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第153行： − − − | url = http://people.brunel.ac.uk/~mastjjb/jeb/or/ip.html − − − Http://people.brunel.ac.uk/~mastjjb/jeb/or/ip.html − − | title = Integer programming − − − 整数规划 − − − | last = Beasley − − | last = Beasley − − | first = J. E. − − − 第一个 = j. e。 − − − | type = lecture notes − − 类型 = 课堂笔记 − − | ref = harv − − | ref = harv − − = harv − − }} − − − }} − − − − | first1 = William J. − − − 1 = William j. − − | last1 = Cook − − − 1 = Cook − − − | author1-link = William J. Cook − − 1-link = William j. Cook − − − | first2 = William H. − − 2 = William h. − − | last2 = Cunningham − − − 2 = Cunningham − − − | first3 = William R. − − 3 = William r. − − | last3 = Pulleyblank − − − 3 = Pulleyblank − − − | author3-link = William R. Pulleyblank − − | author3-link = William r. Pulleyblank − − | last4 = Schrijver − − | last4 = Schrijver − − − | first4 = Alexander − − − 4 = Alexander − − − | author4-link = Alexander Schrijver − − | author4-link = Alexander Schrijver − − | title = Combinatorial Optimization − − − 组合优化 − − − | publisher = Wiley − − | publisher = Wiley − − − | year = 1997 − − 1997年 − − | isbn = 0-471-55894-X − − − | isbn = 0-471-55894-X − − | ref = harv − − | ref = harv − − = harv − − }} − − − }} − − − − | title = Optimal TSP Tours − − − | title = Optimal TSP Tours − − − | url = http://www.tsp.gatech.edu/optimal/index.html − − Http://www.tsp.gatech.edu/optimal/index.html − − − | last = Cook − − | last = Cook − − − | first = William − − 第一名: 威廉 − − − | publisher = University of Waterloo − − 2012年3月24日 | publisher = 滑铁卢大学 − − | year = 2016 − − − 2016年 − − | ref = harv − − | ref = harv − − = harv − − − }} (Information on the largest TSP instances solved to date.) − − }(迄今为止已解决的最大 TSP 实例的信息) − − − − | editor-last1 = Crescenzi − − − 1 = Crescenzi − − − | editor-first1 = Pierluigi − − 1 = Pierluigi − − | editor-last2 = Kann − − − 2 = Kann − − | editor-first2 = Viggo − − − 2 = Viggo − − − | editor-last3 = Halldórsson − − | editor-last3 = Halldórsson − − | editor-first3 = Magnús − − | editor-first3 = Magnús − − − − | editor-last4 = Karpinski − − 4 = Karpinski − − | editor-first4 = Marek − − − 4 = Marek − − | editor4-link = Marek Karpinski − − − 4-link = Marek Karpinski − − − | editor-last5 = Woeginger − − 5 = Woeginger − − | editor-first5 = Gerhard − − − | 编辑器-first5 = Gerhard − − | editor5-link = Gerhard J. Woeginger − − − 5-link = Gerhard j. Woeginger − − | url = http://www.nada.kth.se/%7Eviggo/wwwcompendium/ − − − Http://www.nada.kth.se/%7eviggo/wwwcompendium/ − − − | title = A Compendium of NP Optimization Problems − − 最优化问题概要 − − | ref = harv − − | ref = harv − − = harv − − − }} (This is a continuously updated catalog of approximability results for NP optimization problems.) − − }(这是一个不断更新NP 优化问题的近似结果的目录。) − − − − − | editor-last1 = Das − − 1 = Das − − − | editor-first1 = Arnab − − 1 = Arnab − − − | editor-last2 = Chakrabarti − − 2 = Chakrabarti − − | editor-first2 = Bikas K − − − 2 = Bikas k − − − | editor2-link = Bikas K Chakrabarti − − 2-link = Bikas k Chakrabarti − − − | title = Quantum Annealing and Related Optimization Methods − − 量子退火和相关的优化方法 − − | series = Lecture Notes in Physics − − − | 系列 = 物理学讲义 − − − | volume = 679 − − 679 − − | publisher = Springer − − − | publisher = Springer − − | year = 2005 − − − 2005年 − − | ref = harv − − | ref = harv − − = harv − − | bibcode = 2005qnro.book.....D − − − 2005 qnro. book... d − − }} − − − }} − − − − | last1 = Das − − − 1 = Das − − | first1 = Arnab − − − 1 = Arnab − − − | last2 = Chakrabarti − − 2 = Chakrabarti − − | first2 = Bikas K − − + − 2 = Bikas k − − − − − | title = 学术讨论会: 量子退火和模拟量子计算 − − | journal = Rev. Mod. Phys. − − − | 日记 = rev。