模擬最佳化經常被使用對複雜系統中進行最佳化求解，然而在複雜系統中所包含之問題特性相當錯綜複雜，因考量特性不同而存在許多種不同細緻度的模擬模型。當運用越高細緻度模型進行模擬系統評估時雖然能夠較準確，卻會需要耗費較長的系統評估時間以及越高的成本。而低細緻度模型雖有偏誤但其績效趨勢可能會反映部份高細緻度模型之績效趨勢。因此本論文將探討如何有效結合多細緻度模型，並以低、高細緻度模型之相關趨勢於模擬最佳化中以節省求解時間、提高求解效率。
本研究以彈性製造系統(Flexible Manufacturing System)的同步進行機台與車輛排程為對象，透過區域控制以及替代機台的特性，進行本研究之高、低細緻度模型設置。為了能有效利用低、高細緻度模型之間的關係，本論文將引用MO2TOS(Multi-fidelity Optimization with Ordinal Transformation and Optimal Sampling)架構對此FMS同步排程問題進行求解。
在MO2TOS架構中，如何依據低細緻度模型績效進行抽樣與分組將會是運用MO2TOS進行模擬最佳化的求解重點。由於模型之間相關程度將可反映出模型之間績效趨勢一致性。本研究提出以Adaptive Sampling藉由求解過程中持續增加的高細緻度模型績效，並已逐漸收斂之模型相關程度進行抽樣方法的更新，將可避免選擇到不適當之抽樣方法。導入Adaptive Sampling後除了求解品質有效提升外，在高與低相關程度模型下平均可以節省45.39%與22.71%模擬資源的使用。在分組方法部分，MO2TOS採用等距方式進行方案分組，然後高細緻度模型績效中相似解之個數並不一定相等，使用等距分組易使組間差異不明顯，進而使資源分配不佳。本研究提出Adaptive Grouping以持續抽樣所得到模型相關資訊更新組別，在高與低相關程度之多細緻度模型下，導入Adaptive Grouping平均可以節省28.45%與17.94%模擬資源的使用。

In this research, Multi-fidelity Optimization with Ordinal Transformation and Optimal Sampling (MO2TOS) is exploite to solve the simultaneous scheduling problem of machines and automated guided vehicles (AGVs) in flexible manufacturing system (FMS). Fidelity represented the degree to which a simulation replicates reality. Because of FMS contains lots of system characteristics and flexibilities, and there are many different fidelity models exist which considerd different system features.
Evaluating system via higher fidelity model can be more accurately, but it will cause time-consuming and will bring higher cost. Although lower fidelity model may suffered bias, but faster evaluation and the performance can provide partial of trend between low and high fidelity models. It is important to enhance the efficiency of optimization by using multi-fidelity models.
In MO2TOS, applied an inappropriate sampling method will lead a poor quality of optimization. Hence Adaptive Sampling is proposed to update the sampling method by sample correlation coefficient. The correlation coefficient can present the trend between multi-fidelity models, updating the sampling method according to the sample correlation coefficient can enhance the efficiency of optimization and save 45.39% and 22.71% of simulation resources for higher and lower correlation models.
Grouping method is one of main factors which may affect the quality of optimization significantly. In this research, Adaptive Grouping is proposed to update the group after every iteration of MO2TOS. It may significantly enhance the gap between groups, further to allocate resource effectively and save 28.45% and 17.94 of simulation resources for higher and lower correlation models.

