Abstract
Systems of nonlinear equations come into different range of sciences such as chemistry, economics, medicine, robotics, engineering, and mechanics. There are different methods for solving systems of nonlinear equations such as Newton type methods, imperialist competitive algorithm, particle swarm algorithm, conjugate direction method that each has their own advantages and weaknesses such as low convergence speed and poor quality of solutions. This paper improves cuckoo optimization algorithm for solving systems of nonlinear equations by changing the policy of egg laying radius, and some well-known problems are presented to demonstrate the efficiency and better performance of this new robust optimization algorithm. From obtained results, our approach found more accurate solutions with the lowest number of function evaluations.
Similar content being viewed by others
References
El-Emary IMM, Abd El-Kareem MM (2008) Toward using genetic algorithm for solving nonlinear eqution systems. World Appl Sci J 5:282–289
Zhijian W, Kang L (2003) A fast and elitist parallel evolutionary algorithm for solving systems of non-linear equations. In: The 2003 Congress on Evol Comput vol 2, pp 1026–1028
Mastorakis NE (2005) Solving non-linear equations via genetic algorithms. In: Proceedings of the 6th WSEAS international conference on evoluationary computing vol 6, pp 24–28
Li G, Zeng Z (2008) A neural-network algorithm for solving nonlinear equation systems. In: IEEE international conference on computational intelligence and security, vol 1, pp 20–23
Huan-Tong G, Yi-Jie S, Qing-Xi S, Ting-Ting W (2009) Research of ranking method in evolution strategy for solving nonlinear system of equations. In: 1st international conference on information science and engineering, vol 1, 348–351
Abdollahi M, Isazadeh A, Abdollahi D (2013) Solving the constrained nonlinear optimization based on imperialist competitive algorithm. Int J Nonlinear Sci 15:212–219
Ouyang A, Zhou Y, Luo Q (2009) Hybrid particle swarm optimization algorithm for solving systems of nonlinear equations. In: IEEE international conference on granular computing, GRC09, pp 460–465
Wu J, Cui Z, Liu J (2011) Using hybrid social emotional optimization algorithm with metropolis rule to solve nonlinear equations. In: 10th IEEE international conference on cognitive informatics and cognitive computing, vol 10, pp 405–411
Luo YZ, Tang GJ, Zhou LN (2008) Hybrid approach for solving systems of nonlinear equations using chaos optimization and quasi-Newton method. Appl Soft Comput 8:1068–1073
Grosan C, Abraham A (2008) A new approach for solving nonlinear equations systems. IEEE Trans Syst Man Cybern Part A Syst Hum 38:698–714
Mo Y, Liu H, Wang Q (2009) Conjugate direction particle swarm optimization solving systems of nonlinear equations. Comput Math Appl 57:1877–1882
Jaberipour M, Khorram E, Karimi B (2011) Particle swarm algorithm for solving systems of nonlinear equations. Comput Math Appl 62:566–576
Oliveira HA Jr, Petraglia A (2013) Solving nonlinear systems of functional equations with fuzzy adaptivesimulated annealing. Appl Soft Comput 13:4349–4357
Henderson N, Sacco WF, Platt GM (2010) Finding more than one root of nonlinear equations via a polarization technique: an application to double retrograde vaporization. Chem Eng Res Des 88:551–561
Pourjafari E, Mojallali H (2012) Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering. Swarm Evol Comput 4:33–43
Kuri-Morales AF (2003) Solution of simultaneous non-linear quations using genetic algorithms. WSEAS Trans Syst 2:44–51
Mastorakis NE (2005) solving non-linear equations via genetic algorithms. WSEAS Evolut Comput Lisbon Portugal 6:24–28
Rajabioun R (2011) Cuckoo optimization algorithm. Appl Soft Comput 11:5508–5518
Abdollahi M, Isazadeh A, Abdollahi D (2013) Imperialist competitive algorithm for solving systems of nonlinear equations. Elsevier Comput Math Appl 65:1894–1908
Nedzhibov GH (2008) A family of multi-point iterative methods for solving systems of nonlinear equations. Comput Appl Math 222:244–250
Verschelde J, Verlinden P, Cools R (1994) Homotopies exploiting Newton polytopes for solving sparse polynomial systems. SIAM J Numer Anal 31:915–930
Wang C, Luo R, Wu K, Han B (2011) A new filled function method for an unconstrained nonlinear equation. Comput Appl Math 235:1689–1699
Floudas CA, Pardalos PM, Adjiman CS, Esposito WR, Gumus ZH, Harding ST, Klepeis JL, Meyer CA, Schweiger CA (1999) Handbook of test problems in local and global optimization. Kluwer Academic Publishers, Dordrecht
Bahrami H, Faez K, Abdechiri M (2010) Imperialistic competitive algorithm using chaos theory for optimization. In: 12th international conference on computer modeling and stimulation, vol 12, pp 98–103
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Abdollahi, M., Bouyer, A. & Abdollahi, D. Improved cuckoo optimization algorithm for solving systems of nonlinear equations. J Supercomput 72, 1246–1269 (2016). https://doi.org/10.1007/s11227-016-1660-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11227-016-1660-8