在群飛展演上，即使根據腳本的圖案設計可知某時刻必須在某個座標位置有台無人機閃爍某顏色，但如何指揮各台無人機以保證圖案會依腳本而出現，除需保證這些無人機的移動過程中不可互撞外，我們也希望能用最少數量的無人機群讓整個移動過程的整體能量消耗為最少，這樣的移動路徑軌跡設計問題極為複雜。現行的展演設計頂多只能以人工方式逐一指派各台無人機的避撞移動軌跡，對於整體之能量損耗或無人機個數等並無一套有系統的最佳化方法，導致可能會配置過多台無人機以及多浪費額外的能量耗損，也因此難以編制更長時段展演或變換更複雜的圖案。
本研究將每架無人機在每個時間切點、每個座標位置移動的路徑組合、特定位置是否亮燈的控制燈號等，設計成整數規劃模型之決策變數，而複雜的移動途程可被簡化成各台無人機於每個時間切點間的移動節線；在路徑移動上，屬於具方向性且不可逆的移動；對每架無人機而言，每個時間切點只會飛行到一個位置；就亮燈座標而言，同時刻最多只會有一架無人機經過來發亮；將兩個時間切點間的移動路徑轉換成移動成本，在考量亮燈與否具不同耗電成本的情況下，增加可回到地面點進行電池充換電的設計，來計算整體的能量消耗成本。相較於現行無人機群飛展演所採用的人工編排路徑規劃方式，本研究提出的整數規劃模型可根據腳本計算出理論上最佳的無人機群路線規劃方式。然而該整數規劃模型求解耗時，為能因應實務能在短時間內沙盤推演出不同圖案腳本的展演效果，我們亦設計其對應的高效率啟發式求解演算法，可快速因應各式的圖案展演需求，大幅縮短腳本設計時間，期望可為相關展演業者帶來許多便利與效益。

With the development of the automation and sensing technologies, the light show by a fleet of drones becomes more popular than the conventional firework shows. This gives a more dynamic, environmentally friendly, and cheaper entertainment show, as long as we can plan the flight path for each drone in a way that it does not collide with each other with minimum power consumption. This thesis investigates such a path planning problem for a fleet of drones making such a light show. In particular, assuming the figures in the light show are known, meaning we need to deploy at least a drone in specific locations in the sky at a particular time, how to calculate the movements for each drone with the minimum costs including the fixed equipment costs and the costs of flying and lightening. This problem is very new and challenging, which is solved manually in practice, to the best of our knowledge. To effectively tackle this complex fleet path planning problem, we propose arguably the first integer programming (IP) model for this problem. We divide the entire show into two types of periods: the show period and the transition period, where the former one displays the figures, and the latter one is used for drones to transit to new positions in the sky. If a drone is in a lower power mode, it will land for battery swapping and launch again. Our IP model is based on a time-space network. It can calculate exact optimal paths but is too time-consuming. Finally, we propose randomized greedy heuristics that can calculate a very good solution in 5 sec for a light show of 40 show periods with 4096 points in the sky. We expect the techniques developed in this thesis can be further extended for practical use and benefit the exhibition industry.

中文
工研院無人機講座 揭示台灣產業發展路向 (民107年9月27日)。民108年8月5日，取自https://dronesplayer.com/drone-use/工研院無人機講座-揭示台灣產業發展路向
方志賢 (民108年7月2日)。高雄防治登革熱 首次出動無人機空中噴藥。自由時報。民108年8月5日，取自https://news.ltn.com.tw/news/life/breakingnews/2840555
日本樂天與超市合作　無人機送貨至離島 (民108年6月20日)。民108年8月5日，取自https://dronesplayer.com/drone-use/日本樂天與超市合作-無人機送貨至離島
台無人機送件規模擴大 落實 3月飛進阿里山送茶葉 (民108年2月25日)。民108年8月5日，取自https://dronesplayer.com/drone-use/台無人機送件規模擴大-落實-3-月飛進阿里山送茶葉
吳佩璟 (2018)。無人機應用於農業噴藥推展之研究：以雲林地區為例。南華大學科技學院資訊管理學系碩士論文。取自https://hdl.handle.net/11296/z7gpg3
李志清(民國108年8月10日)。無人機煙火秀。南科AI_ROBOT自造基地4樓
亞馬遜無人機助攻 下單到取貨只要半小時 (民108年6月6日)。自由時報。民108年8月5日，取自https://video.ltn.com.tw/article/LxEoy1E4HA8/PLCvAZ9B-QRHMlV-Ek_VO3Sz1xCz8NGiid
洪哲政(民108年6月19日)。5年800億單位成本 我建構劍翔無人機群攻對岸雷達站。聯合報。民108年8月5日，取自https://udn.com/news/story/10930/3880161
首場無人機考試全法人代表 玩家再等半年 (民108年9月17日) ，取自https://www.cna.com.tw/news/ahel/201909170124.aspx
徐慧珠 (民108年4月27日)。天上有媽祖！百架本土無人機為媽祖暖壽。TVBS。民108年8月5日，取自https://news.tvbs.com.tw/life/1122760
郭建志 (民108年7月29日)。無人機應用商機 明年起飛。工商時報。民108年8月5日，取自https://www.chinatimes.com/newspapers/20190729000217-260202
陳冠㞶（2016）。基於多目標演化式演算法的視角可調之無人機路徑規劃。中華大學資訊工程碩士論文。取自https://hdl.handle.net/11296/qvcnrg
無人機送貨趨勢全球市場規模展望 (DIGITIMES整理) ，取自https://digitimes.com.tw/tech/showimg.asp?source=&filename=548634-1-K92NX.jpg&Sourcetype=1&newskey=548634
黃名揚 (2017)。智慧農業技術對香蕉生產之成本效益分析：以無人機應用為例。中興大學農業經濟與行銷碩士學位學程碩士論文。取自https://hdl.handle.net/11296/f99t49
黃慧雯 (民108年2月20日)。屏東燈會Intel神助攻 無人機排出TAIWAN閃耀天空。中時電子報。民108年8月5日，取自https://www.chinatimes.com/realtimenews/20190220001470-260412
電商大戰升級物流“最後一公里”(民106年4月)。巨頭崛起‧重建運輸行業生態鏈，物流技術與戰略雜誌，86。民108年8月5日，取自https://www.logisticnet.com.tw/publicationArticle.asp?id=492
劉禹慶 (民108年4月10日)。澎湖花火節 22場次主打無人機表演。自由時報。民108年8月5日，取自https://news.ltn.com.tw/news/local/paper/1280418
劉婉君 (民108年6月3日)。高雄防治登革熱 首次出動無人機空中噴藥。自由時報。民108年8月5日，取自https://news.ltn.com.tw/news/life/breakingnews/2811024
臉書與空中巴士攜手合作飛行計畫，取自https://www.bnext.com.tw/article/49670/facebook-aquila-internet-drone-project-shut-down
 
