Commenced in January 2007
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Edition: International
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Improvement of Gregory's formula using Particle Swarm Optimization

Authors: N. Khelil. L. Djerou , A. Zerarka, M. Batouche

Abstract:

Consider the Gregory integration (G) formula with end corrections where h Δ is the forward difference operator with step size h. In this study we prove that can be optimized by minimizing some of the coefficient k a in the remainder term by particle swarm optimization. Experimental tests prove that can be rendered a powerful formula for library use.

Keywords: Numerical integration, Gregory Formula, Particle Swarm optimization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082647

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References:


[1] G.C.ROTA, finite operator calculus, Academic press, Inc., 1975
[2] M.K.Belbahri, Generalized Gregory formula, Doctoral Thesis, Stevens Institute of Technology (1982).
[3] Eberhart, R.C. and Kennedy, J. (1995). A new optimizer using particles swarm theory', Sixth International Symposium on Micro Machine and Human Science, pp.39--43, Nagoya, Japan.
[4] K. E. Parsopoulos and M. N. Vrahatis, 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.
[5] K. E. Parsopoulos et al., Stretching technique for obtaining global minimizers through particle swarm optimization, Proc. of the PSO Workshop, Indianapolis, USA, (2001b),pp. 22-29.
[6] P.C. Fourie, and Groenwold, A.A. Particle swarms in size and shape optimization', Proceedings of the International Workshop on Multidisciplinary Design Optimization, Pretoria, South Africa, August 7ÔÇö 10, (2000), pp.97--106.
[7] P.C. Fourie, 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.
[8] R.C. Eberhart, et al. Computational Intelligence PC Tools, Academic Press Professional, Boston. 1996.
[9] ] J. Kennedy, The behaviour of particles, Evol. Progr. VII (1998), 581- 587.
[10] J. Kennedy and R. C. Eberhart, Swarm Intelligence, Morgan Kaufmann Publishers, San Francisco, 2001.
[11] Y. H. Shi and R. C. Eberhart, Fuzzy adaptive particle swarm optimization, IEEE Int. Conf. on Evolutionary Computation, pp. 101- 106, (2001).
[12] Y. H. Shi and R. C. Eberhart, A modified particle swarm optimizer, Proc. of the 1998 IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, May 4-9, 1998a.
[13] Y. H. Shi and R. C. Eberhart, Parameter selection in particle swarm optimization, Evolutionary Programming VII, Lecture Notes in Computer Science, (1998b), pp. 591-600.
[14] M. Clerc, 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.
[15] R.C. Eberhart, and Shi, Y.. Parameter selection in particle swarm optimization, in Porto, V.W., 1998
[16] T. I. Cristian, The particle swarm optimization algorithm: convergence analysis and parameter selection, Information Processing Letters, Vol. 85, No. 6, (2003), pp.317-- 325.
[17] K. E. Parsopoulos et al., Objective function stretching to alleviate convergence to local minima, Nonlinear Analysis TMA 47 (2001a), 3419-3424.
[18] A. Zerarka and N. Khelil, 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), 152-163.
[19] L. Djerou, M. Batouche, N. Khelil and A. Zerarka. Towards the Best Points of Interpolation Using Particles Swarm Optimisation Approach, IEEE Congress on Evolutionary Computation. Singapore September 25- 28, 2007