Optimization and Engineering

, Volume 2, Issue 3, pp 251–276 | Cite as

Reloading Nuclear Reactor Fuel Using Mixed-Integer Nonlinear Optimization

  • Arie J. Quist
  • Kees Roos
  • Tam#x00E1;s Terlaky
  • Rene Van Geemert
  • Eduard Hoogenboom


A nodal nuclear reactor reload pattern optimization model is solved using mixed-integer nonlinear optimization techniques. Unlike currently used heuristic search methods, this method enables continuous optimization of the amount of Burnable Poisons in fresh fuel bundles in a natural way, which is shown in the first part of the article. The second part treats an algorithmic extension using dedicated cuts in a mixed-integer nonlinear optimization algorithm, which push the optimization towards solutions where local power peaks in parts of the core are avoided.

nonlinear mixed-integer optimization nuclear reactor fuel management reload pattern optimization 


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  1. I. P. Androulakis, C. D. Maranas, and C. A. Floudas, “BB: A global optimization method for general constrained nonconvex problems,” Journal of Global Optimization vol. 7, pp. 337–363, 1995.Google Scholar
  2. J. K. Axmann, “Parallel adaptive evolutionary algorithms for pressurized water reactor reload pattern optimizations,” Nuclear Technology vol. 119, pp. 276–292, 1997.Google Scholar
  3. J. N. Carter, “Genetic algorithms for incore fuel management and other recent developments in optimisation,” Advances in Nuclear Science and Technology vol. 25, pp. 113–154, 1997.Google Scholar
  4. M. D. DeChaine and M. A. Feltus, “Fuel management optimization using genetic algorithms and expert knowledge,” Nuclear Science and Engineering vol. 124, pp. 188–196, 1996.Google Scholar
  5. A. J. de Jong, “Reloading pattern design for batch refuelled nuclear reactors,” Technical Report IRI 131-95-010, Delft University of Technology, 1995.Google Scholar
  6. E. de Klerk, T. Illés, A. J. de Jong, C. Roos, T. Terlaky, J. Valkó, and J. E. Hoogenboom, “Optimization of nuclear reactor reloading patterns,” Annals of Operations Research vol. 69, pp. 65–84, 1997.Google Scholar
  7. J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis, Wiley & Sons: New York, 1976.Google Scholar
  8. R. Horst and H. Tuy, Global Optimization; Deterministic Approaches, Springer-Verlag: Berlin, 1990.Google Scholar
  9. T. K. Kim and C. H. Kim, “Determination of optimized PWR fuel loading pattern by mixed integer programming,” in Proceedings of PHYSOR96, Mito, Japan, 1996, pp. I76–I85.Google Scholar
  10. T. K. Kim and C. H. Kim, “Mixed integer programming for pressurized water reactor fuel-loading-pattern optimization,” Nuclear Science and Engineering vol. 127, pp. 346–357, 1997.Google Scholar
  11. D. J. Kropaczek and P. J. Turinsky, “In-core nuclear fuel management optimization for pressurized water reactors utilizing simulated annealing,” Nuclear Technology vol. 95, pp. 9–32, 1991.Google Scholar
  12. C. Lin, J.-I. Yang, K.-J. Lin, and Z.-D. Wang, “Pressurized water reactor loading pattern design using the simple tabu search,” Nuclear Science and Engineering vol. 129, pp. 61–71, 1998.Google Scholar
  13. G. I. Maldonado, P. J. Turinsky, and D. J. Kropaczek, “Employing nodal generalized perturbation theory for the minimization of feed enrichment during pressurized water reactor in-core fuel management optimization,” Nuclear Science and Engineering vol. 121, pp. 312–325, 1995.Google Scholar
  14. G. T. Parks, “An intelligent stochastic optimization routine for in-core fuel cycle design,” Transactions of the American Nuclear Society vol. 57, pp. 259–260, 1988.Google Scholar
  15. G. T. Parks, “Multi-objective pressurized water reactor reload core design by nondominated genetic algorithm search,” Nuclear Science and Engineering vol. 124, pp. 178–187, 1996.Google Scholar
  16. P. W. Poon and G. T. Parks, “Application of genetic algorithms to in-core fuel management optimization,” in Proceedings Joint International Conference on Mathematics and Supercomputing in Nuclear Applications, Karlsruhe, 1993, vol. 1, pp. 777.Google Scholar
  17. A. J. Quist, R. van Geemert, J. E. Hoogenboom, T. Illés, E. de Klerk, C. Roos, and T. Terlaky, “Application of nonlinear optimization to reactor core fuel reloading,” Annals of Nuclear Energy vol. 26, no. 5, pp. 423–448, 1998.Google Scholar
  18. A. J. Quist, R. van Geemert, J. E. Hoogenboom, T. Illés, E. de Klerk, C. Roos, and T. Terlaky, “Finding optimal nuclear reactor core reload patterns using nonlinear optimization and search heuristics,” Engineering Optimization vol. 32, pp. 143–176, 1999.Google Scholar
  19. T. Šmuc, D. Pevec, and B. Petrovi?, “Annealing strategies for loading pattern optimization,” Annals of Nuclear Energy vol. 21, pp. 325–336, 1994.Google Scholar
  20. J. G. Stevens, K. S. Smith, K. R. Rempe, and T. J. Downar, “Optimization of pressurized water reactor shuffling by simulated annealing with heuristics,” Nuclear Science and Engineering vol. 121, pp. 67–88, 1995.Google Scholar
  21. J. S. Suh and S. H. Levine, “Optimized automatic reload program for pressurized water reactors using simple direct optimization techniques,” Nuclear Science and Engineering vol. 105, pp. 371–382, 1990.Google Scholar
  22. R. van Geemert, A. J. Quist, and J. E. Hoogenboom, “Reload pattern optimization by application of multiple cyclic interchange algorithms,” in Proceedings of PHYSOR96, Mito, Japan, 1996, pp. I38–I47.Google Scholar
  23. F. C. M. Verhagen and M. van der Schaar, “Simulated annealing in LWR fuel management,” in TOPNUX'93 Proceedings, 1993, vol. 2, pp. 37–39.Google Scholar
  24. S. Wei and C. Pingdong, “A new approach for low-leakage reload core multi-cycle optimization design,” in Proceedings of PHYSOR96, Mito, Japan, 1996, pp. I86–I95.Google Scholar
  25. A. Yamamoto, “Comparison between equilibrium cycle and successive multi-cycle optimization methods for in-core fuel management of pressurized water reactors,” in Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing for Nuclear Applications, Saratoga Springs, New York, 1997, pp. 769–781, American Nuclear Society, Inc.Google Scholar
  26. N. Zavaljevski, “A model for fuel shuffling and burnable absorbers optimization in low leakage PWR's,” Annals of Nuclear Energy vol. 17, no. 4, pp. 217–220, 1990.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Arie J. Quist
    • 1
  • Kees Roos
    • 1
  • Tam#x00E1;s Terlaky
    • 2
  • Rene Van Geemert
    • 3
  • Eduard Hoogenboom
    • 3
  1. 1.Faculty of Information Technology and SystemsDelft University of TechnologyDelftThe Netherlands
  2. 2.McMaster UniversityHamiltonCanada
  3. 3.Interfaculty Reactor InstituteDelft University of TechnologyDelftThe Netherlands

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