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Nature Inspired Optimization Algorithms and Their Performance on the Solution of Nonlinear Equation Systems

Year 2018, Volume: 1 Issue: 1, 44 - 57, 02.04.2018

Pakize Erdoğmuş

Abstract

The aim of this article is both to introduce recent published nature-inspired optimization algorithms and to compare the performances of them. Four benchmark test problems(two unimodal, two multimodal) and four nonlinear equations systems were used for the comparison. The results were submitted. It was seen with these test results, we can not say that one of the algorithms outperforms. But all af them can be an alternative for solving the nonlinear equation systems.

Keywords

Nature-Inspired Optimization Algorithms Nonlinear Equation Systems Grey Wolf Optimization Ant-Lion Algorithm Whale Optimization Algorithm Salp Swar Algorithm

References

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  • Seyedali Mirjalili, The Ant Lion Optimizer, Advances in Engineering Software, Volume 83, 2015, Pages 80-98, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2015.01.010.
  • Hadi Eskandar, Ali Sadollah, Ardeshir Bahreininejad, Mohd Hamdi, Water cycle algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems, Computers & Structures, Volumes 110–111, 2012, Pages 151-166, ISSN 0045-7949, https://doi.org/10.1016/j.compstruc.2012.07.010.
  • Seyedali Mirjalili, Andrew Lewis, The Whale Optimization Algorithm, Advances in Engineering Software, Volume 95, 2016, Pages 51-67, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2016.01.008.
  • Seyedali Mirjalili, Seyed Mohammad Mirjalili, Andrew Lewis, Grey Wolf Optimizer, Advances in Engineering Software, Volume 69, 2014, Pages 46-61, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2013.12.007.
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  • Seyedali Mirjalili, Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm, Knowledge-Based Systems, Volume 89, 2015, Pages 228-249, ISSN 0950-7051, https://doi.org/10.1016/j.knosys.2015.07.006.
  • Z. Bayraktar, M. Komurcu and D. H. Werner, "Wind Driven Optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetics," 2010 IEEE Antennas and Propagation Society International Symposium, Toronto, ON, 2010, pp. 1-4. doi: 10.1109/APS.2010.5562213
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  • Fernando Fausto, Erik Cuevas, Arturo Valdivia, Adrián González, A global optimization algorithm inspired in the behavior of selfish herds, Biosystems, Volume 160, 2017, Pages 39-55, ISSN 0303-2647, https://doi.org/10.1016/j.biosystems.2017.07.010.
  • Seyedali Mirjalili, Amir H. Gandomi, Seyedeh Zahra Mirjalili, Shahrzad Saremi, Hossam Faris, Seyed Mohammad Mirjalili, Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems, Advances in Engineering Software, Volume 114, 2017, Pages 163-191, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2017.07.002.
  • Huan, T.T., Kulkarni, A.J., Kanesan, J. et al. Neural Comput & Applic (2017) 28(Suppl 1): 845. https://doi.org/10.1007/s00521-016-2379-4
  • Kulkarni, Anand & Krishnasamy, Ganesh & Abraham, Ajith. (2017). Socio-Inspired Optimization Using Cohort Intelligence. 114. 9-24. 10.1007/978-3-319-44254-9_2.
  • Dennis, J.E., Jr. and Schnabel, R.B., 1983, Numerical methods for unconstrained optimization and nonlinear equations: Englewood Cliffs, N.J., Prentice-Hall, 378 p.
  • More Raju, Lalit Chandra Saikia, Nidul Sinha, Automatic generation control of a multi-area system using ant lion optimizer algorithm based PID plus second order derivative controller, International Journal of Electrical Power & Energy Systems, Volume 80, 2016, Pages 52-63, ISSN 0142-0615, https://doi.org/10.1016/j.ijepes.2016.01.037.
  • E. Emary, Hossam M. Zawbaa, Aboul Ella Hassanien,Binary ant lion approaches for feature selection, Neurocomputing,Volume 213, 2016, Pages 54-65, ISSN 0925-2312, https://doi.org/10.1016/j.neucom.2016.03.101.
  • http://www.insectsimages.org, Whitney Cranshaw, Colorado State University, Bugwood.org [Accesed: 20.02.2018]
  • Karim Illiya, Karim Illıya Studio,https://karimphotography.com, [Accesed: 20.02.2018]
  • Richard Herman, http://www.alertdiver.com/Blue_Water [Accesed: 20.02.2018]
  • A. Yahiaoui, F. Fodhil, K. Benmansour, M. Tadjine, N. Cheggaga, Grey wolf optimizer for optimal design of hybrid renewable energy system PV-Diesel Generator-Battery: Application to the case of Djanet city of Algeria, Solar Energy, Volume 158, 2017, Pages 941-951, ISSN 0038-092X, https://doi.org/10.1016/j.solener.2017.10.040.
  • Ehsan Naderi, Ali Azizivahed, Hossein Narimani, Mehdi Fathi, Mohammad Rasoul Narimani, A comprehensive study of practical economic dispatch problems by a new hybrid evolutionary algorithm,Applied Soft Computing,Volume 61,2017,Pages 1186-1206,ISSN 1568-4946,https://doi.org/10.1016/j.asoc.2017.06.041.
  • Kaur R, Arora S, Nature Inspired Range Based Wireless Sensor Node Localization Algorithms, International Journal of Interactive Multimedia and Artificial Intelligence, Volume 4, Number 6, Pages 7-17, ISSN 1989-1660.
  • M. Jaberipour, E. Khorram, and B. Karimi, “Particle swarm algorithm for solving systems of nonlinear equations,” Comput. Math. Appl., vol. 62, no. 2, pp. 566–576, 2011.
  • G. Joshi and M. B. Krishna, "Solving system of non-linear equations using Genetic Algorithm," 2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI), New Delhi, 2014, pp. 1302-1308.
  • 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, no. 3, pp. 698-714, May 2008.
  • D. H. Wolpert and W. G. Macready, "No free lunch theorems for optimization," in IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 67-82, Apr 1997.

