Research Article
Year 2018,
Volume: 1 Issue: 3, 1 - 11, 18.12.2018
Abstract
The aim of this study
is to bring a new perspective for the solutions of non-linear equation systems.
So this study handles the non-linear equation systems as a constrained
optimization problem, while generally is handled unconstrained optimization
problem or multi objective optimization problem. The object is to minimize the
sum of the squares of nonlinear equations under the nonlinear equality
constraints. A recently developed heuristic optimization algorithm called Grey
Wolf Optimizer (GWO) is proposed for the solution of nonlinear equation
systems. Two results were obtained. Firstly, it has been seen that GWO can be
an alternative solution technique for the solution of nonlinear equation
systems. Secondly, modelling the systems of nonlinear equations as constrained
optimization gives better results.
References
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Cai, "Locating Multiple Optimal Solutions of Nonlinear Equation Systems Based on Multiobjective Optimization," in IEEE Transactions on Evolutionary Computation, vol. 19, no. 3, pp. 414-431, June 2015.[6] A. Majd et al., "Multi-population parallel imperialist competitive algorithm for solving systems of nonlinear equations," 2016 International Conference on High Performance Computing & Simulation (HPCS), Innsbruck, 2016, pp. 767-775.[7] E. Pourjafari and H. Mojallali, “Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering,” Swarm Evol. Comput., vol. 4, pp. 33–43, Jun. 2012.[8] 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.[9] J. Wang, “Immune genetic algorithm for solving nonlinear equations,” in Proc. 2011 Int. Conf. Mechatr. Sci., Electr. Eng. Comput., Jilin, China, pp. 2094–2097.[10] Y. Zhou, J. Liu, and G. Zhao, “Leader glowworm swarm optimization algorithm for solving nonlinear equations systems,” Electr. Rev., vol. 88, no. 1, pp. 101–106, 2012.[11] J. Wu, Z. Cui, and J. Liu, “Using hybrid social emotional optimization algorithm with metropolis rule to solve nonlinear equations,” in Proc. 10th IEEE Int. Conf. Cogn. Inf. Cognit. Comput., Banff, AB, USA, 2011, pp. 405–411.[12] Mirjalili, S. How effective is the grey wolf optimizer in training multi-layer perceptrons. Appl. Intell. 2015, 43, 150–161.[13] Mohd Herwan Sulaiman, Zuriani Mustaffa, Mohd Rusllim Mohamed, Omar Aliman, Using the gray wolf optimizer for solving optimal reactive power dispatch problem, In Applied Soft Computing, Volume 32, 2015, Pages 286-292, ISSN 1568-4946, https://doi.org/10.1016/j.asoc.2015.03.041.[14] H.M. Song, M.H. Sulaiman, M.R. Mohamed. An application of Grey Wolf Optimizer for solving combined economic emission dispatch problems, Int Rev Model Simul (IREMOS), 7 (2014), pp. 838-844.[15] Zhang, Y., Phillips, P., Wang, S., Ji, G., Yang, J., and Wu, J. (2016) Fruit classification by biogeography-based optimization and feedforward neural network. Expert Systems, 33: 239–253. doi: 10.1111/exsy.12146.[16] El-Fergany Attia A, Hasanien Hany M. Single and multi-objective optimal power flow using grey wolf optimizer and differential evolution algorithms. Electr Power Compon Syst 2015;43(13):1548–59.[17] S.A. Medjahed, T. Ait Saadi, A. Benyettou, M. Ouali, Gray Wolf Optimizer for hyperspectral band selection, In Applied Soft Computing, Volume 40, 2016, Pages 178-186, ISSN 1568-4946, https://doi.org/10.1016/j.asoc.2015.09.045.[18] Y. T. K. Priyanto and L. Hendarwin, "Multi objective optimal power flow to minimize losses and carbon emission using Wolf Algorithm," 2015 International Seminar on Intelligent Technology and Its Applications (ISITIA), Surabaya, 2015, pp. 153-158. doi: 10.1109/ISITIA.2015.7219971.[19] Akhilesh Gotmare, Sankha Subhra Bhattacharjee, Rohan Patidar, Nithin V. George, Swarm and evolutionary computing algorithms for system identification and filter design: A comprehensive review, In Swarm and Evolutionary Computation, Volume 32, 2017, Pages 68-84, ISSN 2210-6502, https://doi.org/10.1016/j.swevo.2016.06.007.