這本論文致力於解決一個組合最佳化的問題叫做 Tour Planning Problem (TPP)。解決TPP必須替一些人或物找到符合條件的路徑。TPP是著名的旅行推銷員問題(mTSP)的一種變形。我們從災害防治的研究中得知，找志工帶著智慧型手機，透過網路，走特定的路徑，可以讓防災中心更了解災情。在為了替災害現場的志工找到更好的路徑去探勘災情，我們努力提供解決TPP的方法。我們提供兩種方法來解決TPP，第一是一個分治法的啟發式演算法，透過一些分群的方法，例如K平均演算法，來分割問題，第二是將TPP以混合整數規畫表示，並用求解軟體來找答案。我們希望透過我們的實驗，讓讀者知道簡單的啟發式演算法能得到怎樣程度的答案。
關鍵字 : 組合最佳化，旅行推銷員問題，分治法，K平均演算法，混合整數規畫

The main focus of this thesis is to solve a combinatorial optimization problem called the Tour Planning Problem (TPP).The solution of TPP are tours for people meeting some specific objectives. TPP is a variant of the multiple traveling salesman problem (mTSP). We are dedicated to solve TPP to get a better surveillance of a disaster affected area. We learnt that asking volunteers to travel through specific tours, and send back observations made at certain locations with mobile devices will get much better awareness of the area. Hence, better TPP solutions leads to a clearer the view of the area. We present a divide and conquer algorithm utilizing clustering methods such as k-means clustering, as well as an integer linear programming formulation. Performance of the two ways of solving TPP are compared. We hope to show some insights of what can be done by a simple heuristic on a complex problem.
Keyword: combinatorial optimization, multiple traveling salesman problem,
divide and conquer, k-means clustering, integer linear programming.

[1] Y. Z. Ou, J. W. S. Liu, E. T. H. Chu, P. H. Tsai, “A Framework for Fusion of
Human Sensor and Physical Sensor Data” IEEE Trans. Syst. Man Cybern. Syst., May, 2014
[2] Aggarwal, C. C. and T. Abdelzaher, “Integrating Sensors and Social Networks,” in Social Network Data Analysis, Ed. by C. Aggarawal, Springer, 2011.
[3] Chu, E. T.-H., Y.-L. Chen, J. W. S. Liu and J. K. Zao, “Strategies for Crowdsourcing for Disaster Situation Information,” WIT Transactions on the Built Environment, 2011.
[4] Bektas, T., “The Multiple Traveling Salesman Problem: An Overview of Formulations and Solution Procedures,” Omega, the International Journal of Management Science, Vol. 34,2006
[5] Keld Helsgaun, “Gaeneral k-opt submoves for the Lin-Kernighan TSP heuristic” Springer and Mathematical Programming Society 2009
[6] Miller CE, Tucker AW, Zemlin RA. “Integer programming formulation of traveling salesman problems.” Journal of Association for Computing Machinery 1960
[7] General Algebraic Modeling System. http://www.gams.com/
[8] NEOS. http://neos.mcs.anl.gov/neos/solvers/index.html.
[9] Cbc. http://www.neos-server.org/neos/solvers/milp:Cbc/GAMS.html
[10] Gurobi. http://www.neos-server.org/neos/solvers/milp:Gurobi/GAMS.html
[11] MOSEK. http://www.neos-server.org/neos/solvers/milp:MOSEK/GAMS.html
[12] XpressMP. http://www.neos-server.org/neos/solvers/milp:XpressMP/GAMS.html
[13] SCIP. http://www.neos-server.org/neos/solvers/milp:scip/GAMS.html
[14] Chu, E. T.-H., Y.-L. Chen, J.-Y. Lin and J. W. S. Liu, “Crowdsourcing Support System for Disaster Surveillance and Response” Wireless Personal Multimedia Communications (WPMC), 2012 15th International Symposium on
[15] E. T.-H., Chu, C.-Y. Lin, P . H. Tsai and J. W. S. Liu “Design and Implementation of Participant Selection for Crowdsourcing Disaster Information” Journal of Safety & Security Engineering, to appear.
