以Q-學習法為基礎之群體智慧演算法及其應用

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謝易錚(Yi-Zeng Hsieh) 查詢紙本館藏

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論文名稱

以Q-學習法為基礎之群體智慧演算法及其應用
(A Q-learning-based Swarm Optimization Algorithm and its Applications)

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摘要(中)

本論文採用預期未來所獲得的報酬當作群體在空間中尋找最佳解的依據，並以增強式學習法計算其預期報酬，以期能夠得到最佳解。根據此觀念，提出新的最佳化演算法-以Q學習法為基礎之群體智慧演算法 ( Q-learning-based swarm optimization algorithm, 簡稱QSO )。QSO演算法是一種結合Q-學習法 ( Q-learning ) 與粒子群體最佳化 ( particle swarm optimization, PSO )並以族群為基礎( population-based )的最佳化演算法。
QSO演算法主要是將粒子個體的表現當作是報酬率，並選出逐次演化過程中擁有最大報酬率的個體，視為表現最好的個體，而非以個體單次或是立即的表現作為選擇。在求解過程中，所有的個體都會學習群體中表現最佳的個體，粒子不斷的演化學習得到最佳解。
我們將QSO與現有最佳化演算法利用標準評估函數比較其搜尋最佳解的能力，並將其應用在電力分配問題(the economic dispatch (ED) problem)與手術排程問題(operating schedules problem)。在此兩種問題中，QSO最佳化演算法找到最佳解優於一些現有的最佳化演算法。
本論文在電力分配問題應用中，解決3台發電機與40台發電機的兩類問題。此應用的目標為，在相同輸出總電力中(3台發電機總的電力是850 MW, 40台發電機總電力是10500MW)，並且滿足每台發電機的輸出電力範圍的限制條件下，希望能夠得到最小的電力成本。本論文針對具有限制條件的求解問題中，提出兩種方法-不等式限制方法與等式限制方法。QSO在求解的過程中，透過不等式的限制方法尋找個別發電機的輸出功率；利用等式限制方法調整發電機以期總電力能合乎限制條件。具有限制條件的兩類應用中QSO演算法配合2種限制方法，皆能求得比現有方法更佳的解。
現今醫院的手術排程大都是以人工的方式進行，效率往往不佳，因此本論文試圖將QSO演算法應用於手術排程中，以期提高手術房使用效率。在手術排程的目標是希望能夠安排手術在有限的手術房中，必須符合手術的優先使用順序，以及須符合某些手術使用特定手術房的限制條件。本論文針對此特性提出手術排程編碼方式，將手術順序編碼成以權重為主的向量編碼方式。此編碼方式主要有兩個部分，1.手術房分配向量(operating room assignment vector, ORAV)；2.手術優先權向量(operation order priority vector, OOPV)。個體之ORAV決定如何安排每一件手術在手術房，其OOPV則提供所執行手術之優先使用手術房的權重資訊。並利用所提之QSO最佳化演算法更新權重，所找到的最佳解也優於基因演算法與人工排程的結果。
本論文所提之QSO最佳化演算法是以群體為基礎，在連續空間中採用個體預期報酬當作是評斷個體表現的依據，再逐次演化過程，群體透過相互影響與互相學習(如合作，競爭，模仿)搜尋最佳解。預期表現與立即表現最大的不同，預期表現是我們透過Q-learning評估個體的表現來是否會在環境中得到最大的報酬，而立即表現只是評估當下的行為所得到的環境給予的回饋。本論文認為，因為個體的學習行為是累積持續，個體的行為是會反映在未來的所得到的報酬，並不能根據當下的表現來評估。並將所提之最佳化演算法，應用在電力調度與手術排程兩類實際問題中，所得之最佳解也比現有方法來的更佳。

摘要(英)