[20] E. Emary, Hossam M. Zawbaa, Aboul Ella Hassanien, Binary grey wolf optimization approaches for feature selection, In Neurocomputing, Volume 172, 2016, Pages 371-381, ISSN 0925-2312, https://doi.org/10.1016/j.neucom.2015.06.083.[21] Seyedali Mirjalili, Seyed Mohammad Mirjalili, Andrew Lewis, Grey Wolf Optimizer, In Advances in Engineering Software, Volume 69, 2014, Pages 46-61, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2013.12.007.[22] Chao Lu, Shengqiang Xiao, Xinyu Li, Liang Gao, An effective multi-objective discrete grey wolf optimizer for a real-world scheduling problem in welding production, In Advances in Engineering Software, Volume 99, 2016, Pages 161-176, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2016.06.004.[23] T. Jayabarathi, T. Raghunathan, B.R. Adarsh, Ponnuthurai Nagaratnam Suganthan, Economic dispatch using hybrid grey wolf optimizer, In Energy, Volume 111, 2016, Pages 630-641, ISSN 0360-5442, https://doi.org/10.1016/j.energy.2016.05.105.[24] Zhang, Sen & Luo, Qifang & Zhou, Yong-Quan. (2017). Hybrid Grey Wolf Optimizer Using Elite Opposition-Based Learning Strategy and Simplex Method. International Journal of Computational Intelligence and Applications. 1750012. 10.1142/S1469026817500122.[25] Narinder Singh and S. B. Singh, “Hybrid Algorithm of Particle Swarm Optimization and Grey Wolf Optimizer for Improving Convergence Performance,” Journal of Applied Mathematics, vol. 2017, Article ID 2030489, 15 pages, 2017. https://doi.org/10.1155/2017/2030489.[26] . D. Gupta, C. Anand and T. Dewan, "Enhanced heuristic approach for Traveling Tournament Problem based on Grey Wolf Optimizer," 2015 Eighth International Conference on Contemporary Computing (IC3), Noida, 2015, pp. 235-240. doi: 10.1109/IC3.2015.7346685 [27] D. Jitkongchuen, "A hybrid differential evolution with grey wolf optimizer for continuous global optimization," 2015 7th International Conference on Information Technology and Electrical Engineering (ICITEE), Chiang Mai, 2015, pp. 51-54.doi: 10.1109/ICITEED.2015.7408911
Year 2018,
Volume: 1 Issue: 3, 1 - 11, 18.12.2018
Abstract
References
- [1] 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.[2] 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.[3] Muhammad Aslam Noor, Muhammad Waseem, Some iterative methods for solving a system of nonlinear equations, In Computers & Mathematics with Applications, Volume 57, Issue 1, 2009, Pages 101-106, ISSN 0898-1221, https://doi.org/10.1016/j.camwa.2008.10.067. [4] S. Qin, S. Zeng, W. Dong and X. Li, "Nonlinear equation systems solved by many-objective Hype," 2015 IEEE Congress on Evolutionary Computation (CEC), Sendai, 2015, pp. 2691-2696[5] W. Song, Y. Wang, H. X. Li and Z. Cai, "Locating Multiple Optimal Solutions of Nonlinear Equation Systems Based on Multiobjective Optimization," in IEEE Transactions on Evolutionary Computation, vol. 19, no. 3, pp. 414-431, June 2015.[6] A. Majd et al., "Multi-population parallel imperialist competitive algorithm for solving systems of nonlinear equations," 2016 International Conference on High Performance Computing & Simulation (HPCS), Innsbruck, 2016, pp. 767-775.[7] E. Pourjafari and H. Mojallali, “Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering,” Swarm Evol. Comput., vol. 4, pp. 33–43, Jun. 2012.[8] 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.[9] J. Wang, “Immune genetic algorithm for solving nonlinear equations,” in Proc. 2011 Int. Conf. Mechatr. Sci., Electr. Eng. Comput., Jilin, China, pp. 2094–2097.[10] Y. Zhou, J. Liu, and G. Zhao, “Leader glowworm swarm optimization algorithm for solving nonlinear equations systems,” Electr. Rev., vol. 88, no. 1, pp. 101–106, 2012.[11] J. Wu, Z. Cui, and J. Liu, “Using hybrid social emotional optimization algorithm with metropolis rule to solve nonlinear equations,” in Proc. 10th IEEE Int. Conf. Cogn. Inf. Cognit. Comput., Banff, AB, USA, 2011, pp. 405–411.[12] Mirjalili, S. How effective is the grey wolf optimizer in training multi-layer perceptrons. Appl. Intell. 2015, 43, 150–161.