為了讓核反應器繼續臨界運轉，核反應器需在週期末進行新燃料裝填，而燃料佈局最佳化問題 (nuclear reactor reloaded optimization problem, NRROP) 即是在尋求最佳的裝填佈局。一般，在滿足額定功率的條件下，最佳化的目標在於使多週期燃料的使用率最大。但本研究的單週期燃料佈局設計，若追求最佳燃料使用率將使該週期末之燃料佈局內含之能量耗盡，使後續週期之佈局所含能量過低。故本研究不去追求固定燃料束組成之單週期燃料佈局的最佳燃料使用率，而是將燃料佈局最佳化問題定義為設計出符合安全規範且具有一定經濟效益之佈局。
過去數十年有許多演算法被發展並應用於解決單週期燃料佈局的最佳化問題，其中量子演化式演算法 (quantum evolutionary algorithm) 因其量子疊加態的概念易於展現所有可能的狀態而被重視。在過去的一些研究中，皆提到量子演化式演算法對於區域最佳解有極佳的搜尋能力，但是卻會有過早收斂的情形發生。本研究致力於優化量子演化式演算法的效用，並發展具有自調式學習能力之量子演化式演算法。具自調式學習機制之量子演化式演算法模擬人類於真實世界的自調式學習法，並實際解決此多重目標的最佳化問題。結果顯示，我們所提出的優之量子演化式演算法可有效改善過早收斂的情形，而具自調式學習能力之量子演化式演算法則能延續搜尋過程中的成功經驗，協助設計符合要求的燃料佈局。

To operate in the critical state, the nuclear power plant must be reloaded every cycle. Typically, the goal of nuclear reactor reloaded optimization problem is to design multi-cycle loading patterns that maximize the utilization of fuels. For the single-cycle loading pattern design problem we work on in this study, maximizing fuel utilization rate will lead to over burn-up fuel assemblies and leave less energy for following cycles. Thus, we are instead searching for a pattern that fulfills the nominal power output and satisfies the safety constraints.
For decades, many algorithms have been developed for loading pattern design. The quantum evolutionary algorithm (QEA) is the one that is famous for its capability of probabilistically representing all possible solutions. A small required population of individuals and superior search capability characterize this type of algorithm although it is also reported to have the premature convergence problem. In this study, we dedicate to propose approaches to resolve this issue. Furthermore, we also develop a scheme of self-regulated learning that will be used accompanied by QEA. The self-regulated learning is a process that mimics how human beings learn and can be used to solve the multi-objective optimization problem at hand. Results from several experiments illustrate the efficacy and performance of the proposed approach.

摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 vii
表目錄 viii
第一章 緒論 1
1.1研究目的 1
1.2文獻回顧 2
第二章 燃料佈局問題介紹 3
2.1核反應器介紹 3
2.2燃料束組成介紹 4
2.2.1新燃料束與燃耗燃料束 4
2.2.2整合燃料可燃毒素棒根數 4
2.2.3馬鞍山核電廠燃料束介紹 5
2.3佈局設計參數介紹 6
2.3.1週期末燃耗 6
2.3.2緩和劑溫度係數 6
2.3.3熱通道因子 8
2.4佈局方法介紹 10
第三章 量子演化式演算法 13
3.1適應函數 13
3.2量子演化式演算法 15
3.2.1基本概念 15
3.2.2計算流程 15
3.3解的建構 18
3.4小結與討論 23
第四章 優化之量子演化式演算法 25
4.1演化方式與設計廣度之關係探討 25
4.1.1問題發現 25
4.1.2解決方法 26
4.1.3小結與討論 30
4.2解的建構設計與設計廣度之關係探討 32
4.2.1問題發現 32
4.2.2解決方法 36
4.2.3小結與討論 36
4.3優化之量子演化式演算法結果討論 38
第五章 自調式學習效能之建構 40
5.1自調式學習基本概念 40
5.2應用自調式學習於燃料佈局最佳化問題 42
5.2.1量子個體亂數排列偏好之自調式學習 44
5.2.2對於新燃料束擺放位置之自調式學習 44
5.3具自調式學習效能之量子演化式演算法結果討論 46
第六章 結論 50
6.1量子演化式演算法 50
6.2優化之量子演化式演算法 51
6.2.1優化量子旋轉邏輯閘之量子演化式演算法 51
6.2.2優化解的建構方式及量子旋轉邏輯閘之量子演化式演算法 52
6.3具自調式學習效能之量子演化式演算法 54
第七章 未來展望 56
參考文獻 57

[1] DeChaine, M. D., Feltus, M. A., 1996. “Fuel management optimization using genetic algorithms and expert knowledge.”, Nucl. Sci. Eng. 152, 197–203.
[2] Alim, F., Ivanov, K., Levine, S. H., 2008a. “New genetic algorithms (GA) to optimize PWR reactors Part I: Loading pattern and burnable poison placement optimization techniques for PWRs. ”, Ann. Nucl. Energy 35, 93–112.
[3] Alim, F., Ivanov, K., Levine, S. H., 2008b. “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. Energy 35, 113–120.
[4] Li, Z., Levine, S.H. , “An automatic optimal pressurized water reactor reload design expert system. ”, Nuclear Science and Engineering, Volume: 118:2
[5] Hill, N., Parks, G., 2015. “Pressurized water reactor in-core nuclear fuel management by tabu search. ”, Ann. Nucl. Energy 75, 64–71.
[6] Lin, C., Chen, Y. H., 2014. “The max-min ant system and tabu search for pressurized water reactor loading pattern design. ”, Ann. Nucl. Energy 71, 388–398.
[7] Da Silva, M. H., Schirru, R., 2011. “Optimization of nuclear reactor core fuel reload using the new quantum PBIL. ”, Ann. Nucl. Energy 38, 610–614.
[8] Da Silva, M. H., Schirru, R., 2014. “A self-adaptive quantum PBIL method for the nuclear reload optimization. ”, Prog. Nucl. Energy 74, 103–109.
[9] Han, K. H., Kim, J. H., 2002. “Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans. ”, Evol. Comput. 6, 580–593.
[10] Nicolau, A. D. S., Schirru, R., Lima, A. M. M. D., 2012. “Nuclear reactor reload using quantum inspired algorithm. ”, Prog. Nucl. Energy 55, 40–48.
[11] Wu, S. C., Chan, T.H., Hsieh, M.S., Lin, C.,2016. “Quantum evolutionary algorithm and tabu search in pressurized water reactor loading pattern design. ”,Annals of Nuclear Energy 94,2016,773-782.
[12] 楊昭義、歐陽敏盛,核能發電工程學,水牛出版,臺灣,1997
[13] Lamarsh, J. R., Baratta, A. J., 2001. Introduction to Nuclear Engineering, 3rd Edition. Prentice-Hall.
[14] Lewins, J., Becker, M., 1999. Advances in nuclear science and technology. Kluwer Academic/Plenum Publishers, New York.
[15] Gul, S., Khan, M., Chughtai, M. K., 2001. Technical support to an operating PWR vis-à-vis safety analysis. IAEA-CN-164-4S13.
[16] Studsvik Scandpower, 2007. SIMULATE-3 User’s Manual. STUDSVIK/SOA/95/15-Rev 4.
[17] Barry J. Zimmerman, 1990, Self-Regulated Learning and Academic Achievement: An Overview, Educational Psychologist, 25:1, 3-17, DOI: 10.1207/s15326985ep2017_2
[18] 詹宗翰，「應用量子啟發式演算法與塔佈搜尋法於壓水式反應器爐心燃料佈局設計」，國立清華大學核子工程與科學研究所，碩士論文，中華民國104年。