Mod.女名女子名。 − − − | volume = 80 − − 80 − − − | issue = 3 − − 第三期 − − − | page = 1061 − − 1061 − − | year = 2008 − − − 2008年 − − − | doi = 10.1103/RevModPhys.80.1061 − − | doi = 10.1103/RevModPhys. 80.1061 − − | ref = harv − − | ref = harv − − = harv − − | citeseerx = 10.1.1.563.9990 − − − 10.1.1.563.9990 − − − | bibcode = 2008RvMP...80.1061D − − 2008/rvmp... 80.1061 d − − − | arxiv = 0801.2193 − − 0801.2193 − − }} − − − }} − − − − | last = Lawler − − − | last = Lawler − − | first = Eugene − − − 第一 = 尤金 − − − | author-link = Eugene Lawler − − | 作者链接 = Eugene Lawler − − | title = Combinatorial Optimization: Networks and Matroids − − − 组合优化: 网络与拟阵 − − | year = 2001 − − − 2001年 − − + − | publisher = Dover − − | publisher = Dover − − − − | isbn = 0-486-41453-1 − − | isbn = 0-486-41453-1 − − | <!-- pages = 117–120 --> − − | <!-- pages = 117–120 --> − − | < ! -- pages = 117-120 -- > − − | ref = harv − − | ref = harv − − = harv − − − }} − − }} − − − − | first = Jon − − − | first = Jon − − | last = Lee − − − | last = Lee − − | author-link = Jon Lee (mathematician) − − − 乔恩 · 李(数学家) − − − | url = https://books.google.com/books?id=3pL1B7WVYnAC − − Https://books.google.com/books?id=3pl1b7wvynac − − − | title = A First Course in Combinatorial Optimization − − 组合优化的第一堂课 − − | publisher = Cambridge University Press − − − 剑桥大学出版社 − − − | year = 2004 − − 2004年 − − | isbn = 0-521-01012-8 − − − | isbn = 0-521-01012-8 − − | ref = harv − − | ref = harv − − = harv − − − }} − − }} − − − − | last1 = Papadimitriou − − − 1 = Papadimitriou − − − | first1 = Christos H. − − 1 = Christos h. − − | last2 = Steiglitz − − − 2 = Steiglitz − − | first2 = Kenneth − − − 2 = Kenneth − − − | author2-link = Kenneth Steiglitz − − | author2-link = Kenneth Steiglitz − − | title = Combinatorial Optimization : Algorithms and Complexity − − − 组合优化: 算法与复杂性 − − − | publisher = Dover − − | publisher = Dover − − − | date = July 1998 − − 日期 = 1998年7月 − − | isbn = 0-486-40258-4 − − − | isbn = 0-486-40258-4 − − | ref = harv − − | ref = harv − − = harv − − }} − − }} − − − − − | last = Schrijver − − | last = Schrijver − − − | first = Alexander − − − 第一个 = 亚历山大 − − | title = Combinatorial Optimization: Polyhedra and Efficiency − − − 组合优化: 多面体与效率 − − − | publisher = Springer − − | publisher = Springer − − − | series = Algorithms and Combinatorics − − 序列 = 算法和组合数学 − − | volume = 24 − − − 24 − − − | year = 2003 − − 2003年 − − | ref = harv − − | ref = harv − − = harv − − | url = https://books.google.com/books?id=mqGeSQ6dJycC − − − Https://books.google.com/books?id=mqgesq6djycc − − − | isbn = 9783540443896 − − 9783540443896 − − − }} − − }} − − − − − | last = Schrijver − − | last = Schrijver − − | first = Alexander − − − 第一个 = 亚历山大 − − − | chapter = On the history of combinatorial optimization (till 1960) − − | 第二章: 组合优化的历史(1960年以前) − − − | title = Handbook of Discrete Optimization − − | title = 离散优化手册 − − | editor-last1 = Aardal − − − 1 = Aardal − − − | editor-first1 = K.