In this paper, we treat optimization problems as a kind of reinforcement learning problems by regarding an optimization procedure for searching an optimal solution as a reinforcement learning procedure for finding the best policy to maximize the expected rewards. This viewpoint motivated us to propose a Q-learning-based swarm optimization (QSO) algorithm. The proposed QSO algorithm is a population-based optimization algorithm which integrates the essential properties of Q-learning and particle swarm optimization (PSO). The optimization procedure of the QSO algorithm proceeds as each individual imitates the behavior of the global best one in the swarm. The best individual is chosen based on its future expected performance instead of its momentary performance at each evaluation. Several data sets including a set of benchmark functions and a real-world problem - the economic dispatch (ED) problem for power systems and the operating schedules problem were used to test the performance of the proposed QSO algorithm. The simulation results on the benchmark functions show that the proposed QSO algorithm is comparable to or even outperforms several existing optimization algorithms.
The well-known ED problem was tested to demonstrate the performance of the QSO algorithm for solving optimization problems with inequality constraints and equality constraints. For both the 3 generators and the 40 generators problems, the QSO algorithm has found better solutions than those previously known the best solutions.
In our scheduling algorithm, an operation sequence assignment list is encoded into a weight vector consisted of two component vectors: 1) operating room assignment vector (ORAV) and 2) operation order priority vector (OOPV). The QSO algorithm is used to update the weight vectors to search a better operation schedule.
In this paper, a Q-learning-based swarm optimization (QSO) algorithm is proposed for solving continuous optimization problems. Through the social influence and social learning process (i.e., cooperation, competition, and imitation), good solutions to an optimization problem can be simultaneously explored and exploited.

關鍵字(中)

★ 群體智慧
★ 健康照護
★ 最佳化
★ 粒子群最佳化
★ Q-學習法
★ 排程
★ 手術房
★ 電力系統
★ 資源分配

關鍵字(英)

★ health care.
★ job-shop problem
★ operating room
★ power system
★ economic dispatch problem
★ swarm intelligence
★ Q-learning
★ particle swarm optimization
★ optimization

論文目次

摘要　　　　　　 i
ABSTRACT iv
Acknowledgments vi
Table of Contents vii
List of Figurers x
List of Tables xi
Chapter 1 Introduction 1
1.1 Introduction of optimization 1
1.2 The derivative-based optimization 1
1.3 Swarm intelligence 2
1.4 Reinforcement learning 3
1.5 Discussion 4
Chapter 2 Related works 6
2.1 Social-cognitiation 6
2.2 Particle swarm optimization 7
2.3 Pseudocode for Partical Swarm Optimization 8
2.4 The problem of PSO implementation 9
2.5 Q-learning 9
2.6 Pseudo code for Q-learning 12
2.7 Discussion 14
Chapter 3 A Q-learning-based swarm optimization algorithm 15
3.1 The social learning mechanism 15
3.2 An example for the future expected performance 15
3.3 The proposed QSO algorithm 16
3.4 The learning procedure for the QSO algorithm 18
3.5 Discussion 24
Chapter 4 Performance on benchmark test functions 25
4.1 The benchmark test functions 25
4.2 Modified particle swarm optimization 27
4.3 The parameters for the optimizations 27
4.4 Simulation results 28
4.5 The population size effect 35
4.6 Discussion 37
Chapter 5 The economic dispatch problem for power systems 38
5.1 Economic dispatch problem 38
5.2 The objective function and constrains for the ED problem 39
5.3 The repairing mechanism for the ED problem 40
5.4 Experimental results 45
5.5 Discussion 51
Chapter 6 The operating room scheduling problem 52
6.1 Survey of realted work 52
6.2 Problem formulation 54
6.3 The representation of the scheduling problem 56
6.4 The QSO-based scheduling algorithm 60
6.5 Experimental results 62
6.6 Discussion 68
Chapter 7 Conclusions and future works 69
7.1 Conclusions 69
7.2 Future works 70
References 72

