沸水式反應器燃料再裝填的爐心設計包括燃料佈局設計與控制棒佈局設計，燃料佈局設計在於燃料束的排列組合，目的在找出一個燃料佈局具有足夠的停機餘裕與熱限值餘裕，以確保可以成功設計出合於設計要求且週期長度足夠的控制棒佈局。控制棒佈局設計則是要決定控制棒插入的深度，在每個燃耗點的熱限值如：最小臨界功率比（MCPR）、最大線性熱產生率（MLHGR）、最大平面線性熱產生率（MAPLHGR）要符合設計要求，停機餘裕與週期長度也要符合設計要求。
本研究是以分等螞蟻系統（rank-based ant system, RAS）做為沸水式核電廠燃料佈局與控制棒佈局自動化設計工具的搜尋方法，分等螞蟻系統是蟻群最佳化演算法的一種，適合用來處理最佳化問題，此演算法可納入啟發式的知識與經驗以減少計算時間。在燃料佈局方面，本研究在每一個八分之一爐心的位置上，以蟻群最佳化演算法的機率選擇方式，選擇一根燃料束來放置，其他的七個對稱區域則將同一種型態的燃料束放到對稱的位置上。直到所有位置都已放置燃料束，以黑林燃耗計算週期長度、黑林燃耗週期結束時的熱限值與燃料週期開始時的停機餘裕來評估燃料佈局，並做為費洛蒙濃度更新的依據。在控制棒佈局方面，沸水式核電廠控制棒佈局是依A2-B1-A1-B2或A1-B2-A2-B1的棒序來設計，當一個控制棒佈局產生後，必需以SIMULATE-3程式計算軸向功率分佈、有效中子增殖因數、停機餘裕以及三個熱限值，用以評估此控制棒佈局並更新費洛蒙濃度。本方法以核二廠的兩個燃料週期作驗證，可在合理的計算時間內設計出合於要求的燃料佈局，並可成功的以這些燃料佈局設計出符合設計要求且週期長度足夠的控制棒佈局。

The reload design of a boiling water reactor (BWR) consists of fuel loading pattern design and control rod pattern design. The fuel loading pattern design is to permute the fuel assemblies so that shutdown margin requirement is fulfilled and the thermal limit margin is good enough to guarantee the satisfactory control rod pattern design. The control rod pattern design is to determine the inserted depth of control rods at each exposure point so that the thermal limits such as minimum critical power ratio (MCPR), maximum linear heat generation rate (MLHGR), and maximum average planar linear heat generation rate (MAPLHGR) meet the margin requirement and shutdown margin and cycle length are fulfilled.
Automatic design of boiling water reactor loading pattern and control rod pattern were developed using the rank-based ant system (RAS) which is a variety of ant colony optimization (ACO) algorithm. The ACO algorithm is an effective optimization algorithm for combinatorial optimization problem and the heuristic rules of ACO algorithm were adopted to reduce search space and computation time. In loading pattern design, to reduce design complexity, fuel assemblies (FAs) were chosen to load the positions of one-eighth core geometry using probabilistic solution construction of ACO algorithm and then the corresponding fuel assemblies were loaded into the other part of the core. When the pattern was determined, Haling cycle length, the thermal limits at the end of cycle, and beginning of cycle (BOC) shutdown margin (SDM) were calculated using SIMULATE-3 code, which were used to evaluate the loading pattern for updating pheromone concentration of ACO algorithm. In control rod pattern design which followed either the A2-B1-A1-B2 or A1-B2-A2-B1 sequence in this study. After the control rod pattern was determined, the axial power distribution, effective multiplication factor (keff), shutdown margin, and three thermal limits were calculated using SIMULATE-3 code, which were then used to evaluate the control rod pattern and update the pheromone concentration. The developed design methodology was demonstrated using two fuel reload cycle of Kuosheng nuclear power plant. The results show that the designed satisfactory reload design with an acceptable cycle length can be achieved within a reasonable computation time.

1. J.L. Francois and H.A. Lόpez, “SOPRAG: a system for boiling water reactors reload pattern optimization using genetic algorithms”, Ann. Nucl. Eenrgy, 26, 1053-1063 (1999).
2. Y. Kobayashi and E. Aiyoshi, “Optimization of Boiling Water Reactor Loading Pattern Using Two-Stage Genetic Algorithm”, Nucl. Sci. Eng., 142, 119-139 (2002).