|editor1-link=Karen Aardal − − 1 = k | editor1-link = Karen Aardal − − | editor-last2 = Nemhauser − − − 2 = Nemhauser − − | editor-first2 = G.L. − − − 2 = g.l. − − − | editor-last3 = Weismantel − − 3 = Weismantel − − − | editor-first3 = R. − − 3 = r. − − | publisher = Elsevier − − − | publisher = Elsevier − − | year = 2005 − − − 2005年 − − − | pages = 1–68 − − | 页数 = 1-68 − − | chapter-url = http://homepages.cwi.nl/~lex/files/histco.pdf − − − | chapter-url = http://homepages.cwi.nl/~lex/files/histco.pdf − − | ref = harv − − | ref = harv − − = harv − − − }} − − }} − − − − − | last = Schrijver − − | last = Schrijver − − | first = Alexander − − − 第一个 = 亚历山大 − − − | title = A Course in Combinatorial Optimization − − 文章标题: 组合优化课程 − − − | url = http://homepages.cwi.nl/~lex/files/dict.pdf − − Http://homepages.cwi.nl/~lex/files/dict.pdf − − | date = February 1, 2006 − − − 日期 = 2006年2月1日 − − | ref = harv − − | ref = harv − − = harv − − }} − − }} − − − − − − | last1 = Sierksma − − 1 = Sierksma − − − | first1 = Gerard − − 1 = Gerard − − | last2 = Ghosh − − − 2 = Ghosh − − − | first2 = Diptesh − − 2 = Diptesh − − | author1-link = Gerard Sierksma − − − 1-link = Gerard Sierksma − − | title = Networks in Action; Text and Computer Exercises in Network Optimization − − − 行动中的网络; 网络优化中的文本和计算机练习 − − − | publisher = Springer − − | publisher = Springer − − − | date = 2010 − − 2010年 − − | isbn = 978-1-4419-5512-8 − − − | isbn = 978-1-4419-5512-8 − − | ref = harv − − | ref = harv − − = harv − − }} − − }} − − − − − − | author1=Gerard Sierksma − − 1 = Gerard Sierksma − − | author2=Yori Zwols − − − 2 = Yori Zwols − − | title=Linear and Integer Optimization: Theory and Practice − − − | title = 线性和整数优化: 理论与实践 − − − | year=2015 − − 2015年 − − | publisher=CRC Press − − − | publisher = CRC Press − − − | isbn=978-1-498-71016-9 − − | isbn = 978-1-498-71016-9 − − }} − − }} − − − − − − | last = Pintea − − | last = pinter − − − | first = C-M. − − | first = C-M. − − | title = Advances in Bio-inspired Computing for Combinatorial Optimization Problem − − − | title = 组合优化问题的仿生计算进展 − − − | url = https://www.springer.com/la/book/9783642401787 − − Https://www.springer.com/la/book/9783642401787 − − | publisher = Springer − − − | publisher = Springer − − | year = 2014 − − − 2014年 − − − | isbn = 978-3-642-40178-7 − − | isbn = 978-3-642-40178-7 − − | ref = harv − − | ref = harv − − = harv − − | series = Intelligent Systems Reference Library − − − | series = 智能系统参考库 − − − }} − − }} −
无编辑摘要
'''组合优化'''主要是从一个有限的对象[[集合]]中寻找一个最佳对象。<ref>{{harvnb|Schrijver|2003|p=1}}.</ref>在许多这样的问题中，'''穷举搜索 exhaustive search '''是不易处理的。如果这些优化问题可行解集是离散的，或者可行解集可以化为离散的，那么可以在问题范围内进行运算，其目标是找到最优解。典型的问题是'''旅行商问题 Traveling Salesman Problem'''(“ TSP”)、最小[[生成树]]问题(“ MST”)和'''背包问题 Knapsack Problem'''。
'''组合优化'''主要是从一个有限的对象集合中寻找一个最佳对象。<ref>{{harvnb|Schrijver|2003|p=1}}.</ref>在许多这样的问题中，'''穷举搜索 exhaustive search '''是不易处理的。如果这些优化问题可行解集是离散的，或者可行解集可以化为离散的，那么可以在问题范围内进行运算，其目标是找到最优解。典型的问题是'''旅行商问题 Traveling Salesman Problem'''(“ TSP”)、最小[[生成树]]问题(“ MST”)和'''背包问题 Knapsack Problem'''。
==参考文献==
==参考文献==
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| url = http://people.brunel.ac.uk/~mastjjb/jeb/or/ip.html
| url = http://people.brunel.ac.uk/~mastjjb/jeb/or/ip.html
| title = Integer programming
| title = Integer programming
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| first1 = William J.
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| title = Combinatorial Optimization
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| title = Optimal TSP Tours
| title = Optimal TSP Tours
| url = http://www.tsp.gatech.edu/optimal/index.html
| url = http://www.tsp.gatech.edu/optimal/index.html