參考文獻

[1] J. H. Holland, “Adaptation in Natural and Artificial Systems,” University of Michigan Press, Ann Arbor, 1975.
[2] D. E. Goldberg, “Genetic Algorithms in Search, Optimization, and Machine Learning,” Addison-Wesley Publishing Company, Reading, MA, 1989.
[3] L. J. Fogel, “Evolutionary Programming in Perspective: the Top-down View,” in Computational Intelligence: Imitating Life, Piscataway, NJ, 1994.
[4] I. Rechenberg, “Cybernetic solution path of an experimental problem,” Royal Aircraft Establishment, Library translation 1122, Farnborough, Hants, U.K. 1965.
[5] I. Rechenberg, “Evolutiosstrategie: optimierung technischer system nach prinzipien der biologischen evolution,” Stuttgart, Germany: Frommann-Holzboog Verlag, , 1973.
[6] M. Dorigo, V. Maniezzo, and A. Colorni, “Ant system: optimization by a colony of cooperating agents,” IEEE Trans. Systems, Man, and Cybernetics, part B, vol. 26, no. 1, pp. 29-41, 1996.
[7] M. Dorigo and T. Stutzle, “Ant Colony Optimization, Cambridge,” MIT, 2004.
[8] M. C. Su and Y. X. Zhao, “A variant of the SOM algorithm and its interpretation in the viewpoint of social influence and learning,” Neural Computing & Applications, vol. 18, no. 8, pp.1043-1055, 2009.
[9] J. H. Chen, M. C. Su, Y. X. Zhao, Y. J. Hsieh, and W.H. Chen, “Application of SOMO based clustering in building renovation,” International Journal of Fuzzy Systems, vol. 10, no. 3, pp. 195-201, 2008.
[10] J. H. Chen, L. R. Yang, and M. C. Su, “Comparison of SOM-based optimization and particle swarm optimization for minimizing the construction time of a secant pile wall,” Automation in Construction, vol. 18, no. 6, pp. 844-848, 2009.
[11] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in IEEE International Conference on Neural Networks, vol. 4, pp.1942-1948, Dec. 1995.
[12] R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proc. of the Sixth International Symposium on Micro Machine and Human Science, pp. 39-43, Oct. 1995.
[13] J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence, New York: Academic Press, 2001.
[14] R. C. Eberhart and Y. Shi, “Comparison between genetic algorithms and particle swarm optimization,” in Proc. of the Seventh International Conference of Evolutionary Programming, pp. 611-616, 1998.
[15] J. Kennedy, “Small worlds and mega-minds: effects of neighborhood topology on particle swarm optimization,” in Proc. of IEEE International Conference on Evolutionary Computation, pp.1931-1938, Dec. 1999.
[16] M. Clerc, “The swarm and the queen: Towards a deterministic and adaptive particle swarm optimization,” in Proc. of Congress Evolutionary Computation., vol. 3, pp. 1951–1957, Jul. 1999.
[17] M. Løvbjerg, T. K. Rasmussen, and T. Krink, “Hybrid particle swarm optimizer with breeding and subpopulations,” in Proc. of IEEE International Conference on Genetic Evolutionary, pp. 469–476, 2001.
[18] J. Robinson, S. Sinton, and Y. Rahmat-Samii, “Particle swarm, genetic algorithm, and their hybrids: Optimization of a profiled corrugated horn antenna,” in Proc. of IEEE International Symposium on Antennas and Propagation, pp. 314–317, San Antonio, TX, 2002.
[19] J. Kennedy and R. Mendes, “Topological structure and particle swarm performance,” in Proc. of the Congress on Evolutionary Computation, pp. 1671 - 1676, 2002.
[20] R. Mendes, J. Kennedy, and J. Neves, “Watch thy neighbor or how the swarm can learn from its environment,” in Iberoamerican Conference on Artificial Intelligence, Seville, pp. 88-94, 2002.
[21] T. M. Balckwell and P. J. Bentley, “Dynamic search with charged swarms,” in Proc. of IEEE International Conference on Genetic and Evolutionary, pp. 19-26, 2002.
