimizasyon algoritmalarının optimizasyonu,” Düzce Üniversitesi Bilim and Teknoloji Dergisi, ss. 293-304, 2016.
  • [2] J. H. Holland, “Control and artificial intelligence,” in Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Cambridge: MIT Press, 1992.
  • [3] J. Kennedy and R. Eberhar, “Particle swarm optimization,” presented at Neural Networks Proceedings, IEEE International Conference, Australia, 1995.
  • [4] M. Dorigo, M. Birattari and T. Stutzle, “Ant colony optimization,” IEEE Computational Intelligence Magazine, vol. 1, no. 4, pp. 28-39, 2006.
  • [5] M. Laumanns, L. Thiele, K. Deb and E. Zitzler, “Combining convergence and diversity in evolutionary multiobjective optimization,” Evolutionary Computation, vol. 10, no. 3, pp. 263-282, 2002.
  • [6] N. Srinivas and K. Deb, “Muiltiobjective optimization using nondominated sorting in genetic algorithms,” Evolutionary Computation, vol. 2, no. 3, pp. 221-248, 1994.
  • [7] S. Rostami and A. Shenfield, “A multi-tier adaptive grid algorithm for the evolutionary multi-objective optimisation of complex problems,” Soft Computing, vol. 21, no. 17, pp. 4963–4979, 2017.
  • [8] D. E. Goldberg, “Genetic algorithms and classifier systems,” in Genetic Algorithms in Search, Optimization and Machine Learning, USA: Addison-Wesley Publishing Company, 1989, ch. 3, pp. 60-61.
  • [9] M. F. P. Costa, A. M. A. Rocha and E. M. Fernandes, “Combining nondominance, objective-order and spread metric to extend Firefly Algorithm to multi-objective optimization,” presented at International Conference On Evolutionary Multi-Criterion Optimization, Guimares, Portugal, 2015.
  • [10] C. M. Fonseca and P. J. Fleming, “Genetic Algorithms for multiobjective optimization: Formulation discussion and generalization,” ICGA, vol. 93, 1993.
  • [11] J. Horn, N. Nafpliotis and D. Goldberg, “A niched pareto genetic algorithm for multiobjective optimization,” presented at IEEE World Congress on Computational Intelligence, Orlandı, USA, 1994.
  • [12] K. Deb, S. Agrawal, A. Pratap and T. Meyarivan et al. "A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II.,” presented at International Conference On Parallel Problem Solving From Nature, Berlin, Germany, 2000.
  • [13] S. Mirjalili, S. M. Mirjalili and A. Lewis, “Grey Wolf Optimizer,” Advances in Engineering Software, vol. 69, pp. 46-61, 2014.
  • [14] S. Mirjalili, S.. Saremi, S. M. Mirjalili and L. D. S. Coelho, “Multi-Objective Grey Wolf Optimizer: A novel algorithm for multi-criterion optimization,” Expert Systems with Applications, vol. 47, pp. 106-119, 2016.
  • [15] S. Saremi, no. Mirjalili and A. Lewis, “Grasshopper Optimization Algorithm: Theory and application,” Advances in Engineering Software, vol. 105, pp. 30-47, 2017.
  • [16] S. Z. Mirjalili, . S. Mirjalili, S. Saremi, H. Faris and I. Aljarah, “Grasshopper Optimization Algorithm for multi-objective optimization problems,” Applied Intelligence, vol. 48, pp. 805-820, 2018.
  • [17] S. Y. Zeng , L. S. Kang and L. X. Ding, “An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints,” Evolutionary Computation, vol. 12, no. 1, pp. 77-98, 2004.
  • [18] M. J. Reddy and D. Kumar, “An efficient multi-objective optimization algorithm based on swarm intelligence for engineering design,” Engineering Optimization, vol. 39, no. 1, pp. 49-68, 2007.
  • [19] O. Jadaan and C. R. Rao, “Non-dominated ranked genetic algorithm for solving multi-objective optimization problems: NRGA,” Journal of Theoretical and Applied Information Technology, pp. 60-67, 2008.
  • [20] H. Ghiasi, D. Pasini and L. Lessard, “A non-dominated sorting hybrid algorithm for multi-objective optimization of engineering problems,” Engineering Optimization, vol. 43, pp. 39-59, 2011.
  • [21] H. Nobahari, M. Nikusokhan and P. Siarry, “A multi-objective Gravitational Search Algorithm based on non-dominated sorting,” International Journal of Swarm Intelligence Research, vol. 3, no. 3, pp. 32-49, 2012.
  • [22] S. Sanz, A. Figueras, Á. Sánchez and L. Prieto, “Effective multi-objective optimization with the Coral Reefs Optimization Algorithm,” Engineering Optimization, vol. 48, pp. 966-984, 2015.
  • [23] Z. Bayraktar and M. Kömürcü, “Multiobjective Adaptive Wind Driven Optimization,” presented at The 8th International Conference On Computational Intelligence (IJCCI 2016), Porto, Portugal, 2016.