英文
Avellar, G., Pereira, G., Pimenta, L., & Iscold, P. (2015). Multi-UAV Routing for Area Coverage and Remote Sensing with Minimum Time. Sensors, 15(11), 27783–27803.
Cabral-Pacheco, E. G., Villarreal-Reyes, S., Galaviz-Mosqueda, A., Villarreal-Reyes, S. D., Rivera-Rodriguez, R., & Pérez-Ramos, A. E. (2016). Performance analysis of multi-hop broadcast protocols for distributed UAV formation control applications. Implementation, and Evaluation. Electronics, 7, 113548–113577.
Chen, Q.Y., Sun, Z.P., Liu, D.X., Fang, Y.Q.,& Li, X.H. (2012). Local path planning for an unmanned ground vehicle based on SVM. Int. J. Adv. Robot. Syst., 9, doi:10.5772/54130.
Drexl, M. (2012). Synchronization in Vehicle Routing—A Survey of VRPs with Multiple Synchronization Constraints. Transportation Science, 46(3), 297–316. doi:10.1287/trsc.1110.0400.
Grand View Research. (2019) Anti-drone Market Size & Share, Global Industry Report. Retrieved from https://www.grandviewresearch.com/industry-analysis/anti-drone-market
Huang, C. X., Lan, Y. S., Liu, Y. C., Zhou, W., Pei, H. B., Yang, L. Z., & Peng, Y. H. (2018). A New Dynamic Path Planning Approach for Unmanned Aerial Vehicles. Complexity, 17,doi:10.1155/2020/6549572.
Ju, C., & Son, H. (2018). Multiple UAV Systems for Agricultural Applications: Control, Implementation, and Evaluation. Electronics, 7(9), pp.21–26.
Luo, Z., Liu, Z., & Shi, J. (2017). A two-echelon cooperated routing problem for a ground vehicle and its carried unmanned aerial vehicle, Sensors, vol. 17, no. 5, pp. 1-17.
Mor, A., & Speranza, M. G. (2020). Vehicle routing problems over time: a survey. 4OR. doi:10.1007/s10288-020-00433-2.
Nedjati, A., Izbirak, G., Vizvari,B. & Arkat, J. (2016), Complete coverage path planning for a multi-UAV response system in post-earthquake assessment, Robotics, vol. 26, no. 5,doi:10.3390/robotics5040026.
Oz, I., Topcuoglu, H. R., & Ermis, M. (2013). A meta-heuristic based three-dimensional path planning environment for unmanned aerial vehicles. Simulation-Transactions of the Society for Modeling and Simulation International, 89(8), 903-920.
Papatheodorou, S., Tzes, A., & Stergiopoulos, Y. (2017). Collaborative visual area coverage. Robotics and Autonomous Systems, 92, 126–138.
Ropero, F., Muñoz, P., & R-Moreno, M. D. (2019). Terra: A path planning algorithm for cooperative ugv-uav exploration. Engineering Applications of Artificial Intelligence, 78, 260–272.
Schneider, M., & Drexl, M. (2017). A survey of the standard location-routing problem. Annals of Operations Research, 259(1-2), 389–414. doi:10.1007/s10479-017-2509-0
Silva, S. H., Rad, P., Beebe, N., Choo, K.-K. R., & Umapathy, M. (2019). Cooperative unmanned aerial vehicles with privacy preserving deep vision for real-time object identification and tracking. Journal of Parallel and Distributed Computing, 131, 147–160.
Yilmaz, O., Yakici, E., & Karatas, M. (2019). A UAV location and routing problem with spatio-temporal synchronization constraints solved by ant colony optimization. Journal of Heuristics, 25(4-5), 673-701.
Yu, K., Budhiraja, A. K., Buebel, S., & Tokekar, P. (2019). Algorithms and experiments on routing of unmanned aerial vehicles with mobile recharging stations. Journal of Field Robotics, 36(3), 602-616.
Zhen, L., Li, M., Laporte, G., & Wang, W. (2019). A vehicle routing problem arising in unmanned aerial monitoring. Computers & Operations Research, 105, 1–11.