[22] J. Kennedy and R. Mendes, “Neighborhood topologies in fully-informed and best-of-neighborhood particle swarms,” in IEEE SMC Workshop on Soft Computing in Industrial Applications, pp. 515-519, Jun 2003.
[23] S. C. Esquivel and C. A. CoelloCoello, “On the use of particle swarm optimization with multimodal functions,” in Proc. of IEEE Congress on Evolutionary Computation, vol. 2, pp. 1130–1136, 2003.
[24] X. H. Shi, Y. H. Lu, C. G. Zhou, H. P. Lee, W. Z. Lin, and Y. C. Liang, “Hybrid evolutionary algorithms based on PSO and GA,” in Proc. of IEEE Congress Evolutionary Computation, pp. 2393–2399, 2003.
[25] K. M. Christopher and K. D. Seppi, “The Kalman swarm. A new approach to particle motion in swarm optimization,” in Proc. of IEEE Conference on Genetic Evolutionary Computation, pp. 140–150, 2004.
[26] D. Devicharan and C. K. Mohan, “Particle swarm optimization with adaptive linkage learning,” in Proc. of IEEE Congress Evolutionary Computation, pp. 530–535, 2004.
[27] M. Settles and T. Soule, “Breeding swarms: A GA/PSO hybrid,” in Proc. of IEEE Conference on Genetic Evolutionary Computation, pp. 161–168, 2005.
[28] X. Chen and Y. Li, “A modified PSO structure resulting in high exploration ability with convergence guaranteed,” IEEE Trans. on Systems, Man, and Cybernetics, Part B, vol. 37, no. 5, pp. 1271–1289, Oct. 2007.
[29] Y. P. Chen, W. C. Peng, and M. C. Jian, “Particle swarm optimization with recombination and dynamic linkage discovery,” IEEE Trans. on Systems, Man, and Cybernetics, Part B, vol. 37, no. 6, pp. 1460–1470, Dec. 2007.
[30] S. Kiranyaz, T. Ince, A. Yildirim, and M. Gabbouj, “Fractional particle swarm optimization in multi-dimensional search space,” IEEE Trans on Systems, Man, and Cybernetics, Part B, vol. 40, no. 2, pp. 298–319, 2010.
[31] R. S. Sutton and A. G. Barto, Reinforcement learning: An introduction. Cambridge, MA: MIT Press, 1998.
[32] C. Ribeiro, “Reinforcement learning agents,” Artificial Intelligence Review, vol. 17, pp. 223-250, 2002.
[33] L. P. Kaelbling, M. L. Littman, and A.W. Moore, “Reinforcement learning: a survey,” Journal of Artificial Intelligence Research, vol. 4, pp. 237-285, 1996.
[34] A.G. Barto, R.S. Sutton, and C.W. Anderson, “Neuronlike adaptive elements that can solve difficult learning control problems,” IEEE Trans on Systems, Man, and Cybernetics, vol.13, no.5, pp. 834-846, 1983.
[35] C. J. C. H. Watkins and P. Dayan, “Q-learning machine,” Machine Learning, vol. 8, pp. 279-292, 1992.
[36] M. Khajenejad, F. Afshinmanesh, A. Marandi, and B. N. Araabi, “Intelligent particle swarm optimization using Q-learning,” in Proc. of IEEE International Symposium on Swarm Intelligence, pp. 7–12, 2006.
[37] H. Iima and Y. Kuroe, “Swarm reinforcement learning algorithm based on exchanging information among agents,” Trans. on the Society of Instrument and Control Engineers, vol. 42, pp. 1244-1251, 2006.
[38] K. A. De Jong, “An analysis of the behaviour of a class of genetic adaptive systems,” University of Michigan, Ann Arbor, 1975. (University Microfilms No. 76-9381)
[39] G. B. Fogel, G. W. Greenwood, and K. Chellapilla, “Evolutionary computation with extinction: Experiments and analysis,” in Proc. of the 2000 Congress on Evolutionary Computation, pp. 1415–1420, 2000.
[40] R. Salomon, “Reevaluating Genetic Algorithm Performance under Coordinate Rotation of Benchmark Functions,” Elsevier Science on BioSystems, vol. 39, pp. 263–278, 1995.
[41] T. Krink and R. Thomsen, “Self-organized criticality and mass extinction in evolutionary algorithms,” in Proc. of IEEE International Conference on Evolutionary Computation, pp. 1155-1161, 2001.
