Abstract
Hesaplama teknolojilerindeki hızlı gelişmelerle
orantılı olarak, optimizasyon problemlerinin çözümünde
evrimsel/sezgisel/metasezgisel algoritmalardan birçok alandaki uygulamalarda
sıklıkla faydalanılmaktadır. Günümüzde, yeni algoritmalar geliştirilmekte ve
mevcut algoritmalara yenilikler uygulanmaya devam edilmektedir. Bu çalışmada,
son zamanlarda geliştirilmiş olan metasezgisel algoritmalardan olan: Geri
İzleme Arama (BS), Gri Kurt Optimizasyon (GWO) ve Girdap Arama (VS)
algoritmalarına kaos tabanlı modifikasyonlar önerilmiş ve algoritmaların,
kıyaslamalarla detaylı analizleri gerçekleştirilmiştir. Önerilen yaklaşımlar,
algoritmaların çözümlerini geliştirmek için işlemlerinde kullandıkları bazı
rassal değişkenler yerine, kaos haritalarına dayanan yeni değişkenlerin
üretilmesi temeline dayanmaktadır. Bunun yanında, kaos tabanlı bu değişkenler kullanılarak algoritmaların optimizasyon
sürecinde kullandıkları yapısal işlemlerinde modifikasyonlar gerçekleştirilmektedir.
Algoritmaların performansları; istatistiksel ve yakınsama hızları açısından,
iki yönlü olarak analiz edilmektedir. Kaotik haritalara dayanan yaklaşımların,
orijinal algoritmalar üzerinde daha iyi veya en azından karşılaştırılabilir
sonuçlar ürettiği, gerçekleştirilen deneylerde gösterilmiştir.
References
- Alatas, B., Akin, E. and Ozer, A. B. (2009) Chaos embedded particle swarm optimization algorithms, Chaos, Solitons Fractals, 40(4), 1715-1734. doi: 10.1016/j.chaos.2007.09.063
- Civicioglu, P. (2013) Backtracking search optimization algorithm for numerical optimization problems, Applied Mathematics and Computation, 219(15), 8121-8144, 2013. doi: 10.1016/j.amc.2013.02.017
- Dogan, B. and Olmez, T. A. (2015) A new metaheuristic for numerical function optimization: vortex search algorithm, Information Sciences, 293, 125-145. doi: 10.1016/j.ins.2014.08.053
- Gandomi, A., Yang, X-S., Talatahari, S. and Alavi, A. (2013) Firefly algorithm with chaos, Communications in Nonlinear Science and Numerical Simulation., 18(1), 89-98. doi: 10.1016/j.cnsns.2012.06.009
- Geem, Z., Kim, J. and Loganathan, G. (2001) A new heuristic optimization algorithm: harmony search, Simulation, 76(2), 60-68. doi: 10.1177/003754970107600201
- Goldberg D. E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing, USA.
- Kellert, S. (1993) In the Wake of Chaos:Unpredictable Order in Dynamical Systems, University of Chicago Press, USA.
- Kennedy J. and Eberhart R. (1995) Particle swarm optimization, IEEE International Conference on Neural Networks, 1942-1948. doi:10.1109/ICNN.1995.488968
- Li, Y., Deng, S. and Xiao, D. (2011) A novel hash algorithm construction based on chaotic neural network, Neural Computing and Applications, 20(1), 133–141. doi: 10.1007/s00521-010-0432-2
- Li-Jiang, Y. and Tian-Lun, C. (2002) Application of chaos in genetic algorithms, Communications in Theoretical Physics, 38(2), 168. doi: 10.1088/0253-6102/38/2/168
- Liang, J. J., Suganthan, P. N. and Hernandez-Diaz, A. G. (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization, Zhengzhou University and Nanyang Technological University, 3-18. Technical report:201212
- Mirjalili, S., Mirjalili, S. M. and Lewis, A. (2014) Grey wolf optimizer, Advances in Engineering Software, 69, 46-61. doi: 10.1016/j.advengsoft.2013.12.007
- Pecora, L. and Carroll, T. (1990) Synchronization in chaotic system, Physical Review Letters, 64(8), 821-824. doi: 10.1103/PhysRevLett.64.821
- Saremi, S., Mirjalili, S. M. and Mirjalili, S. (2014) Chaotic krill herd optimization algorithm, Procedia Techno, 12, 180-185. doi: 10.1016/j.protcy.2013.12.473
- Schuster, H. G. and Just, W. (2006) Deterministic chaos: an introduction, John Wiley & Sons, Germany.