[16] Dantzig GB, Fulkerson DR, Johnson SM. “Solution of a large-scale traveling salesman problem.” Operations Research, 1954
[17] Kara I, Bektas T. “Integer programming formulations of multiple salesman problems and its variations.” European Journal of Operational Research, 2006
[18] Laporte G, Nobert Y. “A cutting planes algorithm for the m-salesmen problem.” Journal of the Operational Research Society 1980
[19] Christofides N, Mingozzi A, Toth P. “Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations.” Mathematical Programming 1981.
[20] Ali AI, Kennington JL. “The asymmetricm-traveling salesmen problem: a duality based branch-and-bound algorithm.” Discrete Applied Mathematics 1986.
[21] Gavish B, Srikanth K. “An optimal solution method for large-scale multiple traveling salesman problems.” Operations Research, 1986.
[22] Russell RA. “An effective heuristic for them-tour traveling salesman problem with some side conditions.” Operations Research 1977
[23] Wacholder E, Han J, Mann RC. “A neural network algorithm for the multiple traveling salesmen problem.” Biology in Cybernetics 1989
[24] Likas, A., Vlassis, N.A., Verbeek, J.J, “The global k-means clustering algorithm.” Pattern Recognition, 2003
[25] Nallusamy, R., K. Duraiswamy, D. Dhanalaksmi, and P. Parthiban, “Optimization Non-Linear Multiple Traveling Salesman Problem Using K-Mean Clustering, Shrink Wrap Algorithm and Meta-Heuristics,” International Journal of Nonlinear Science, 2009.
[26] Qingsheng Yu, Dong Wang, Dongmei Lin, Ya Li, Chen Wu, “A Novel Two-Level Hybrid Algorithm for Multiple Traveling Salesman Problems”, Advances in Swarm Intelligence, 2012
[27] Sofge D, Schultz A, De Jong K. “Evolutionary computational approaches to solving the multiple traveling salesman problem using a neighborhood attractor schema.” Lecture notes in computer science, 2002.
[28] Vakhutinsky IA, Golden LB. “Solving vehicle routing problems using elastic net.” Proceedings of the IEEE international conference on neural network, 1994.
[29] Torki A, Somhon S, Enkawa T. “A competitive neural network algorithm for solving vehicle routing problem.” Computers and Industrial Engineering 1997.
[30] Modares A, Somhom S, Enkawa T. "A self-organizing neural network approach for multiple traveling salesman and vehicle routing problems.” International Transactions in OperationalResearch 1999.
[31] Somhom S, Modares A, Enkawa T. “Competition-based neural network for the multiple traveling salesmen problem with minmax objective.” Computers and Operations Research 1999.
[32] Zhang T, Gruver WA, Smith MH. “Team scheduling by genetic search.” Proceedings of the second international conference on intelligent processing and manufacturing of materials, vol. 2,1999.
[33] Tang L, Liu J, Rong A, Yang Z. “A multiple traveling salesman problem model for hot rolling scheduling in Shangai Baoshan Iron & Steel Complex.” European Journal of Operational Research 2000.
[34] Yu Z, Jinhai L, Guochang G, Rubo Z, Haiyan Y, “An implementation of evolutionary computation for path planning of cooperative mobile robots.” Proceedings of the fourth world congress on intelligent control and automation, vol. 3, 2002.
[35] J.L. Ryan, T.G. Bailey, J.T. Moore, W.B. Carlton, “Reactive Tabu search in unmanned aerial reconnaissance simulations.” Proceedings of the 1998 winter simulation conference, vol. 1,1998.
[36] Tobias Achterberg, Timo Berthold, Thorten Koch, Kati Wolter, “Constraint Integer Programming: a New Approach to Integrate CP and MIP” 5th International Conference, CPAIOR, 2008
[37] Anderberg, M.R. “Cluster analysis for applications.” Academic press, 1973
[38] A. Buluc, H. Meyerhenke, I. Safro, P. Sander, and C. Schulz, “Recent Advances in Graph Partition.” Algorithm Engineering – Selected Topics, 2014
[39] Metis : “A Fast and Highly Quality Multilevel Scheme for Partitioning Irregular Graphs”. George Karypis and Vipin Kumar. SIAM Journal on Scientific Computing, Vol. 20, No. 1, pp. 359—392, 1999.