[42] M. Richards and D. Ventura, “Dynamic sociometry in particle swarm optimization”, International Conference on Computational Intelligence and Natural Computing, pp. 1557-1560, 2003.
[43] Y. Shi and R. Eberhart, “Fuzzy adaptive particle swarm optimization,” in Proc. of the Congress on Evolutionary Computation, pp. 101-106, 2001.
[44] J. Vesterstrom and R. Thomsen, “A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems,” in Proc. of the 2004 Congress on Evolutionary Computation, vol. 2, pp. 1980-1987, 2004.
[45] The software packages for the GAs and the PSO algorithm:www.engr.iupui.edu/~ebergart/web/PSObook.html.
[46] J. W. Allen and F. W. Bruce, Power Generation, Operation, and Control. New York: Wiley, 1984.
[47] D. C. Walters and G. B. Sheble, “Genetic algorithm solution of economic dispatch with valve point loading,” IEEE Trans. on Power System, vol. 8, no. 3, pp. 1325–1332, Aug. 1993.
[48] G. B. Sheble and K. Brittig, “Refined genetic algorithm—Economic dispatch example,” IEEE Trans. on Power System, vol. 10, no. 1, pp. 117–124, Feb. 1995.
[49] P. H. Chen and H. C. Chang, “Large-scale economic-dispatch by genetic algorithm,” IEEE Trans. on Power System, vol. 10, no. 4, pp. 1919–1926, Nov. 1995.
[50] H. T. Yang, P. C. Yang, and C. L. Huang, “Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions,” IEEE Trans. on Power System, vol. 11, no. 1, pp. 112–117, Feb. 1996.
[51] Y. M. Park, J. R. Won, and J. B. Park, “New approach to economic load dispatch based on improved evolutionary programming,” Engineering Intelligence System on Electronic Engineering Communication, vol. 6, no. 2, pp. 103–110, Jun. 1998.
[52] K. P. Wong and J. Yuryevich, “Evolutionary-programming-based algorithm for environmentally-constrained economic dispatch,” IEEE Trans. on Power System, vol. 13, no. 2, pp. 301–306, May 1998.
[53] T. Yalcinoz, H. Altun, and M. Uzam, “Economic dispatch solution using a genetic algorithm based on arithmetic crossover,” in Proc. of IEEE Conference on Power Technical, vol. 2. Sep. 10–13, 2001.
[54] W. M. Lin, F. S. Cheng, and M. T. Tsay, “Am improved Tabu search for economic dispatch with multiple minima,” IEEE Trans. on Power Systems, vol. 17, no. 1, pp. 108-112, 2002.
[55] N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay, “Evolutionary programming technique for economic load dispatch,” IEEE Trans. on Evolutionary Computation, vol. 7, no. 1, pp. 83–94, Feb. 2003.
[56] S. Baskar, P. Subbaraj, and M. V. C. Rao, “Hybrid real coded genetic algorithm solution to economic dispatch problem,” Computation Electronic Engineering, vol. 29, no. 3, pp. 407–419, May 2003.
[57] Z. L. Gaing, “Particle swarm optimization to solving the economic dispatch considering the generator constraints,” IEEE Trans. on Power System, vol. 18, no. 3, pp. 1187–1195, Aug. 2003.
[58] T. A. A. Victoire and A. E. Jeyakumar, “Hybrid PSO-SQP for economic dispatch with valve-point effect,” Electronic Power System Res., vol. 71, no. 1, pp. 51–59, 2004.
[59] T. A. A. Victoire and A. E. Jeyakumar, “Particle swarm optimization to solving the economic dispatch considering the generator constraints,” IEEE Trans. on Power System, vol. 19, no. 4, pp. 2121–2122, 2004.
[60] J. B. Park, K. S. Lee, J. R. Shin, and K. Y. Lee, “A particle swarm optimization for economic dispatch with nonsmooth cost functions,” IEEE Trans. on Power System, vol. 20, no. 1, pp. 34–42, Feb. 2005.
[61] T. Jayabarathia, K. Jayaprakasha, D. N. Jeyakumarb, and T. Raghunathan, “Evolutionary programming techniques for different kinds of economic dispatch problems,” Electronic Power System Res., vol. 73, no. 2, pp. 169–176, 2005.
[62] R. Cheng, M. Gen, and Y. Tsujimura, “A tutorial survey of job-shop scheduling problems using genetic algorithms-I. Representation,” Computers and Engineering, vol. 30, no. 4, pp. 983-997, 1996.