- Storn, R. and Price K. (1995) Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces, International Computer Science Institute, 1-12. Technical report:TR-95-012
- Wang, N., Liu, L. M. and L. L. Liu. (2001) Genetic algorithm in chaos, Or Transactions, 5(5), 1-10.
- Wang, L. and Zhong, Y. (2015) Cuckoo search algorithm with chaotic maps, Mathematical Problems in Engineering, 6(6), 546-554. doi: 10.1155/2015/715635
- Wang,, G.-G., Guo, L., Gandomi, A., Hao, G.-S. and Wang, H. (2014) Chaotic krill herd algorithm, Information Sciences, 274, 17-34. doi: 10.1016/j.ins.2014.02.123
- Wolpert, D. H. and Macready, W. G. (1997) No free lunch theorems for optimization, IEEE Transactions on Evolutionary Computation, 1(1), 67-82. doi: 10.1109/4235.585893
- Yang, X-S. (2010) Nature-inspired Metaheuristic Algorithms, Luniver Press, UK.
- Yang, X-S. and Deb, S. (2009) Cuckoo search via L´evy flights, Proceeding of World Congress on Nature Biologically Inspired Computing, 210-214, doi: 10.1109/NABIC.2009.5393690
- Yao, J. F., Mei, C., Peng, X. Q., Hu, Z. K. and Hu, J (2001) A new optimization approach-chaos genetic algorithm, Systems Engineering, 1, 1-5.
- Zaharie, D. (2003) Control of population diversity and adaptation in differential evolution algorithms, Mendel 9th International Conference on Soft Computing, Brno, 41-46.
- Zhenyu, G. Bo, Y. C. and Min, C. B. (2006) Self-adaptive chaos differential evolution, International Conference on Natural Computation, 972-975. doi: 10.1007/11881070_128
Abstract
Along with rapid developments in computational technologies,
evolutionary/heuristic/metaheuristic algorithms have frequently become used in
many applications to solve optimization problems. Nowadays, new algorithms are
being developed and improvements have been made to existing algorithms. In this
study, chaos-based modifications have been proposed for recently introduced metaheuristic
algorithms: Backtracking Search (BS), Grey Wolf Optimizer (GWO) and Vortex
Search (VS), and the algorithms have been analyzed by detailed comparisons. The
proposed approaches are based on generating new values through chaos maps,
rather than some random numbers normally used in the algorithms, to improve
their solutions. In addition, some modifications are performed to the
structural operations of the algorithms used in the optimization process by
taking advantage of chaos-based values. The performances of the algorithms are
evaluated by considering two metrics: convergence rates and statistical
results. Experiments demonstrated that the performance of the algorithms with
the proposed modifications based on the chaos approach, are better than, or at least comparable to,
the original algorithms.
References
- Alatas, B., Akin, E. and Ozer, A. B. (2009) Chaos embedded particle swarm optimization algorithms, Chaos, Solitons Fractals, 40(4), 1715-1734. doi: 10.1016/j.chaos.2007.09.063
- Civicioglu, P. (2013) Backtracking search optimization algorithm for numerical optimization problems, Applied Mathematics and Computation, 219(15), 8121-8144, 2013. doi: 10.1016/j.amc.2013.02.017
- Dogan, B. and Olmez, T. A. (2015) A new metaheuristic for numerical function optimization: vortex search algorithm, Information Sciences, 293, 125-145. doi: 10.1016/j.ins.2014.08.053
- Gandomi, A., Yang, X-S., Talatahari, S. and Alavi, A. (2013) Firefly algorithm with chaos, Communications in Nonlinear Science and Numerical Simulation., 18(1), 89-98. doi: 10.1016/j.cnsns.2012.06.009
- Geem, Z., Kim, J. and Loganathan, G. (2001) A new heuristic optimization algorithm: harmony search, Simulation, 76(2), 60-68. doi: 10.1177/003754970107600201
- Goldberg D. E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing, USA.
