Optimizing the dynamic response of the H. B. Robinson nuclear plant using multiobjective particle swarm optimization
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M. A. Elsays
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) 299Suche 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)90013-3Suche in Google Scholar
3 Shampine, L. F.; Reichelt, M. W.: The MATLAB ODE suite. SIAM Journal on Scientific Computing18 (1997) 110.1137/S1064827594276424Suche in Google Scholar
4 Shampine, L. F.: Numerical Solution of Ordinary Differential Equations. Chapman & Hall, New York, 1994Suche in Google Scholar
5 Daniel, C.; Wood, F. S.: Fitting Equations to Data. John Wiley & Sons, New York, 1980Suche in Google Scholar
6 Marquardt, D.: An Algorithm for Least Squares Estimation of Nonlinear Parameters. SIAM Journal on Applied Mathematics11 (1963) 431Suche in Google Scholar
7 Edgeworth, F. Y.: Mathematical Physics. P. Keagan, London, 1881Suche in Google Scholar
8 Steuer, R. E.: Multiple criteria optimization. Theory, computation, and application. John Wiley & Sons, New York, 1986Suche in Google Scholar
9 Pareto, V.: Cours D'Economie Politique, volume I and II, F. Rouge, Lausanne, 1896Suche in Google Scholar
10 Coello, C.; Van Veldhuizen, A.; Lamont, B.: Evolutionary algorithms for solving multiobjective problems. Kluwer Academic Publishers, Boston, 200210.1007/978-1-4757-5184-0Suche in Google Scholar
11 Coello, C.: A comprehensive survey of evolutionary based multiobjective optimization techniques. Knowledge and Info. Sys.3 (1999) 269.Suche 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 1999Suche 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.1995.3.1.1Suche in Google Scholar
14 Kennedy, J.; Eberhart, C.: Particle swarm optimization. Proceedings of the International Conference on Neural Networks, IEEE, NJ, (1995) 1942–1948Suche 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) 39–43Suche in Google Scholar
16 Kennedy, J.: The particles swarm: social adaptation of knowledge. Proceedings of the International Conference on Evolutionary Computation, IEEE, NJ, (1997) l303–1308Suche in Google Scholar
17 Kennedy, J.: The behavior of particles. In 7th International Conference on Evolutionary Programming, San Diego, California, (1998) 582–589Suche in Google Scholar
18 Kennedy, J.; Eberhart, R. C.: Swarm intelligence. Morgan Kaufmann Publishers, California, 2001Suche in Google Scholar
19 Parsopoulos, E.; Vrahatis, N.: Particle swarm optimization method in multiobjective problems. Proceedings ACM Symposium on Applied Computing, SAC (2002) 603–607Suche in Google Scholar
20 Moore, J.; Chapman, R.: Application of particle swarm to multiobjective optimization. Unpublished paper, 1999Suche in Google Scholar
© 2009, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- AVR prototype pebble bed reactor: a safety re-evaluation of its operation and consequences for future reactors
- Design Concept of the High Performance Light Water Reactor
- Behavior of CANDU fuel under power pulse conditions at the TRIGA reactor of INR Pitesti
- Plate heat exchanger – inertia flywheel performance in loss of flow transient
- Performance analyses of the communication networks of a modern supervision and control system of research reactors
- Thermal analytical model for MoO3 ampoules irradiated in a high neutron flux
- Effect of using various grades of plutonium in the protective liquid wall of an IFE type fusion reactor
- A discrete ordinates scheme for void fraction evaluation with nonstandard reflective conditions and weakly divergent beams
- Application of the Laplace transform method for the albedo boundary conditions in multigroup neutron diffusion eigenvalue problems in slab geometry
- Modified Chebyshev polynomial (UN) approximation in the neutron transport theory and computation of critical half thicknesses
- Optimizing the dynamic response of the H. B. Robinson nuclear plant using multiobjective particle swarm optimization
- Assessment for inside building dispersion of aerosol from an outdoor radiological release
- Technical Notes/Technische Mitteilungen
- Analysis of a steam generator tube rupture under realistic initial and boundary conditions
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- AVR prototype pebble bed reactor: a safety re-evaluation of its operation and consequences for future reactors
- Design Concept of the High Performance Light Water Reactor
- Behavior of CANDU fuel under power pulse conditions at the TRIGA reactor of INR Pitesti
- Plate heat exchanger – inertia flywheel performance in loss of flow transient
- Performance analyses of the communication networks of a modern supervision and control system of research reactors
- Thermal analytical model for MoO3 ampoules irradiated in a high neutron flux
- Effect of using various grades of plutonium in the protective liquid wall of an IFE type fusion reactor
- A discrete ordinates scheme for void fraction evaluation with nonstandard reflective conditions and weakly divergent beams
- Application of the Laplace transform method for the albedo boundary conditions in multigroup neutron diffusion eigenvalue problems in slab geometry
- Modified Chebyshev polynomial (UN) approximation in the neutron transport theory and computation of critical half thicknesses
- Optimizing the dynamic response of the H. B. Robinson nuclear plant using multiobjective particle swarm optimization
- Assessment for inside building dispersion of aerosol from an outdoor radiological release
- Technical Notes/Technische Mitteilungen
- Analysis of a steam generator tube rupture under realistic initial and boundary conditions