  • [24] Z. Bayraktar, M. Komurcu and D. H. Werner, “Wind Driven Optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetics,” Antennas and Propagation Society International Symposium (APSURSI), Toronto, Canada, 2010.
  • [25] Z. Bayraktar and M. Komurcu, “Adaptive Wind Driven Optimization,” presented at BICT'15 Proceedings of The 9th EAI International Conference On Bio-Inspired Information and Communications Technologies, New York City, USA, 2015.
  • [26] A. Dias and J. D. Vasconcelos, “Multiobjective Genetic Algorithms applied to solve optimization problems,” IEEE Transactions On Magnetics, vol. 38, no. 2, pp. 1133-1136, 2002.
  • [27] K. Mahesh, P. Nallagownden and I. Elamvazuthi, “Advanced Pareto Front Non-Dominated Sorting Multi-Objective Particle Swarm Optimization for optimal placement and sizing of distributed generation,” Energies, vol. 9, no. 12, 2016.
  • [28] K. E. Parsopoulos and M. N. Vrahatis, “Particle Swarm Optimization method in multiobjective problems,” presented at SAC '02 Proceedings of The 2002 ACM Symposium On Applied Computing, Madrid, Spain, 2002.
  • [29] C. M. Fonseca and P. J. Fleming, “Multiobjective optimization and multiple constraint handling with evolutionary algorithms-part II: Application example,” IEEE Trans. Syst., Man, Cybern. A, vol. 28, pp. 38-47, 1998.
  • [30] F. Kursawe, “A variant of evolution strategies for vector optimization,” presented at PPSN I Proceedings of The 1st Workshop On Parallel Problem Solving From Nature, Berlin, Germany, 1990.
  • [31] C. Poloni, “Hybrid GA for Multiobjective Aerodynamic Shape Optimization,” presented at Genetic Algorithms in Engineering and Computer Science, Japan, 1997.
  • [32] J. D. Schaffer, “Multiple objective optimization with Vector Evaluated Genetic Algorithms,” in Proceedings of The First International Conference On Genetic Algorithms, USA, 1987, pp. 93-100.
  • [33] E. Zitzler, K. Deb and L. Thiele, “Comparison of multiobjective evolutionary algorithms: Empirical results,” Evolutionary Computation, vol. 8, no. 2, 2000.
  • [34] P. Erdoğmuş, “Parçacık Sürü Optimizasyonu ile doğrusal olmayan denklem köklerinin bulunması ve Genetik Algoritma ile mukayesesi,” İleri Teknoloji Bilimleri Dergisi, c. 5, s. 1, 2016.
  • [35] S. Qin, no. Zeng, W. Dong and X. Li, “noınlinear equation system solved by many-objective hype,” presented at IEEE Congress On Evolutionary Computation (CEC), Sendai, Japan, 2015.
  • [36] W. Song, Y. Wang, X. Li and Z. Cai, “Locating multiple optimal solutions of nonlinear equation systems based on multobjective optimization,” IEEE Transactions On Evolutionary Computation, vol. 19, no. 3, pp. 414-431, 2015.
  • [37] C. Brezinski, “Projection methods for systems of equations,” North-Holland, vol. 7, 1997.
  • [38] J. Denis, “On newton's method and nonlinear simultaneous replacements,” SIAM J. Numer. Anal., vol. 4, pp. 103-108, 1967.
  • [39] J. Denis, “On newton like methods,” Numer. Math., vol. 11, pp. 324-330, 1968.
  • [40] J. Denis, “On the convergence of broyden's method for nonlinear systems of equations,” Math. Comput., vol. 25, pp. 559-567, 1971.
  • [41] J. Denis and H. Wolkowicz, “Least change secant methods sizing and shifting,” SIAM J. Numer. Anal., vol. 30, pp. 1291-1314, 1993.
  • [42] J. Denis, M. El Alem and K. Williamson, “A trust-region algorithm for least-squares solutions of nonlinear systems of equalities and inequalities,” SIAM J. Opt., vol. 9, pp. 291-315, 1999.
  • [43] J. Ortega and W. Rheinboldt, “On the convergence of Halley's method,” in Iterative Solution of Nonlinear Equations in Several Variables, New York, USA: Academic Press, 1970, ch. 2, pp. 179-179.
  • [44] A. Conn, N. Gould and P. Toint, “Trust-Region methods,” presented at SIAM, Philadelphia, USA, 2000.
  • [45] C. Broyden, “A class of methods for solving nonlinear simultaneous equations,” Math. Comput., vol. 19, pp. 577-593, 1965.
  • [46] C. Grosan and A. Abraham, “A new approach for solving nonlinear equations systems,” in IEEE Transactions On Systems, Man, and Cybernetics - Part A: Systems and Humans, vol. 38, pp. 698-714, 2008.
  • [47] P. Erdoğmuş, “A new solution approach for non-linear equation systems with Grey Wolf Optimizer,” Sakarya University Journal of Computer and Information Sciences, pp. 1-11, 2018.

