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Optimizing the dynamic response of the H. B. Robinson nuclear plant using multiobjective particle swarm optimization

  • M. A. Elsays , M. Naguib Aly and A. A. Badawi
Published/Copyright: April 5, 2013
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Abstract

In this paper, the Particle Swarm Optimization (PSO) algorithm is modified to deal with Multiobjective Optimization Problems (MOPs). A mathematical model for predicting the dynamic response of the H. B. Robinson nuclear power plant, which represents an Initial Value Problem (IVP) of Ordinary Differential Equations (ODEs), is solved using Runge-Kutta formula. The resulted data values are represented as a system of nonlinear algebraic equations by interpolation schemes for data fitting. This system of fitted nonlinear algebraic equations represents a nonlinear multiobjective optimization problem. A Multiobjective Particle Swarm Optimizer (MOPSO) which is based on the Pareto optimality concept is developed and applied to maximize the above mentioned problem. Results show that MOPSO efficiently cope with the problem and finds multiple Pareto optimal solutions.

Kurzfassung

In dieser Arbeit wird der Partikel-Schwarm Optimierungsalgorithmus (PSO) modifiziert, um multiobjektive Optimierungsprobleme (MOP) zu behandeln. Ein mathematisches Modell für die Vorhersage der Leistungsfähigkeit des H. B. Robinson Kernkraftwerks, die ein Anfangswertproblem (IVP) für gewöhnliche Differenzialgleichungen (ODEs) darstellt, wurde unter Verwendung der Runge-Kutta-Gleichung gelöst. Die Ergebnisse werden dargestellt als System nicht-linearer algebraischer Gleichungen mit Interpolationsschemata für die Datenanpassung. Dieses System nicht-linearer algebraischer Gleichungen repräsentiert ein nicht-lineares multiobjektives Optimierungsproblem. Ein Multiobjektiver Partikel-Schwarm-Optimierer (MOPSO) auf der Basis des Pareto-Optimierungskonzepts wurde entwickelt und auf das beschriebene Problem angewendet. Experimentelle Ergebnisse zeigen, dass MOPSO das beschriebene Problem effizient löst und optimale, multiple Pareto-Lösungen findet.

References

1 Kerlin, T. W.; Katz, E. M.; Strange, J. E.: Theoretical and experimental dynamic analysis of the H. B. Robinson nuclear plant. Nuclear Technology30 (1976) 299Search in Google Scholar

2 Dormand, J. R.; Prince, P. J.: A family of embedded Runge-Kutta formulae. J. Comp. Applied Mathematics6 (1980) 1910.1016/0771-050X(80)90013-3Search in Google Scholar

3 Shampine, L. F.; Reichelt, M. W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing18 (1997) 110.1137/S1064827594276424Search in Google Scholar

4 Shampine, L. F.: Numerical Solution of Ordinary Differential Equations. Chapman & Hall, New York, 1994Search in Google Scholar

5 Daniel, C.; Wood, F. S.: Fitting Equations to Data. John Wiley & Sons, New York, 1980Search in Google Scholar

6 Marquardt, D.: An Algorithm for Least Squares Estimation of Nonlinear Parameters. SIAM Journal on Applied Mathematics11 (1963) 431Search in Google Scholar

7 Edgeworth, F. Y.: Mathematical Physics. P. Keagan, London, 1881Search in Google Scholar

8 Steuer, R. E.: Multiple criteria optimization. Theory, computation, and application. John Wiley & Sons, New York, 1986Search in Google Scholar

9 Pareto, V.: Cours D'Economie Politique, volume I and II, F. Rouge, Lausanne, 1896Search in Google Scholar

10 Coello, C.; Van Veldhuizen, A.; Lamont, B.: Evolutionary algorithms for solving multiobjective problems. Kluwer Academic Publishers, Boston, 200210.1007/978-1-4757-5184-0Search in Google Scholar

11 Coello, C.: A comprehensive survey of evolutionary based multiobjective optimization techniques. Knowledge and Info. Sys.3 (1999) 269.Search in Google Scholar

12 Zitzler, E.: Evolutionary algorithms for multiobjective optimizations: methods and applications, Ph. D. thesis, Swiss Federal Institute of Technology Zurich, Switzerland, November 1999Search in Google Scholar

13 Fonseca, M.; Fleming, J.: An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation vol. 3, no. 1, (1995) 1–16 10.1162/evco.1995.3.1.1Search in Google Scholar

14 Kennedy, J.; Eberhart, C.: Particle swarm optimization. Proceedings of the International Conference on Neural Networks, IEEE, NJ, (1995) 19421948Search in Google Scholar

15 Eberhart, R. C.; Kennedy, J.: A new optimizer using particle swarm theory. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, (1995) 3943Search in Google Scholar

16 Kennedy, J.: The particles swarm: social adaptation of knowledge. Proceedings of the International Conference on Evolutionary Computation, IEEE, NJ, (1997) l303–1308Search in Google Scholar

17 Kennedy, J.: The behavior of particles. In 7th International Conference on Evolutionary Programming, San Diego, California, (1998) 582589Search in Google Scholar

18 Kennedy, J.; Eberhart, R. C.: Swarm intelligence. Morgan Kaufmann Publishers, California, 2001Search in Google Scholar

19 Parsopoulos, E.; Vrahatis, N.: Particle swarm optimization method in multiobjective problems. Proceedings ACM Symposium on Applied Computing, SAC (2002) 603607Search in Google Scholar

20 Moore, J.; Chapman, R.: Application of particle swarm to multiobjective optimization. Unpublished paper, 1999Search in Google Scholar

Received: 2008-12-13
Published Online: 2013-04-05
Published in Print: 2009-04-01

© 2009, Carl Hanser Verlag, München

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