Year 2018, Volume: 1 Issue: 1, 44 - 57, 02.04.2018

Pakize Erdoğmuş

Abstract

References

  • H. Wang, G. Ren, J. Chen, G. Ding and Y. Yang, "Unmanned Aerial Vehicle-Aided Communications: Joint Transmit Power and Trajectory Optimization," in IEEE Wireless Communications Letters, vol. PP, no. 99, pp. 1-1. doi: 10.1109/LWC.2018.2792435
  • M. Song and M. Zheng, "Energy Efficiency Optimization for Wireless Powered Sensor Networks with Non-orthogonal Multiple Access," in IEEE Sensors Letters, vol. PP, no. 99, pp. 1-1. doi: 10.1109/LSENS.2018.2792454
  • S. Medya, P. Bogdanov and A. Singh, "Making a Small World Smaller: Path Optimization in Networks," in IEEE Transactions on Knowledge and Data Engineering, vol. PP, no. 99, pp. 1-1. doi: 10.1109/TKDE.2018.2792470
  • E. Elhamifar and R. Vidal, "Sparse Subspace Clustering: Algorithm, Theory, and Applications," in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 11, pp. 2765-2781, Nov. 2013. doi: 10.1109/TPAMI.2013.57
  • W. Zhu, S. Liang, Y. Wei and J. Sun, "Saliency Optimization from Robust Background Detection," 2014 IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, 2014, pp. 2814-2821. doi: 10.1109/CVPR.2014.360
  • M. Qiu, Z. Ming, J. Li, K. Gai and Z. Zong, "Phase-Change Memory Optimization for Green Cloud with Genetic Algorithm," in IEEE Transactions on Computers, vol. 64, no. 12, pp. 3528-3540, Dec. 1 2015. doi: 10.1109/TC.2015.2409857
  • Alireza Askarzadeh, A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm, Computers & Structures, Volume 169, 2016, Pages 1-12, ISSN 0045-7949, https://doi.org/10.1016/j.compstruc.2016.03.001.
  • 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, Volume 33, 2015, Pages 292-303, ISSN 1568-4946, https://doi.org/10.1016/j.asoc.2015.04.048.
  • Seyedali Mirjalili, The Ant Lion Optimizer, Advances in Engineering Software, Volume 83, 2015, Pages 80-98, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2015.01.010.
  • Hadi Eskandar, Ali Sadollah, Ardeshir Bahreininejad, Mohd Hamdi, Water cycle algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems, Computers & Structures, Volumes 110–111, 2012, Pages 151-166, ISSN 0045-7949, https://doi.org/10.1016/j.compstruc.2012.07.010.
  • Seyedali Mirjalili, Andrew Lewis, The Whale Optimization Algorithm, Advances in Engineering Software, Volume 95, 2016, Pages 51-67, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2016.01.008.
  • Seyedali Mirjalili, Seyed Mohammad Mirjalili, Andrew Lewis, Grey Wolf Optimizer, Advances in Engineering Software, Volume 69, 2014, Pages 46-61, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2013.12.007.
  • Wang, GG., Deb, S. & Cui, Z. Neural Comput & Applic (2015). https://doi.org/10.1007/s00521-015-1923-7
  • Seyedali Mirjalili, Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm, Knowledge-Based Systems, Volume 89, 2015, Pages 228-249, ISSN 0950-7051, https://doi.org/10.1016/j.knosys.2015.07.006.
  • Z. Bayraktar, M. Komurcu and D. H. Werner, "Wind Driven Optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetics," 2010 IEEE Antennas and Propagation Society International Symposium, Toronto, ON, 2010, pp. 1-4. doi: 10.1109/APS.2010.5562213
  • D. Simon, "Biogeography-Based Optimization," in IEEE Transactions on Evolutionary Computation, vol. 12, no. 6, pp. 702-713, Dec. 2008. doi: 10.1109/TEVC.2008.919004
  • Fernando Fausto, Erik Cuevas, Arturo Valdivia, Adrián González, A global optimization algorithm inspired in the behavior of selfish herds, Biosystems, Volume 160, 2017, Pages 39-55, ISSN 0303-2647, https://doi.org/10.1016/j.biosystems.2017.07.010.
