組合最佳化
組合最佳化(英語:Combinatorial optimization)是數學最佳化的一個子領域,在應用數學和理論電腦科學的領域中,組合最佳化是在一個有限的對象集中找出最佳對象的一類問題。[1]在很多組合最佳化的問題中,窮舉搜尋/列舉法是不可行的。組合最佳化的問題的特徵是可行解的集是離散或者可以簡化到離散的,並且目標是找到最佳解。常見的例子有旅行推銷員問題和最小生成樹。
組合最佳化涉及運籌學、演算法理論和計算複雜性理論,在人工智能、機器學習、拍賣理論、軟件工程、超大規模集成電路、應用數學和理論電腦科學等多個領域有重要的應用。
組合最佳化的難處主要是加入拓撲分析的情況,不同的拓撲形態下,不同部分的約束關係便不同,演算法也就要調整。如果給定一個拓撲形態,組合最佳化往往退化成一個整數最佳化的問題。
應用
編輯特定問題
編輯參考文獻
編輯- ^ Schrijver 2003,第1頁.
- ^ Sbihi, Abdelkader; Eglese, Richard W. Combinatorial optimization and Green Logistics (PDF). 4OR. 2007, 5 (2): 99–116 [2019-12-26]. S2CID 207070217. doi:10.1007/s10288-007-0047-3. (原始內容存檔 (PDF)於2019-12-26).
- ^ Eskandarpour, Majid; Dejax, Pierre; Miemczyk, Joe; Péton, Olivier. Sustainable supply chain network design: An optimization-oriented review (PDF). Omega. 2015, 54: 11–32 [2019-12-26]. doi:10.1016/j.omega.2015.01.006. (原始內容存檔 (PDF)於2019-12-26).
引注
編輯- Beasley, J. E. Integer programming (lecture notes). [2022-10-16]. (原始內容存檔於2022-10-16).
- Cook, William J.; Cunningham, William H.; Pulleyblank, William R.; Schrijver, Alexander. Combinatorial Optimization. Wiley. 1997. ISBN 0-471-55894-X.
- Cook, William. Optimal TSP Tours. University of Waterloo. 2016 [2022-10-16]. (原始內容存檔於2012-07-22). (Information on the largest TSP instances solved to date.)
- Crescenzi, Pierluigi; Kann, Viggo; Halldórsson, Magnús; Karpinski, Marek; Woeginger, Gerhard (編). A Compendium of NP Optimization Problems. [2022-10-16]. (原始內容存檔於2007-04-05). (This is a continuously updated catalog of approximability results for NP optimization problems.)
- Das, Arnab; Chakrabarti, Bikas K (編). Quantum Annealing and Related Optimization Methods. Lecture Notes in Physics 679. Springer. 2005. Bibcode:2005qnro.book.....D.
- Das, Arnab; Chakrabarti, Bikas K. Colloquium: Quantum annealing and analog quantum computation. Rev. Mod. Phys. 2008, 80 (3): 1061. Bibcode:2008RvMP...80.1061D. CiteSeerX 10.1.1.563.9990 . S2CID 14255125. arXiv:0801.2193 . doi:10.1103/RevModPhys.80.1061.
- Lawler, Eugene. Combinatorial Optimization: Networks and Matroids. Dover. 2001. ISBN 0-486-41453-1.
- Lee, Jon. A First Course in Combinatorial Optimization. Cambridge University Press. 2004. ISBN 0-521-01012-8.
- Papadimitriou, Christos H.; Steiglitz, Kenneth. Combinatorial Optimization : Algorithms and Complexity. Dover. July 1998. ISBN 0-486-40258-4.
- Schrijver, Alexander. Combinatorial Optimization: Polyhedra and Efficiency. Algorithms and Combinatorics 24. Springer. 2003. ISBN 9783540443896.
- Schrijver, Alexander. On the history of combinatorial optimization (till 1960) (PDF). Aardal, K.; Nemhauser, G.L.; Weismantel, R. (編). Handbook of Discrete Optimization. Elsevier. 2005: 1–68 [2022-10-16]. (原始內容存檔 (PDF)於2020-11-24).
- Schrijver, Alexander. A Course in Combinatorial Optimization (PDF). February 1, 2006 [2022-10-16]. (原始內容存檔 (PDF)於2022-12-02).
- Sierksma, Gerard; Ghosh, Diptesh. Networks in Action; Text and Computer Exercises in Network Optimization. Springer. 2010. ISBN 978-1-4419-5512-8.
- Gerard Sierksma; Yori Zwols. Linear and Integer Optimization: Theory and Practice. CRC Press. 2015. ISBN 978-1-498-71016-9.
- Pintea, C-M. Advances in Bio-inspired Computing for Combinatorial Optimization Problem. Intelligent Systems Reference Library. Springer. 2014 [2022-10-16]. ISBN 978-3-642-40178-7. (原始內容存檔於2021-04-27).