A Hybrid Multi-Objective Wind Driven Optimization Algorithm

Yıl 2020, Cilt: 8 Sayı: 4, 2566 - 2582, 29.10.2020

Fetiye Sultan Özpehlivan Ay Pakize Erdoğmuş

https://doi.org/10.29130/dubited.765012

Öz

Basically, optimization is the process of finding the best solutions for one or more problems under certain conditions. Today, classical methods and heuristic methods are used to solve these problems. Wind Driven Optimization algorithm, which is one of the heuristic methods, is an algorithm that seeks solutions for single-objective optimization problems that benefit from atmospheric dynamic equality based on the movement of the wind in the atmosphere.

In this study, Wind Driven Optimization algorithm was rearranged to solve multi-objective optimization problems. In multi-objective optimization problems, the performance of the used method depends on how closely the results obtained converge to the actual results and how diverse these results are. Methods such as non-dominant sorting, weighted sum, normal boundary intersection are frequently used approaches in multi-objective optimization problems. While some of these approaches have more diverse to results, others have been observed to better converge. The main purpose of this study is to optimize the solutions obtained in terms of both diversity and convergence.

Within this scope, a new hybrid approach has been developed by using non-dominant sorting and adaptive grid approaches. Non-dominant sorting used for better convergence and adaptive grid approach is used for diversity. The developed hybrid approach has been tested in test problems and nonlinear equation systems. Results have been compared with Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO). When the experimental results were examined, it was observed that the hybrid approach developed in terms of diversity and convergence performance was acceptable.