第一章 緒論
1.1 研究背景與動機
1.2 研究目的
1.3 研究範圍
1.4 研究步驟與方法
第二章 文獻回顧
2.1 模型細緻度相關文獻
2.1.1 細緻度定義
2.1.2 多細緻度模型相關研究
2.2 彈性製造系統
2.2.1 同步排程
2.2.2 替代機台
2.2.3 區域控制
2.3 模擬最佳化方法
第三章 運用高、低細緻度模型於彈性製造系統
3.1 問題描述
3.2 MO2TOS
3.2.1 Ordinal Transformation (OT)
3.2.2 Optimal Sampling (OS)
3.2.3 MO2TOS流程圖
3.3 彈性製造系統之多細緻度模型設定
3.3.1 低細緻度模型1
3.3.2 低細緻度模型2
3.3.3 高細緻度模型
3.4 模擬模式建構
3.5 MO2TOS應用
第四章 MO2TOS深入分析
4.1 多細緻度模型相關程度探討
4.2 MO2TOS效益
4.2.1 Ordinal Transformation效益
4.2.2 Optimal Sampling效益
第五章 導入Adaptive Sampling
5.1 Adaptive Sampling方法論
5.1.1 模型相關係數選擇
5.1.2 Adaptive Sampling
5.1.3 驗證結果與分析
5.2 與MO2TOS-E進行比較
5.2.1 MO2TOS-E方法
5.2.2 驗證結果與分析
5.3 實驗結論
第六章 導入Adaptive Grouping
6.1 Adaptive Grouping方法論
6.1.1 K-means方法
6.1.2 Adaptive Grouping
6.1.3 驗證結果與分析
6.2 實驗結論
第七章 結論與建議
7.1 結論
7.2 建議
參考文獻

[1] 林則孟，“系統模擬理論與應用”，滄海書局，2001。
[2] 張祐翔，“應用模擬最佳化於FMS之機台與車輛同步排程”，清華大學工業工程與工程管理研究所碩士論文，2013。
[3] 許雅寧，“粒子群聚演算法於FMS之機台與車輛同步排程”，清華大學工業工程與工程管理研究所碩士論文，2014。
[4] 黎士賢，”網路式移動區域控制無人搬運車系統”，中央大學工業管理研究所碩士論文，1999。
[5] Abdelmaguid, T. F., Nassef, A. O., Kamal, B. A., & Hassan, M. F. (2004). A hybrid GA/heuristic approach to the simultaneous scheduling of machines and automated guided vehicles. International journal of production research, 42(2), 267-281.
[6] Alessi, S. M. (2000). Simulation design for training and assessment. Aircrew training and assessment, 197-222.
[7] Anwar, M. F., & Nagi, R. (1998). Integrated scheduling of material handling and manufacturing activities for just-in-time production of complex assemblies.International Journal of Production Research, 36(3), 653-681.
[8] Bagchi, T. P. (1999). Multiobjective scheduling by genetic algorithms. Springer Science & Business Media.
[9] Balabanov, V., & Venter, G. (2004, August). Multi-fidelity optimization with high-fidelity analysis and low-fidelity gradients. In 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (Vol. 4459).
[10] Bilge, Ü., & Ulusoy, G. (1995). A time window approach to simultaneous scheduling of machines and material handling system in an FMS. Operations Research, 43(6), 1058-1070.
[11] Butler, K. W., Veltre, D. E., & Brady, D. (2009). Implementation of active learning pedagogy comparing low-fidelity simulation versus high-fidelity simulation in pediatric nursing education. Clinical Simulation in Nursing, 5(4), e129-e136.
[12] Chan, F. T. S., Chaube, A., Mohan, V., Arora, V., & Tiwari, M. K. (2010). Operation allocation in automated manufacturing system using GA-based approach with multifidelity models. Robotics and Computer-Integrated Manufacturing, 26(5), 526-534.
[13] Chen, C. H. (2010). Stochastic simulation optimization: an optimal computing budget allocation (Vol. 1). World scientific.
[14] Conway, R. W., Maxwell, W. L., & Miller, L. W. (2012). Theory of scheduling. Courier Corporation.
[15] Dahl, Y., Alsos, O. A., & Svanæs, D. (2010). Fidelity considerations for simulation-based usability assessments of mobile ICT for hospitals. Intl. Journal of Human–Computer Interaction, 26(5), 445-476.
[16] Davis, P. K., & Bigelow, J. H. (1998). Experiments in multiresolution modeling (MRM) (No. RAND/MR-1004-DARPA). RAND CORP SANTA MONICA CA.
[17] Dieckmann, P., Gaba, D., & Rall, M. (2007). Deepening the theoretical foundations of patient simulation as social practice. Simulation in Healthcare,2(3), 183-193.
[18] Fanti, M. P. (2002). Event-based controller to avoid deadlock and collisions in zone-control AGVS. International Journal of Production Research, 40(6), 1453-1478.
[19] Fernández, E., & Besuievsky, G. (2012). Inverse lighting design for interior buildings integrating natural and artificial sources. Computers & Graphics,36(8), 1096-1108.
[20] Forrester, A. I., Sóbester, A., & Keane, A. J. (2007, December). Multi-fidelity optimization via surrogate modelling. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 463, No. 2088, pp. 3251-3269). The Royal Society.
[21] Gano, S. E., Renaud, J. E., & Sanders, B. (2005). Hybrid variable fidelity optimization by using a kriging-based scaling function. Aiaa Journal, 43(11), 2422-2433.
[22] Gnanavel Babu, A., Jerald, J., Noorul Haq, A., Muthu Luxmi, V., & Vigneswaralu, T. P. (2010). Scheduling of machines and automated guided vehicles in FMS using differential evolution. International Journal of Production Research, 48(16), 4683-4699.