  • Seyedali Mirjalili, Amir H. Gandomi, Seyedeh Zahra Mirjalili, Shahrzad Saremi, Hossam Faris, Seyed Mohammad Mirjalili, Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems, Advances in Engineering Software, Volume 114, 2017, Pages 163-191, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2017.07.002.
  • Huan, T.T., Kulkarni, A.J., Kanesan, J. et al. Neural Comput & Applic (2017) 28(Suppl 1): 845. https://doi.org/10.1007/s00521-016-2379-4
  • Kulkarni, Anand & Krishnasamy, Ganesh & Abraham, Ajith. (2017). Socio-Inspired Optimization Using Cohort Intelligence. 114. 9-24. 10.1007/978-3-319-44254-9_2.
  • Dennis, J.E., Jr. and Schnabel, R.B., 1983, Numerical methods for unconstrained optimization and nonlinear equations: Englewood Cliffs, N.J., Prentice-Hall, 378 p.
  • More Raju, Lalit Chandra Saikia, Nidul Sinha, Automatic generation control of a multi-area system using ant lion optimizer algorithm based PID plus second order derivative controller, International Journal of Electrical Power & Energy Systems, Volume 80, 2016, Pages 52-63, ISSN 0142-0615, https://doi.org/10.1016/j.ijepes.2016.01.037.
  • E. Emary, Hossam M. Zawbaa, Aboul Ella Hassanien,Binary ant lion approaches for feature selection, Neurocomputing,Volume 213, 2016, Pages 54-65, ISSN 0925-2312, https://doi.org/10.1016/j.neucom.2016.03.101.
  • http://www.insectsimages.org, Whitney Cranshaw, Colorado State University, Bugwood.org [Accesed: 20.02.2018]
  • Karim Illiya, Karim Illıya Studio,https://karimphotography.com, [Accesed: 20.02.2018]
  • Richard Herman, http://www.alertdiver.com/Blue_Water [Accesed: 20.02.2018]
  • A. Yahiaoui, F. Fodhil, K. Benmansour, M. Tadjine, N. Cheggaga, Grey wolf optimizer for optimal design of hybrid renewable energy system PV-Diesel Generator-Battery: Application to the case of Djanet city of Algeria, Solar Energy, Volume 158, 2017, Pages 941-951, ISSN 0038-092X, https://doi.org/10.1016/j.solener.2017.10.040.
  • Ehsan Naderi, Ali Azizivahed, Hossein Narimani, Mehdi Fathi, Mohammad Rasoul Narimani, A comprehensive study of practical economic dispatch problems by a new hybrid evolutionary algorithm,Applied Soft Computing,Volume 61,2017,Pages 1186-1206,ISSN 1568-4946,https://doi.org/10.1016/j.asoc.2017.06.041.
  • Kaur R, Arora S, Nature Inspired Range Based Wireless Sensor Node Localization Algorithms, International Journal of Interactive Multimedia and Artificial Intelligence, Volume 4, Number 6, Pages 7-17, ISSN 1989-1660.
  • M. Jaberipour, E. Khorram, and B. Karimi, “Particle swarm algorithm for solving systems of nonlinear equations,” Comput. Math. Appl., vol. 62, no. 2, pp. 566–576, 2011.
  • G. Joshi and M. B. Krishna, "Solving system of non-linear equations using Genetic Algorithm," 2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI), New Delhi, 2014, pp. 1302-1308.
  • 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, no. 3, pp. 698-714, May 2008.
  • D. H. Wolpert and W. G. Macready, "No free lunch theorems for optimization," in IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 67-82, Apr 1997.
There are 33 citations in total.

Details

Primary Language English
Subjects Computer Software
Journal Section Articles
Authors

Pakize Erdoğmuş

Publication Date April 2, 2018
Submission Date March 25, 2018
Acceptance Date March 31, 2018
Published in Issue Year 2018Volume: 1 Issue: 1

Cite

IEEE P. Erdoğmuş, “Nature Inspired Optimization Algorithms and Their Performance on the Solution of Nonlinear Equation Systems”, SAUCIS, vol. 1, no. 1, pp. 44–57, 2018.
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