组合优化
组合优化（英语：Combinatorial optimization）是数学优化的一个子领域，在应用数学和理论计算机科学的领域中，组合优化是在一个有限的对象集中找出最优对象的一类问题。[1]在很多组合优化的问题中，穷举搜索／枚举法是不可行的。组合优化的问题的特征是可行解的集是离散或者可以简化到离散的，并且目标是找到最优解。常见的例子有旅行推销员问题和最小生成树。
组合优化涉及运筹学、算法理论和计算复杂性理论，在人工智能、机器学习、拍卖理论、软件工程、超大规模集成电路、应用数学和理论计算机科学等多个领域有重要的应用。
组合优化的难处主要是加入拓扑分析的情况，不同的拓扑形态下，不同部分的约束关系便不同，算法也就要调整。如果给定一个拓扑形态，组合优化往往退化成一个整数优化的问题。
应用
特定问题
参考文献
- ^ Schrijver 2003，第1页.
- ^ 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. （原始内容存档 (PDF)于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. （原始内容存档 (PDF)于2019-12-26）.
引注
- Beasley, J. E. Integer programming (lecture notes). [2022-10-16]. （原始内容存档于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]. （原始内容存档于2012-07-22）. (Information on the largest TSP instances solved to date.)
- Crescenzi, Pierluigi; Kann, Viggo; Halldórsson, Magnús; Karpinski, Marek; Woeginger, Gerhard (编). A Compendium of NP Optimization Problems. [2022-10-16]. （原始内容存档于2007-04-05）. (This is a continuously updated catalog of approximability results for NP optimization problems.)
- Das, Arnab; Chakrabarti, Bikas K (编). 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. (编). Handbook of Discrete Optimization. Elsevier. 2005: 1–68 [2022-10-16]. （原始内容存档 (PDF)于2020-11-24）.
- Schrijver, Alexander. A Course in Combinatorial Optimization (PDF). February 1, 2006 [2022-10-16]. （原始内容存档 (PDF)于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. （原始内容存档于2021-04-27）.