Anahtar Kelimeler

Multi-objective Optimization Optimization Wind Driven Optimization Algorithm

Kaynakça

  • [1] P. Erdoğmuş, “Doğadan esinlenen optimizasyon algoritmaları ve optimizasyon algoritmalarının optimizasyonu,” Düzce Üniversitesi Bilim and Teknoloji Dergisi, ss. 293-304, 2016.
  • [2] J. H. Holland, “Control and artificial intelligence,” in Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Cambridge: MIT Press, 1992.
  • [3] J. Kennedy and R. Eberhar, “Particle swarm optimization,” presented at Neural Networks Proceedings, IEEE International Conference, Australia, 1995.
  • [4] M. Dorigo, M. Birattari and T. Stutzle, “Ant colony optimization,” IEEE Computational Intelligence Magazine, vol. 1, no. 4, pp. 28-39, 2006.
  • [5] M. Laumanns, L. Thiele, K. Deb and E. Zitzler, “Combining convergence and diversity in evolutionary multiobjective optimization,” Evolutionary Computation, vol. 10, no. 3, pp. 263-282, 2002.
  • [6] N. Srinivas and K. Deb, “Muiltiobjective optimization using nondominated sorting in genetic algorithms,” Evolutionary Computation, vol. 2, no. 3, pp. 221-248, 1994.
  • [7] S. Rostami and A. Shenfield, “A multi-tier adaptive grid algorithm for the evolutionary multi-objective optimisation of complex problems,” Soft Computing, vol. 21, no. 17, pp. 4963–4979, 2017.
  • [8] D. E. Goldberg, “Genetic algorithms and classifier systems,” in Genetic Algorithms in Search, Optimization and Machine Learning, USA: Addison-Wesley Publishing Company, 1989, ch. 3, pp. 60-61.
  • [9] M. F. P. Costa, A. M. A. Rocha and E. M. Fernandes, “Combining nondominance, objective-order and spread metric to extend Firefly Algorithm to multi-objective optimization,” presented at International Conference On Evolutionary Multi-Criterion Optimization, Guimares, Portugal, 2015.
  • [10] C. M. Fonseca and P. J. Fleming, “Genetic Algorithms for multiobjective optimization: Formulation discussion and generalization,” ICGA, vol. 93, 1993.
  • [11] J. Horn, N. Nafpliotis and D. Goldberg, “A niched pareto genetic algorithm for multiobjective optimization,” presented at IEEE World Congress on Computational Intelligence, Orlandı, USA, 1994.
  • [12] K. Deb, S. Agrawal, A. Pratap and T. Meyarivan et al. "A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II.,” presented at International Conference On Parallel Problem Solving From Nature, Berlin, Germany, 2000.
  • [13] S. Mirjalili, S. M. Mirjalili and A. Lewis, “Grey Wolf Optimizer,” Advances in Engineering Software, vol. 69, pp. 46-61, 2014.
  • [14] S. Mirjalili, S.. Saremi, S. M. Mirjalili and L. D. S. Coelho, “Multi-Objective Grey Wolf Optimizer: A novel algorithm for multi-criterion optimization,” Expert Systems with Applications, vol. 47, pp. 106-119, 2016.
  • [15] S. Saremi, no. Mirjalili and A. Lewis, “Grasshopper Optimization Algorithm: Theory and application,” Advances in Engineering Software, vol. 105, pp. 30-47, 2017.
  • [16] S. Z. Mirjalili, . S. Mirjalili, S. Saremi, H. Faris and I. Aljarah, “Grasshopper Optimization Algorithm for multi-objective optimization problems,” Applied Intelligence, vol. 48, pp. 805-820, 2018.
  • [17] S. Y. Zeng , L. S. Kang and L. X. Ding, “An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints,” Evolutionary Computation, vol. 12, no. 1, pp. 77-98, 2004.
  • [18] M. J. Reddy and D. Kumar, “An efficient multi-objective optimization algorithm based on swarm intelligence for engineering design,” Engineering Optimization, vol. 39, no. 1, pp. 49-68, 2007.
  • [19] O. Jadaan and C. R. Rao, “Non-dominated ranked genetic algorithm for solving multi-objective optimization problems: NRGA,” Journal of Theoretical and Applied Information Technology, pp. 60-67, 2008.
  • [20] H. Ghiasi, D. Pasini and L. Lessard, “A non-dominated sorting hybrid algorithm for multi-objective optimization of engineering problems,” Engineering Optimization, vol. 43, pp. 39-59, 2011.
  • [21] H. Nobahari, M. Nikusokhan and P. Siarry, “A multi-objective Gravitational Search Algorithm based on non-dominated sorting,” International Journal of Swarm Intelligence Research, vol. 3, no. 3, pp. 32-49, 2012.
  • [22] S. Sanz, A. Figueras, Á. Sánchez and L. Prieto, “Effective multi-objective optimization with the Coral Reefs Optimization Algorithm,” Engineering Optimization, vol. 48, pp. 966-984, 2015.
  • [23] Z. Bayraktar and M. Kömürcü, “Multiobjective Adaptive Wind Driven Optimization,” presented at The 8th International Conference On Computational Intelligence (IJCCI 2016), Porto, Portugal, 2016.