3. Yoko Kobayashi, Eitaro Aiyoshi, “Optimization of a Boiling Water Reactor Loading Pattern Using an Improved Genetic Algorithm”, Nucl. Technol., 143, 144-151 (2003).
4. J.J. Oritz and I. Requena, “An Order Coding Genetic Algorithm to Optimize Fuel Reloads in a Nuclear Boiling Water Reactor”, Nucl. Sci. Eng., 146, 88-98 (2004).
5. C. Martin-del-Campo, J.L. Francois, L. Avendano, and M. Gonzalez, “Development of a BWR loading pattern design system based on modified genetic algorithms and knowledge”, Ann. Nucl. Eenrgy, 31, 1901-1911 (2004).
6. Juan Jose Ortiz, Alejandro, Jose Luis Montes, and Raul Perusquia, “A New System to Fuel Loading and Control Rod Pattern Optimization in Boiling Water Reactors”, Nucl. Sci. Eng., 157, 236-244 (2007).
7. C. Martin-del-Campo, M.A Palomera-Perez, and J.L. Francois, “Advanced and flexible genetic algorithms for BWR fuel loading pattern optimization”, Ann. Nucl. Eenrgy, 36, 1553-1559 (2009).
8. Michael D. DeChaine and Madline Anne Feltus, “Nuclear Fuel Management Optimization Using Genetic Algorithms”, Nucl. Technol., 111, 109-114 (1995).
9. G. T. Parks, “Multiobjective Pressurized Water Reactor Reload Core Design by Nondominated Genetic Algorithm Search”, Nucl. Sci. Eng., 124, 178-187 (1996).
10. Michael D. DeChaine and Madeline A. Feltus, “Fuel Management Optimization Using Genetic Algorithms and Expert Knowledge”, Nucl. Sci. Eng., 124, 188-196 (1996).
11. Jun Zhao, Brian Knight, Ephraim Nissan, Alan Soper, “FuelGen: a genetic algorithm-based system for fuel loading pattern design in nuclear power reactors”, Expert Systems with Applications, 14, 461-470 (1998).
12. Jorge Luiz C. Chapot, Fernando Carvalho Da Silva, Roberto Schirru, “A new approach to the use of genetic algorithms to solve the pressurized water reactor's fuel management optimization problem” , Ann. Nucl. Eenrgy, 26, 641-655 (1999).
13. Wu Hongchun, “Pressurized water reactor reloading optimization using genetic algorithms”, Ann. Nucl. Eenrgy, 28, 1329-1341 (2001).
14. Adem Erdoğan, Melih Geckinli, “A PWR reload optimisation code (XCore) using artificial neural networks and genetic algorithms”, Ann. Nucl. Eenrgy, 30, 35-53 (2003).
15. Fatih Alim, Kostadin Ivanov, Samuel H. Levine, “New genetic algorithms (GA) to optimize PWR reactors Part I: Loading pattern and burnable poison placement optimization techniques for PWRs”, Ann. Nucl. Eenrgy, 35, 93-112 (2008).
16. Fatih Alim, Kostadin N. Ivanov, Serkan Yilmaz, Samuel H. Levine, “New genetic algorithms (GA) to optimize PWR reactors Part II: Simultaneous optimization of loading pattern and burnable poison placement for the TMI-1 reactor”, Ann. Nucl. Eenrgy, 35, 113-120 (2008).
17. Fatih Alim, Kostadin Ivanov, Samuel H. Levine, “New genetic algorithms (GA) to optimize PWR reactors Part III: The Haling power depletion method for in-core fuel management analysis”, Ann. Nucl. Eenrgy, 35, 121-131 (2008).
18. Wagner F. Sacco, Marcelo D. Machado, Claudio M. N. A. Pereira, Roberto Schirru, “The fuzzy clearing approach for a niching genetic algorithm applied to a nuclear reactor core design optimization problem”, Ann. Nucl. Eenrgy, 31, 55-69 (2004).
19. A. Kemal Ziver, Jonathan N. Carter, Christopher C. Pain, Cassiano R. E. de Oliveira, Antony J. H. Goddard, Richard S. Overton, “Multicycle Optimization of Advanced Gas-Cooled Reactor Loading Patterns Using Genetic Algorithms”, Nucl. Technol., 141, 122-141 (2004).
20. A. K. Ziver, C. C Pain, J. N. Carter, C. R. E. de Oliveira, A. J. H. Goddard, R. S. Overton, “Genetic algorithms and artificial neural networks for loading pattern optimisation of advanced gas-cooled reactors”, Ann. Nucl. Eenrgy, 31, 431-457 (2004).