[23] Groover, M. P. (2007). Automation, production systems, and computer-integrated manufacturing. Prentice Hall Press.
[24] Han, M. H., & McGinnis, L. F. (1989). Control of material handling transporter in automated manufacturing. IIE transactions, 21(2), 184-190.
[25] Henderson, S. G., & Nelson, B. L. (Eds.). (2006). Handbooks in Operations Research and Management Science: Simulation: Simulation (Vol. 13). Elsevier.
[26] Hao, W., Shaoping, W., & Tomovic, M. M. (2010). Modified sequential Kriging optimization for multidisciplinary complex product simulation. Chinese Journal of Aeronautics, 23(5), 616-622.
[27] Harmonosky, C. M. (1995, December). Simulation-based real-time scheduling: review of recent developments. In Proceedings of the 27th conference on Winter simulation (pp. 220-225). IEEE Computer Society.
[28] Ho, Y. C., & Wang, C. R. (1997). A Shifting-Zone Control Strategy for Vehicle-Collision Prevention in a Multiple-Vehicle AGV System. In Proceedings of the 14th International Conference on Production Research, OSAKA, Japan.
[29] Huang, E., Xu, J., Zhang, S., & Chen, C. H. (2015). Multi-fidelity Model Integration for Engineering Design. Procedia Computer Science, 44, 336-344.
[30] Huang, D., Allen, T. T., Notz, W. I., & Miller, R. A. (2006). Sequential kriging optimization using multiple-fidelity evaluations. Structural and Multidisciplinary Optimization, 32(5), 369-382.
[31] Jerald, J., Asokan, P., Saravanan, R., & Rani, A. D. C. (2006). Simultaneous scheduling of parts and automated guided vehicles in an FMS environment using adaptive genetic algorithm. The International Journal of Advanced Manufacturing Technology, 29(5-6), 584-589.
[32] Kanazaki, M., Takagi, H., & Makino, Y. (2013). Mixed-fidelity efficient global optimization applied to design of supersonic wing. Procedia Engineering, 67, 85-99.
[33] Karabtik, S., & Sabuncuolu, I. (1993, May). A beam search based algorithm for scheduling machines and AGVs in an FMS. In Proceedings of the Second Industrial Engineering Research Conference, Los Angeles (pp. 308-312).
[34] Kim, C. W., & Tanchoco, J. M. (1991). Conflict-free shortest-time bidirectional AGV routeing. THE INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, 29(12), 2377-2391.
[35] Koziel, S., & Leifsson, L. Þ. (2013, June). Shape-Preserving Response Prediction for Engineering Design Optimization. In ICCS (pp. 879-888).
[36] Kumar, M. S., Janardhana, R., & Rao, C. S. P. (2011). Simultaneous scheduling of machines and vehicles in an FMS environment with alternative routing. The International Journal of Advanced Manufacturing Technology, 53(1-4), 339-351.
[37] Lacomme, P., Moukrim, A., & Tchernev*, N. (2005). Simultaneous job input sequencing and vehicle dispatching in a single-vehicle automated guided vehicle system: a heuristic branch-and-bound approach coupled with a discrete events simulation model. International Journal of Production Research, 43(9), 1911-1942.
[38] Lee, C. C., & Lin, J. T. (1995). Deadlock prediction and avoidance based on Petri nets for zone-control automated guided vehicle systems. International journal of production research, 33(12), 3249-3265.
[39] Leifsson, L., Koziel, S., & Bekasiewicz, A. (2014). Fast Low-fidelity Wing Aerodynamics Model for Surrogate-based Shape Optimization. Procedia Computer Science, 29, 811-820.
[40] Li, W., Li, M., Chen, C. S., & Liu, X. (2015). Compactly supported radial basis functions for solving certain high order partial differential equations in 3D.Engineering Analysis with Boundary Elements, 55, 2-9.
[41] Madan, M., Son, Y. J., Cho, H., & Kulvatunyou, B. (2005). Determination of efficient simulation model fidelity for flexible manufacturing systems.International Journal of Computer Integrated Manufacturing, 18(2-3), 236-250.
[42] March, A., & Willcox, K. (2012). Provably convergent multifidelity optimization algorithm not requiring high-fidelity derivatives. AIAA journal, 50(5), 1079-1089.
[43] Moon, I., & Lee, J. (2000). Genetic algorithm application to the job shop scheduling problem with alternative routings. Pusan National University.