[63] J. Gao, M. Gen, and L. Sun, “A Hybrid of Genetic Algorithm and Bottleneck Shifting for Flexible Job Shop Scheduling Problem,” in Proc. of IEEE Conference on Genetic Evolutionary Computation, pp.1157-1163, 2006.
[64] G. Beni, and J. Wang, “Swarm Intelligence in Cellular Robotic Systems”, in Proc. of the NATO Advanced Workshop on Robots and Biological Systems, Tuscany, Italy, pp. 26-30, June 1989.
[65] P. P. Grasse, “La reconstruction du nid et les coordinations inter-individuelles chez bellicoitermes natalenis et cubitermes sp. La theorie de la stigmergie: Essaid’interpretation du comportement des termites constructeurs,” Insect Societies, vol. 6, pp. 41-83.
[66] E. Bonabeau, M. Dorigo, and G. Theraulaz, Swarm Intelligence: From Natural to Artificial Systems, Oxford University Press, 1999.
[67] Health Care Financial Management Association Report, “Achieving operating room efficiency through processes integration,” 2005.
[68] I. Ozkarahan, “Allocation of Surgeries to Operating Rooms by Goal Programming,” Journal Medical Systems, vol.24, no.6, pp. 339-378, 2000.
[69] B. Denton, J. Viapiano, and A. Vogl, “Optimization of Surgery Sequencing and Scheduling Decisions under Uncertainty,” Health Care Manage Science, vol. 10, pp.13-24, 2007.
[70] Goldman, et al., “A study of the variability of surgical estimates,” Management 110, 1970.
[71] B. Denton, J. Viapiano, and A. Vogl, “Optimization of Surgery Sequencing and Scheduling Decisions under Uncertainty,” Health Care Manage Science, vol. 10, pp. 13-24, 2007.
[72] A. Guinet and S. Chaabane, “Operating Theatre Planning,” International Journal of Production Economics, vol. 85, pp.69-81, 2003.
[73] K. H. Hanson, “Computer-Assisted Operating Room Scheduling”, International Journal of Production Economics, vol. 99, pp. 52-62, 2006.
[74] A. Jebaili, A. B. H. Alouane, and P. Ladet, “Operating rooms scheduling”, International Journal of Production Economics, vol. 99, pp. 52-62, 2006.
[75] P. J. Kuzdrall, N. K. Kwak, and H. H. Schmitz, “Monte Carlo Simulation of Operating-Room and Recovery-Room Usage,” Operations Research, vol. 22, no. 2, pp.434-440, 1974.
[76] M. Lamiri, J. Dreo, and X. Xie, “Operating Room Planning with Random Surgery Times,” in Proc. of the third Annual IEEE Conference on Automation Science and Engineering Scottsdale, USA, pp. 521-526, Sep. 22-25, 2007.
[77] P. Bruker and R. Schlie, “Job-shop scheduling with multi-purpose machines,” Computing, vol. 45, pp. 369-375, 1990.
[78] P. Brandimarte, “Routing and scheduling in flexible job shops by tabu search,” Application in Production and Scheduling, vol. 41, pp. 157–183, 1993.
[79] J. Hurink, B. Jurisch, and M. Thole, “Tabu search for the job-shop scheduling problem with multi-purpose machines,” OR Spectrum, vol. 15, pp. 205–215, 1994.
[80] H. Zhang and M. Gen, “Multistage-based genetic algorithm for flexible job-shop scheduling problem,” Journal of Complexity International, vol. 11, pp. 223-232, 2005.
[81] J. Gao, M. Gen, and L. Sun, “A Hybrid of Genetic Algorithm and Bottleneck Shifting for Flexible Job Shop Scheduling Problem,” in Proc. of IEEE Conference on Genetic Evolutionary Computation, pp.1157-1163, 2006.
[82] N. Zribi, I. Kacem, A. E. Kamel, and P. Born, “Assignment and Scheduling in Flexible Job-Shops by Hierarchical Optimization,” IEEE Trans. on Systems, Man, and Cybernetics, part C, vol. 37, no. 4, pp. 652-661, July 2007.
[83] W. Xia and Z. Wu, “An effective hybrid optimization approach for muti-objective flexible job-shop scheduling problem,” Computers & Industrial Engineering, vol. 48, pp. 409-425, 2005.

指導教授

蘇木春(Mu-Chun Su)

審核日期

2012-3-26

推文