21. C. Martin del Campo, J. L. Francois, H. A. Lopez, “AXIAL: a system for boiling water reactor fuel assembly axial optimization using genetic algorithms”, Ann. Nucl. Eenrgy, 28, 1667-1682 (2001).
22. Cecilia Martin-del-Campo, Juan Luis Francois, Roberto Carmona, Ivonne P. Oropeza, “Optimization of BWR fuel lattice enrichment and gadolinia distribution using genetic algorithms and knowledge”, Ann. Nucl. Eenrgy, 34, 248-253 (2007).
23. S. Jagawa, T. Yoshii, and A. Fukao, “Boiling Water Reactor Loading Pattern Optimization Using Simple Linear Perturbation and Modified Tabu Search Methods”, Nucl. Sci. Eng., 138, 67-77 (2001).
24. A. Castillo, G. Alonso, L.B. Morales, C. Martin-del-Campo, J.L. Francois, and E. del Valle, “BWR fuel reloads design using Tabu search technique”, Ann. Nucl. Eenrgy, 31, 151-161 (2004).
25. A. Castillo, J.J. Oritz, J.L. Montes, and R. Perusquia, “Fuel loading and control rod patterns optimization in a BWR using tabu search”, Ann. Nucl. Eenrgy, 34, 207-212 (2007).
26. C. Martin-del-Campo, A.M. Barragan, and M.A Palomera-Perez, “Boiling Water Reactor Fuel Lattice Enrichment Distribution Optimization Using Tabu Search and Fuzzy Logic”, Nucl. Technol., 157, 251-260 (2007)
27. Brian R. Moore, Paul J. Turinsky, Atul A. Karve, “FORMOSA-B: A Boiling Water Reactor In-Core Fuel Management Optimization Package”, Nucl. Technol., 126, 153-169 (1999).
28. Atul A. Karve, Paul J. Turinsky, “FORMOSA-B: A Boiling Water Reactor In-Core Fuel Management Optimization Package II”, Nucl. Technol., 131, 48-68 (2000).
29. A.A. Karve and P.J. Turinsky, “FORMOSA-B: a Boiling Water Reactor In-Core Fuel Management Optimization Package III”, Nucl. Technol., 135, 241-251 (2001).
30. T.K. Park, H.G. Joo, C.H. Kim, and H.C. Lee, “Multiobjective Loading Pattern Optimization by Simulated Annealing Employing Discontinuous Penalty Function and Screening Technique”, Nucl. Sci. Eng., 162, 134-147 (2009).
31. Juan Jose Ortiz, Ignacio Requena, “Using a multi-state recurrent neural network to optimize loading patterns in BWRs”, Ann. Nucl. Eenrgy, 31, 789-803 (2004).
32. Mostafa Sadighi, Saeid Setayeshi, Ali Akbar Salehi, “PWR fuel management optimization using neural networks”, Ann. Nucl. Eenrgy, 29, 41-51 (2002).
33. Eduardo Fernandes Faria, Claubia Pereira, “Nuclear fuel loading pattern optimisation using a neural network”, Ann. Nucl. Eenrgy, 30, 603-613 (2003).
34. Joachim K. Axmann, “Parallel Adaptive Evolutionary Algorithms for Pressurized Water Reactor Reload Pattern Optimizations”, Nucl. Technol., 119, 276-291 (1997).
35. J.J. Ortiz, A. Castillo, J.L. Montes, and R. Perusquia, “Nuclear Fuel Lattice Optimization Using Networks and a Fuzzy Logic System”, Nucl. Sci. Eng., 162, 148-157 (2009).
36. J. Esquivel-Estrada, J.J. Ortiz-Servin, J.A. Castillo, and R. Perusquia, “Azcaxalli: Asystem Based on Ant Colony Optimization Algorithms, Applied to Reloads Design in a Boiling Water Reactor”, Ann. Nucl. Eenrgy, 38, 103-111 (2011).
37. A.M.M. de Lima, R. Schirru, F.C. da Silva, and J.A.C.C. Medeiros, “A Nuclear Reactor Core Fuel Reload Optimization Using Artificial Ant Colony Connective Networks”, Ann. Nucl. Eenrgy, 35, 1606-1612 (2008).
38. L. Machado, and R. Schirru, “The Ant-Q Algorithm Applied to the Nuclear Reload Problem”, Ann. Nucl. Eenrgy, 29, 1455-1470 (2002).