[44] Nasr, N., & Elsayed, E. A. (1990). Job shop scheduling with alternative machines. The international journal of production research, 28(9), 1595-1609.
[45] Ombuki, B. M., & Ventresca, M. (2004). Local search genetic algorithms for the job shop scheduling problem. Applied Intelligence, 21(1), 99-109.
[46] Ono, I., Yamamura, M., & Kobayashi, S. (1996, May). A genetic algorithm for job-shop scheduling problems using job-based order crossover. In Evolutionary Computation, 1996., Proceedings of IEEE International Conference on (pp. 547-552). IEEE.
[47] Paige, J. B., & Morin, K. H. (2013). Simulation fidelity and cueing: a systematic review of the literature. Clinical Simulation in Nursing, 9(11), e481-e489.
[48] Parthasarathy, S., & Rajendran, C. (1997). A simulated annealing heuristic for scheduling to minimize mean weighted tardiness in a flowshop with sequence-dependent setup times of jobs-a case study. Production Planning & Control,8(5), 475-483.
[49] Pandit, R., & Palekar, U. S. (1993). Job shop scheduling with explicit material handling considerations. Working paper, Iowa State University, Ames, Iowa.
[50] Raman, N. (1986). Simultaneous scheduling of machines and material handling devices in automated manufacturing. In Proc. of the Second ORSA/TIMS Conference on Flexible Manufacturing Systems: Operations Research Models and Applications, 1986.
[51] Reddy, B. S. P., & Rao, C. S. P. (2006). A hybrid multi-objective GA for simultaneous scheduling of machines and AGVs in FMS. The International Journal of Advanced Manufacturing Technology, 31(5-6), 602-613.
[52] Rehmann, A. J., Mitman, R. D., & Reynolds, M. C. (1995). A Handbook of Flight Simulation Fidelity Requirements for Human Factors Research. CREW SYSTEM ERGONOMICS INFORMATION ANALYSIS CENTER WRIGHT-PATTERSON AFB OH.
[53] Rinott, Y. (1978). On two-stage selection procedures and related probability-inequalities. Communications in Statistics-Theory and methods, 7(8), 799-811.
[54] Sawik, T. (1996). A multilevel machine and vehicle scheduling in a flexible manufacturing system. Mathematical and computer modelling, 23(7), 45-57.
[55] Satishkumar, M. V. (2011). Simultaneous scheduling of machines and Agvs using evolutionary optimization algorithms.
[56] Stecke, K. E. (1985). Design, planning, scheduling, and control problems of flexible manufacturing systems. Annals of Operations research, 3(1), 1-12.
[57] Subbaiah, K. V., Rao, M. N., & Rao, K. N. (2009). Scheduling of AGVs and machines in FMS with makespan criteria using sheep flock heredity algorithm.International Journal of Physical Sciences, 4(2), 139-148.
[58] Ulusoy, G., & Bilge, Ü. (1993). Simultaneous scheduling of machines and automated guided vehicles. THE INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, 31(12), 2857-2873.
[59] Ulusoy, G., Sivrikaya-Şerifoǧlu, F., & Bilge, Ü. (1997). A genetic algorithm approach to the simultaneous scheduling of machines and automated guided vehicles. Computers & Operations Research, 24(4), 335-351.
[60] Vis, I. F. (2006). Survey of research in the design and control of automated guided vehicle systems. European Journal of Operational Research, 170(3), 677-709.
[61] Wang, F. K., & Lin, J. T. (2004). Performance evaluation of an automated material handling system for a wafer fab. Robotics and Computer-Integrated Manufacturing, 20(2), 91-100.
[62] Wilhelm, W. E., & Shin, H. M. (1985). Effectiveness of alternate operations in a flexible manufacturing system. International Journal of Production Research,23(1), 65-79.
[63] Xu, J., Zhang, S., Huang, E., Chen, C. H., Lee, L. H., & Celik, N. (2014, August). An ordinal transformation framework for multi-fidelity simulation optimization. In Automation Science and Engineering (CASE), 2014 IEEE International Conference on (pp. 385-390). IEEE.
[64] Xu, J., Zhang, S., Huang, E., Chen, C. H., Lee ,L. H., & Celik, N. (2015). MO2TOS: Multi-fidelity Optimization with Ordinal Transformation and Optimal Sampling. to appear in Asia-Pacific Journal of Operational Research.
[65] Yeh, M. S., & Yeh, W. C. (1998). Deadlock prediction and avoidance for zone-control AGVS. International Journal of Production Research, 36(10), 2879-2889.