[13] Mohd Herwan Sulaiman, Zuriani Mustaffa, Mohd Rusllim Mohamed, Omar Aliman, Using the gray wolf optimizer for solving optimal reactive power dispatch problem, In Applied Soft Computing, Volume 32, 2015, Pages 286-292, ISSN 1568-4946, https://doi.org/10.1016/j.asoc.2015.03.041.[14] H.M. Song, M.H. Sulaiman, M.R. Mohamed. An application of Grey Wolf Optimizer for solving combined economic emission dispatch problems, Int Rev Model Simul (IREMOS), 7 (2014), pp. 838-844.[15] Zhang, Y., Phillips, P., Wang, S., Ji, G., Yang, J., and Wu, J. (2016) Fruit classification by biogeography-based optimization and feedforward neural network. Expert Systems, 33: 239–253. doi: 10.1111/exsy.12146.[16] El-Fergany Attia A, Hasanien Hany M. Single and multi-objective optimal power flow using grey wolf optimizer and differential evolution algorithms. Electr Power Compon Syst 2015;43(13):1548–59.[17] S.A. Medjahed, T. Ait Saadi, A. Benyettou, M. Ouali, Gray Wolf Optimizer for hyperspectral band selection, In Applied Soft Computing, Volume 40, 2016, Pages 178-186, ISSN 1568-4946, https://doi.org/10.1016/j.asoc.2015.09.045.[18] Y. T. K. Priyanto and L. Hendarwin, "Multi objective optimal power flow to minimize losses and carbon emission using Wolf Algorithm," 2015 International Seminar on Intelligent Technology and Its Applications (ISITIA), Surabaya, 2015, pp. 153-158. doi: 10.1109/ISITIA.2015.7219971.[19] Akhilesh Gotmare, Sankha Subhra Bhattacharjee, Rohan Patidar, Nithin V. George, Swarm and evolutionary computing algorithms for system identification and filter design: A comprehensive review, In Swarm and Evolutionary Computation, Volume 32, 2017, Pages 68-84, ISSN 2210-6502, https://doi.org/10.1016/j.swevo.2016.06.007.[20] E. Emary, Hossam M. Zawbaa, Aboul Ella Hassanien, Binary grey wolf optimization approaches for feature selection, In Neurocomputing, Volume 172, 2016, Pages 371-381, ISSN 0925-2312, https://doi.org/10.1016/j.neucom.2015.06.083.[21] Seyedali Mirjalili, Seyed Mohammad Mirjalili, Andrew Lewis, Grey Wolf Optimizer, In Advances in Engineering Software, Volume 69, 2014, Pages 46-61, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2013.12.007.[22] Chao Lu, Shengqiang Xiao, Xinyu Li, Liang Gao, An effective multi-objective discrete grey wolf optimizer for a real-world scheduling problem in welding production, In Advances in Engineering Software, Volume 99, 2016, Pages 161-176, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2016.06.004.[23] T. Jayabarathi, T. Raghunathan, B.R. Adarsh, Ponnuthurai Nagaratnam Suganthan, Economic dispatch using hybrid grey wolf optimizer, In Energy, Volume 111, 2016, Pages 630-641, ISSN 0360-5442, https://doi.org/10.1016/j.energy.2016.05.105.[24] Zhang, Sen & Luo, Qifang & Zhou, Yong-Quan. (2017). Hybrid Grey Wolf Optimizer Using Elite Opposition-Based Learning Strategy and Simplex Method. International Journal of Computational Intelligence and Applications. 1750012. 10.1142/S1469026817500122.[25] Narinder Singh and S. B. Singh, “Hybrid Algorithm of Particle Swarm Optimization and Grey Wolf Optimizer for Improving Convergence Performance,” Journal of Applied Mathematics, vol. 2017, Article ID 2030489, 15 pages, 2017. https://doi.org/10.1155/2017/2030489.[26] . D. Gupta, C. Anand and T. Dewan, "Enhanced heuristic approach for Traveling Tournament Problem based on Grey Wolf Optimizer," 2015 Eighth International Conference on Contemporary Computing (IC3), Noida, 2015, pp. 235-240. doi: 10.1109/IC3.2015.7346685 [27] D. Jitkongchuen, "A hybrid differential evolution with grey wolf optimizer for continuous global optimization," 2015 7th International Conference on Information Technology and Electrical Engineering (ICITEE), Chiang Mai, 2015, pp. 51-54.doi: 10.1109/ICITEED.2015.7408911
There are 1 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Computer Software |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 18, 2018 |
| Submission Date | October 28, 2018 |
| Acceptance Date | December 6, 2018 |
| Published in Issue | Year 2018Volume: 1 Issue: 3 |
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