  • [24] Z. Bayraktar, M. Komurcu and D. H. Werner, “Wind Driven Optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetics,” Antennas and Propagation Society International Symposium (APSURSI), Toronto, Canada, 2010.
  • [25] Z. Bayraktar and M. Komurcu, “Adaptive Wind Driven Optimization,” presented at BICT'15 Proceedings of The 9th EAI International Conference On Bio-Inspired Information and Communications Technologies, New York City, USA, 2015.
  • [26] A. Dias and J. D. Vasconcelos, “Multiobjective Genetic Algorithms applied to solve optimization problems,” IEEE Transactions On Magnetics, vol. 38, no. 2, pp. 1133-1136, 2002.
  • [27] K. Mahesh, P. Nallagownden and I. Elamvazuthi, “Advanced Pareto Front Non-Dominated Sorting Multi-Objective Particle Swarm Optimization for optimal placement and sizing of distributed generation,” Energies, vol. 9, no. 12, 2016.
  • [28] K. E. Parsopoulos and M. N. Vrahatis, “Particle Swarm Optimization method in multiobjective problems,” presented at SAC '02 Proceedings of The 2002 ACM Symposium On Applied Computing, Madrid, Spain, 2002.
  • [29] C. M. Fonseca and P. J. Fleming, “Multiobjective optimization and multiple constraint handling with evolutionary algorithms-part II: Application example,” IEEE Trans. Syst., Man, Cybern. A, vol. 28, pp. 38-47, 1998.
  • [30] F. Kursawe, “A variant of evolution strategies for vector optimization,” presented at PPSN I Proceedings of The 1st Workshop On Parallel Problem Solving From Nature, Berlin, Germany, 1990.
  • [31] C. Poloni, “Hybrid GA for Multiobjective Aerodynamic Shape Optimization,” presented at Genetic Algorithms in Engineering and Computer Science, Japan, 1997.
  • [32] J. D. Schaffer, “Multiple objective optimization with Vector Evaluated Genetic Algorithms,” in Proceedings of The First International Conference On Genetic Algorithms, USA, 1987, pp. 93-100.
  • [33] E. Zitzler, K. Deb and L. Thiele, “Comparison of multiobjective evolutionary algorithms: Empirical results,” Evolutionary Computation, vol. 8, no. 2, 2000.
  • [34] P. Erdoğmuş, “Parçacık Sürü Optimizasyonu ile doğrusal olmayan denklem köklerinin bulunması ve Genetik Algoritma ile mukayesesi,” İleri Teknoloji Bilimleri Dergisi, c. 5, s. 1, 2016.
  • [35] S. Qin, no. Zeng, W. Dong and X. Li, “noınlinear equation system solved by many-objective hype,” presented at IEEE Congress On Evolutionary Computation (CEC), Sendai, Japan, 2015.
  • [36] W. Song, Y. Wang, X. Li and Z. Cai, “Locating multiple optimal solutions of nonlinear equation systems based on multobjective optimization,” IEEE Transactions On Evolutionary Computation, vol. 19, no. 3, pp. 414-431, 2015.
  • [37] C. Brezinski, “Projection methods for systems of equations,” North-Holland, vol. 7, 1997.
  • [38] J. Denis, “On newton's method and nonlinear simultaneous replacements,” SIAM J. Numer. Anal., vol. 4, pp. 103-108, 1967.
  • [39] J. Denis, “On newton like methods,” Numer. Math., vol. 11, pp. 324-330, 1968.
  • [40] J. Denis, “On the convergence of broyden's method for nonlinear systems of equations,” Math. Comput., vol. 25, pp. 559-567, 1971.
  • [41] J. Denis and H. Wolkowicz, “Least change secant methods sizing and shifting,” SIAM J. Numer. Anal., vol. 30, pp. 1291-1314, 1993.
  • [42] J. Denis, M. El Alem and K. Williamson, “A trust-region algorithm for least-squares solutions of nonlinear systems of equalities and inequalities,” SIAM J. Opt., vol. 9, pp. 291-315, 1999.
  • [43] J. Ortega and W. Rheinboldt, “On the convergence of Halley's method,” in Iterative Solution of Nonlinear Equations in Several Variables, New York, USA: Academic Press, 1970, ch. 2, pp. 179-179.
  • [44] A. Conn, N. Gould and P. Toint, “Trust-Region methods,” presented at SIAM, Philadelphia, USA, 2000.
  • [45] C. Broyden, “A class of methods for solving nonlinear simultaneous equations,” Math. Comput., vol. 19, pp. 577-593, 1965.
  • [46] C. Grosan and A. Abraham, “A new approach for solving nonlinear equations systems,” in IEEE Transactions On Systems, Man, and Cybernetics - Part A: Systems and Humans, vol. 38, pp. 698-714, 2008.
  • [47] P. Erdoğmuş, “A new solution approach for non-linear equation systems with Grey Wolf Optimizer,” Sakarya University Journal of Computer and Information Sciences, pp. 1-11, 2018.
Toplam 47 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Fetiye Sultan Özpehlivan Ay 0000-0002-3437-513X