39. I.M.S. de Oliverira, and R. Schirru, “Swarm Intelligence of Artificial Bees Applied to In-Core Fuel Management Optimization”, Ann. Nucl. Eenrgy, 38, 1039-1045 (2011).
40. A.A. de Moura Meneses, M.D. Machado, and R. Schirru, “Particle Swarm Optimization Applied to the Nuclear Reload Problem of a Pressurized Water Reactor”, Prog. Nucl. Eenrgy, 51, 319-326 (2009).
41. D. Babazadeh, M. Boroushaki, and C. Lucas, “Optimization of Fuel Core Loading Pattern Design in a VVER Nuclear Power Reactors Using Particle Swarm Optimization (PSO)”, Ann. Nucl. Eenrgy, 36, 923-930 (2009).
42. M. Waintraub, R. Schirru, and C. M.N.A. Pereira, “Multiprocessor Modeling of Parallel Particle Swarm Optimization Applied to Nuclear Engineering Problems”, Prog. Nucl. Eenrgy, 51, 680-688 (2009).
43. A.A. de Moura Meneses, L.M. Gambardella, and R. Schirru, “A New Approach for Heuristics-Guided Search in the In-Core Fuel Management Optimization”, Prog. Nucl. Eenrgy, 52, 339-351 (2010).
44. F. Khoshahval, A. Zolfaghari, H. Minuchehr, M. Sadighi, and A. Norouzi, “PWR Fuel Management Optimization Using Continuous Particle Swarm Intelligence”, Ann. Nucl. Eenrgy, 37, 1263-1271 (2010).
45. Roberto P. Domingos, Roberto Schirru and Claudio M. N. A. Pereira, “Particle Swarm Optimization in Reactor Core Design”, Nucl. Sci. Eng., 152, 197-203 (2006).
46. Michael V. McMahon, Michael J. Driscoll, Edward E. Pilat, Neil E. Todreas, “Reload Light Water Reactor Core Designs for an Ultralong Operating Cycle”, Nucl. Technol., 126, 32-47 (1999).
47. Elizebeth M. Maag, Dave Knott, “BWR Reload Strategy Based on Fixing Once-Burnt Fuel Between Cycles”, Nucl. Technol., 136, 278-291 (2001).
48. Yoko Kobayashi, Eitaro Aiyoshi, “Automated Core Design”, Nucl. Technol., 151, 77-85 (2005).
49. G.H.F. Caldas, and R. Schirru, “Parameterless Evolutionary Algorithm Applied to the Nuclear Reload Problem”, Ann. Nucl. Eenrgy, 35, 583-590 (2008).
50. J.J. Ortiz, A. Castillo, J.L. Montes, R. Perusquia, and J.L. Hernandez, “Nuclear Fuel Lattice Optimization Using Neural Networks and a Fuzzy Logic System”, Nucl. Sci. Eng., 162, 148-157 (2009).
51. A.A. de Moura Meneses, P. Rancoita, R. Schirru, and L.M. Gambardella, “A Class-Based Search for the In-Core Fuel Management Optimization of a Pressurized Water Reactor”, Ann. Nucl. Eenrgy, 37, 1554-1560 (2010).
52. A.H. Fadaei, N.M. Moghaddam, E. Zahedinejad, M.M. Fadaei, and S. Kia, “Fuel management optimization based on power profile by Cellular Automata”, Ann. Nucl. Eenrgy, 37, 1712-1722 (2010).
53. S. Jiang, A.K. Ziver, J.N. Carter, C.C. Pain, A.J.H. Goddard, S. Franklin, H.J. Phillips, “Estimation of distribution algorithms for nuclear reactor fuel management optimization”, Ann. Nucl. Eenrgy, 33, 1039-1057 (2006).
54. Juan-Luis Francois, Cecilia Martin-del-Campo, Luis B. Morales, Miguel-Angel Palomera, “Development of a Scatter Search Optimization Algorithm for Boiling Water Reactor Fuel Lattice Design”, Nucl. Sci. Eng., 155, 367-377 (2007).
55. M. Dorigo, “Optimization, learning and natural algorithms”, PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy [in Italian] (1992).
56. M. Dorigo, and L.M. Gambardella, “Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem”, IEEE Trans Evolutionary Comput, 1997;1(1): 53-66.
57. V. Maniezzo, and A. Colorni, “The ant system applied to the quadratic assignment problem”, IEEE Trans. Data Knowledge Eng. 11 (5) (1999) 769–778.
58. Blum C, “Ant colony optimization: Introduction and recent trends”, Physics of Life Reviews, 2, 353-373 (2005).