| last = Cook
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| first = William
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| publisher = [[University of Waterloo]]
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| year = 2016
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}} ''(Information on the largest TSP instances solved to date.)''
}} ''(Information on the largest TSP instances solved to date.)''
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| editor-last1 = Crescenzi
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| editor-first1 = Pierluigi
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| editor-last2 = Kann
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| editor-first2 = Viggo
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| editor-last3 = Halldórsson
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| editor-first3 = Magnús
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| editor-last4 = Karpinski
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| editor-last5 = Woeginger
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| url = http://www.nada.kth.se/%7Eviggo/wwwcompendium/
| url = http://www.nada.kth.se/%7Eviggo/wwwcompendium/
| title = A Compendium of NP Optimization Problems
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| editor-first2 = Bikas K
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| series = Lecture Notes in Physics
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| bibcode = 2005qnro.book.....D
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| title = Colloquium: Quantum annealing and analog quantum computation
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| doi = 10.1103/RevModPhys.80.1061
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| citeseerx = 10.1.1.563.9990
| citeseerx = 10.1.1.563.9990
| bibcode = 2008RvMP...80.1061D
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| title = A First Course in Combinatorial Optimization
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| title = Combinatorial Optimization : Algorithms and Complexity
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| series = Algorithms and Combinatorics
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| author1-link = Gerard Sierksma
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| title = Networks in Action; Text and Computer Exercises in Network Optimization
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| author1=Gerard Sierksma
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| author2=Yori Zwols
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| title=Linear and Integer Optimization: Theory and Practice
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| year=2015
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| last = Pintea
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| first = C-M.
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| title = Advances in Bio-inspired Computing for Combinatorial Optimization Problem
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| url = https://www.springer.com/la/book/9783642401787
| url = https://www.springer.com/la/book/9783642401787
| publisher = Springer
| publisher = Springer
| year = 2014
| year = 2014
| isbn = 978-3-642-40178-7
| isbn = 978-3-642-40178-7
| series = Intelligent Systems Reference Library
| series = Intelligent Systems Reference Library
}}
}}