Pakize Erdoğmuş 0000-0003-2172-5767

Yayımlanma Tarihi 29 Ekim 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 4

Kaynak Göster

APA Özpehlivan Ay, F. S., & Erdoğmuş, P. (2020). Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, 8(4), 2566-2582. https://doi.org/10.29130/dubited.765012
AMA Özpehlivan Ay FS, Erdoğmuş P. Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması. DÜBİTED. Ekim 2020;8(4):2566-2582. doi:10.29130/dubited.765012
Chicago Özpehlivan Ay, Fetiye Sultan, ve Pakize Erdoğmuş. “Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi 8, sy. 4 (Ekim 2020): 2566-82. https://doi.org/10.29130/dubited.765012.
EndNote Özpehlivan Ay FS, Erdoğmuş P (01 Ekim 2020) Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 8 4 2566–2582.
IEEE F. S. Özpehlivan Ay ve P. Erdoğmuş, “Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması”, DÜBİTED, c. 8, sy. 4, ss. 2566–2582, 2020, doi: 10.29130/dubited.765012.
ISNAD Özpehlivan Ay, Fetiye Sultan - Erdoğmuş, Pakize. “Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması”. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 8/4 (Ekim 2020), 2566-2582. https://doi.org/10.29130/dubited.765012.
JAMA Özpehlivan Ay FS, Erdoğmuş P. Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması. DÜBİTED. 2020;8:2566–2582.
MLA Özpehlivan Ay, Fetiye Sultan ve Pakize Erdoğmuş. “Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, c. 8, sy. 4, 2020, ss. 2566-82, doi:10.29130/dubited.765012.
Vancouver Özpehlivan Ay FS, Erdoğmuş P. Hibrit Çok-Amaçlı Rüzgar Güdümlü Optimizasyon Algoritması. DÜBİTED. 2020;8(4):2566-82.
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