- Kellert, S. (1993) In the Wake of Chaos:Unpredictable Order in Dynamical Systems, University of Chicago Press, USA.
- Kennedy J. and Eberhart R. (1995) Particle swarm optimization, IEEE International Conference on Neural Networks, 1942-1948. doi:10.1109/ICNN.1995.488968
- Li, Y., Deng, S. and Xiao, D. (2011) A novel hash algorithm construction based on chaotic neural network, Neural Computing and Applications, 20(1), 133–141. doi: 10.1007/s00521-010-0432-2
- Li-Jiang, Y. and Tian-Lun, C. (2002) Application of chaos in genetic algorithms, Communications in Theoretical Physics, 38(2), 168. doi: 10.1088/0253-6102/38/2/168
- Liang, J. J., Suganthan, P. N. and Hernandez-Diaz, A. G. (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization, Zhengzhou University and Nanyang Technological University, 3-18. Technical report:201212
- Mirjalili, S., Mirjalili, S. M. and Lewis, A. (2014) Grey wolf optimizer, Advances in Engineering Software, 69, 46-61. doi: 10.1016/j.advengsoft.2013.12.007
- Pecora, L. and Carroll, T. (1990) Synchronization in chaotic system, Physical Review Letters, 64(8), 821-824. doi: 10.1103/PhysRevLett.64.821
- Saremi, S., Mirjalili, S. M. and Mirjalili, S. (2014) Chaotic krill herd optimization algorithm, Procedia Techno, 12, 180-185. doi: 10.1016/j.protcy.2013.12.473
- Schuster, H. G. and Just, W. (2006) Deterministic chaos: an introduction, John Wiley & Sons, Germany.
- Storn, R. and Price K. (1995) Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces, International Computer Science Institute, 1-12. Technical report:TR-95-012
- Wang, N., Liu, L. M. and L. L. Liu. (2001) Genetic algorithm in chaos, Or Transactions, 5(5), 1-10.
- Wang, L. and Zhong, Y. (2015) Cuckoo search algorithm with chaotic maps, Mathematical Problems in Engineering, 6(6), 546-554. doi: 10.1155/2015/715635
- Wang,, G.-G., Guo, L., Gandomi, A., Hao, G.-S. and Wang, H. (2014) Chaotic krill herd algorithm, Information Sciences, 274, 17-34. doi: 10.1016/j.ins.2014.02.123
- Wolpert, D. H. and Macready, W. G. (1997) No free lunch theorems for optimization, IEEE Transactions on Evolutionary Computation, 1(1), 67-82. doi: 10.1109/4235.585893
- Yang, X-S. (2010) Nature-inspired Metaheuristic Algorithms, Luniver Press, UK.
- Yang, X-S. and Deb, S. (2009) Cuckoo search via L´evy flights, Proceeding of World Congress on Nature Biologically Inspired Computing, 210-214, doi: 10.1109/NABIC.2009.5393690
- Yao, J. F., Mei, C., Peng, X. Q., Hu, Z. K. and Hu, J (2001) A new optimization approach-chaos genetic algorithm, Systems Engineering, 1, 1-5.
- Zaharie, D. (2003) Control of population diversity and adaptation in differential evolution algorithms, Mendel 9th International Conference on Soft Computing, Brno, 41-46.
- Zhenyu, G. Bo, Y. C. and Min, C. B. (2006) Self-adaptive chaos differential evolution, International Conference on Natural Computation, 972-975. doi: 10.1007/11881070_128
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 31, 2018 |
| Submission Date | May 2, 2018 |
| Acceptance Date | October 17, 2018 |
| Published in Issue | Year 2018 Volume: 23 Issue: 3 |
Cite
Cited By
Operational framework for recent advances in backtracking search optimisation algorithm: A systematic review and performance evaluation
Applied Mathematics and Computation
Bryar A. Hassan
https://doi.org/10.1016/j.amc.2019.124919
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