Manuscript Number : IJSRCE18253
Optimization of Civil Engineering Initial Value Problems by Particle Swarm Optimization Algorithm
Authors(2) :-Fatima OUAAR, Naceur KHELIL
A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. They are useful in many domains. Traditionally, Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) can be solved by classical mathematical methods, which are not very precise namely in the difficult problems. Swarm Intelligence Algorithms are considerate a crucial factor of modern optimization when large sort of Nature Inspired Algorithms have emerged recently to treaty successfully a variety of problems. In this paper, Particle Swarm Optimization Algorithm (PSO) is used to solve approximately an (IVP), by a selected example; the efficiency of the considered method is verified by means of a simulation study compared by a Runge Kutta method that shows very good results.
Fatima OUAAR
Department of Mathematics, University Mohamed KHEIDER, Biskra, Algeria
Naceur KHELIL
Department of Mathematics, University Mohamed KHEIDER, Biskra, Algeria
Optimization Problems, Initial-Value Problem (IVP); Runge Kutta method; Particle Swarm Optimization Algorithm (PSO).
- Cagnina L.C, Esquivel S.C., and Coello C.A., “Solving engineering optimization problems with the simple constrained particle swarm optimizer”, Informatica 2008, Vol. 32, pp.319- 326.
- Clerc, M., “The swarm and the queen: towards a deterministic and adaptive particle swarm optimization”, Proceedings of the 1999 IEEE Congress on Evolutionary Computation, Washington DC, 1999, pp.1951—1957.
- Cristian, T. I., “The particle swarm optimization algorithm: convergence analysis and parameter selection”, Information Processing Letters, Vol. 85, No. 6, 2003, pp.317-325.
- Djerou, L., Khelil, N., and Batouche, M., “Numerical Integration Method Based on Particle Swarm Optimization” Y. Tan et al. (Eds.) : Part I, LNCS 6728, Springer-Verlag Berlin Heidelberg, 2011, pp. 221-226.
- Dorigo, M., Maniezzo, V., and Colorni, A., “The ant system: optimization by a colony of cooperating agents”. IEEE Trans. Syst. Man Cybern1996; B 26, pp.29—41.
- Eberhart, R.C., and Shi, Y., “Parameter selection in particle swarm optimization”, in Porto, V.W., 1998.
- Eberhart, R.C. and Kennedy, J., “A new optimizer using particles swarm theory” Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995, pp.39--43,
- Fourie, P.C., and Groenwold, A.A., “Particle swarms in size and shape optimization,” Proceedings of the International Workshop on Multi-disciplinary Design Optimization, Pretoria, South Africa, August 7—10, 2000, pp.97—106.
- Fourie, P.C., and Groenwold, A.A., “Particle swarms in topology optimization” Extended Abstracts of the Fourth World Congress of Structural and Multidisciplinary Optimization, Dalian, China, June 4—8, 2001, pp.52, 53.
- Goldberg, D.E., “Genetic Algorithms in Search. Optimization and Machine Learning”. Addison Wesley, 1989.
- Holland, J.H., “Adaptation in Natural and Artificial Systems”. University of Michigan Press, 1975.
- Henrici, P., “Elements of Numerical Analysis, ” New York: McGraw-Hill, 1964.
- Kennedy, J., and Eberhart, R.C., “Swarm Intelligence, ” Morgan Kaufmann Publishers, San Francisco, 2001.
- Kennedy, J., and Eberhart, R.C., “Particle swarm optimization”. In: Proceedings of IEEE International Conference on Neural Networks 1995; No. IV. 27 Nov--1 Dec, pp. 1942--1948, Perth Australia.
- Kennedy, J., “The behaviour of particles, ” Evol. Progr. VII, , 1998. pp.581-587.
- Nakrani, S., Tovey C., “On honey bees and dynamic allocation in an internet server colony”. Adapt. Behav, 2004; 12(3--4). 223—240.
- Parsopoulos, K.E., and Vrahatis, M.N., “Modification of the Particle Swarm Optimizer for Locating all the Global Minima”, V. Kurkova et al., eds., Artificial Neural Networks and Genetic Algorithms, Springer, New York, 2001, pp.324-327 .
- Shi, Y.H., and Eberhart, R.C., “Fuzzy adaptive particle swarm optimization,” IEEE Int. Conf. on Evolutionary Computation, 2001 , pp.101-106.
- Shi, Y.H., and Eberhart, R.C., “A modified particle swarm optimizer,” Proc. of the 1998 IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, May 4-9, 1998.
- Yang, X.S., (2010), “Engineering Optimization: An Introduction with Metaheuristic Applications”, Wiley, New York.
- Yang X.S., “Book Nature Inspired Optimization Algorithm”, Elsevier, 2014.
- Yang, X.S., Gandomi A.H., “Bat algorithm: a novel approach for global engineering optimization”, Eng. Comput 2012, Vol.29, Num.5, 464—483.
- Yang, X.S., “Nature-Inspired Metaheuristic Algorithms”, Luniver Press, 2008.
- Zerarka, A., and Khelil, N., “A generalized integral quadratic method: improvement of the solution for one dimensional Volterra integral equation using particle swarm optimization,” Int. J. Simulation and Process Modelling, 2(1-2), 2006, pp.152-163.
- Zerarka, A., Soukeur, A., Khelil, N., “The particle swarm optimization against the Runge's phenomenon,” Application to the generalized integral quadrature method, International Journal of Mathematical and Statistical Sciences, pp-171-1761 :3 2009.
Publication Details
Published in : Volume 3 | Issue 1 | January-February 2019
Date of Publication : 2019-01-30
License: This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 01-07
Manuscript Number : IJSRCE18253
Publisher : Technoscience Academy
URL : https://ijsrce.com/IJSRCE18253
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