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Fifty-Plus Years of Combinatorial Integer Programming [chapter]

William Cook
<span title="2009-11-06">2009</span> <i title="Springer Berlin Heidelberg"> 50 Years of Integer Programming 1958-2008 </i> &nbsp;
Throughout the history of integer programming, the field has been guided by research into solution approaches to combinatorial problems.  ...  We discuss some of the highlights and defining moments of this area.  ...  The TSP in the 1950s The birth of combinatorial integer programming occurred in the spring of 1954, pre-dating the start of general integer-programming research by several years.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-68279-0_12">doi:10.1007/978-3-540-68279-0_12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dapp75vgxbaa3oy5eyydr2qyly">fatcat:dapp75vgxbaa3oy5eyydr2qyly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922025720/http://www.math.uwaterloo.ca/~bico//papers/ip50.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6c/60/6c60c990db66e998b08564baa9e71d42e9f03976.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-68279-0_12"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Lp-based combinatorial problem solving

K. Hoffman, M. Padberg
<span title="">1985</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kov3rwzipzf2dmxyohqwfpxrsm" style="color: black;">Annals of Operations Research</a> </i> &nbsp;
A tutorial outline of the polyhedral theory that underlies linear programming (LP)-based combinatorial problem solving is given.  ...  the optimal triangulation of input/output matrices, and the third the optimization of large-scale zero-one linear programming problems.  ...  By the theorem of Weyt [67] , there exists a finite (integer) matrix H and a vector h (of integers) such that holds and, consequently, our combinatorial optimization problem (2.1) becomes the linear program  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf02022040">doi:10.1007/bf02022040</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vqiaqfg2gjgrvc6m6n46yoizuy">fatcat:vqiaqfg2gjgrvc6m6n46yoizuy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190224141828/http://pdfs.semanticscholar.org/6336/50ecbcc98ea896e4fd482c3438ab31675a1d.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/63/36/633650ecbcc98ea896e4fd482c3438ab31675a1d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf02022040"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Confusion in the Church-Turing Thesis [article]

Barry Jay, Jose Vergara
<span title="2014-11-06">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
However, a modern combinatory calculus, the SF-calculus, can define equality of its closed normal forms, and so yields a model of computability that is equivalent to the Turing model.  ...  In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is not equivalent to the Turing model.  ...  Acknowledgments We thank Jacques Carette, Robin Cockett, John Crossley, Nachum Dershowitz, Thomas Given-Wilson, Neil Jones, Jens Palsberg, Reuben Rowe, Peter Selinger, and Eric Torreborre for comments on drafts of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1410.7103v2">arXiv:1410.7103v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ybkzeatss5bdrpvhsj5c5p5bii">fatcat:ybkzeatss5bdrpvhsj5c5p5bii</a> </span>
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Herbert S. Wilf (1931–2012)

Fan Chung, Curtis Greene, Joan Hutchinson, Donald E. Knuth, Aviezri S. Fraenkel, Doron Zeilberger, Marko Petkovšek, Neil Calkin, Rodney Canfield, Albert Nijenhuis, Carla D. Savage, Richard P. Stanley (+1 others)
<span title="2015-04-01">2015</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o5hwtvfzwza2tdpaa2xm3sqpqe" style="color: black;">Notices of the American Mathematical Society</a> </i> &nbsp;
We became closer during the years. Ruth and Herb were always adventurous with food.  ...  Monthly, and was on the advisory board of Integers and the Electronic Journal of Combinatorial Number Theory.  ...  By the end of the year he had proved a result [4] which he described as his "debut": The chromatic number of a graph G is at most 1 plus the largest eigenvalue of its adjacency matrix, with equality  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/noti1247">doi:10.1090/noti1247</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t3t7bvprrzh7hjhybbxxjt3afq">fatcat:t3t7bvprrzh7hjhybbxxjt3afq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809065921/http://www.math.udel.edu/%7Elazebnik/papers/Notices_Of_AMS_H_Wilf.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7c/69/7c694038cbe7c27f18d733718cf37867912668c6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/noti1247"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Evolutionary Computing [article]

Aguston E. Eiben
<span title="2005-11-01">2005</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It amounts to building, applying and studying algorithms based on the Darwinian principles of natural selection. In this paper we briefly introduce the main concepts behind evolutionary computing.  ...  We present the main components all evolutionary algorithms (EA), sketch the differences between different types of EAs and survey application areas ranging from optimization, modeling and simulation to  ...  Introduction Surprisingly enough, the idea to apply Darwinian principles to automated problem solving originates from the fifties, long before the breakthrough of computers [9] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0511004v1">arXiv:cs/0511004v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mjhh3xtvavfh5hxonpdyfaomhe">fatcat:mjhh3xtvavfh5hxonpdyfaomhe</a> </span>
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Evolutionary computing

A.E. Eiben, M. Schoenauer
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5xfy4fcdxvcvdiybp6iqbffqc4" style="color: black;">Information Processing Letters</a> </i> &nbsp;
The contemporary terminology denotes the whole field by evolutionary computing and considers evolutionary programming, evolution strategies, genetic algorithms, and genetic programming as subareas. 0020  ...  It amounts to building, applying and studying algorithms based on the Darwinian principles of natural selection. In this paper we briefly introduce the main concepts behind evolutionary computing.  ...  ., parse-trees of Genetic Programming, see Section 5.4).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0020-0190(02)00204-1">doi:10.1016/s0020-0190(02)00204-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w3vk5sfzyvh65az56smq7aagcu">fatcat:w3vk5sfzyvh65az56smq7aagcu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830050412/http://www.cs.vu.nl/~gusz/papers/ec-intro-Eiben-Schoenauer.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/09/25/09252ffe16e614ecb084354b604bd88d1e9653e5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0020-0190(02)00204-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Evolutionary Computing [chapter]

<span title="2013-04-22">2013</span> <i title="John Wiley &amp; Sons Ltd"> Computational Intelligence </i> &nbsp;
It amounts to building, applying and studying algorithms based on the Darwinian principles of natural selection. In this paper we briefly introduce the main concepts behind evolutionary computing.  ...  We present the main components all evolutionary algorithms (EA), sketch the differences between different types of EAs and survey application areas ranging from optimization, modeling and simulation to  ...  Introduction Surprisingly enough, the idea to apply Darwinian principles to automated problem solving originates from the fifties, long before the breakthrough of computers [9] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/9781118534823.ch6">doi:10.1002/9781118534823.ch6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vghiaafnbjdqffosdz434wbvca">fatcat:vghiaafnbjdqffosdz434wbvca</a> </span>
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Programming pearls: the back of the envelope

Jon Bentley
<span title="1984-03-01">1984</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/i6iajiiyxvgz3ob6jwcn2pufni" style="color: black;">Communications of the ACM</a> </i> &nbsp;
Do readers know of more work on the fascinating combinatorial puzzle of multiword anagrams?  ...  and a quarter of all the bridges of any type built in the U.S. in the 1870s collapsed within ten years of construction.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/357994.381168">doi:10.1145/357994.381168</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cg3qltszavgfrfttugadq6qq74">fatcat:cg3qltszavgfrfttugadq6qq74</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20040420013721/http://www.csie.fju.edu.tw:80/~yeh/research/papers/OS-reading-list/Performance-Evaluation/required/bentley-cacm84-envelope.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f6/0f/f60f8871e9db9c0476c46d3077bd9843297bc956.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/357994.381168"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

George B. Dantzig [chapter]

Saul I. Gass
<span title="">2011</span> <i title="Springer US"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eu7t5yl3jbh5piucndzcckjubu" style="color: black;">International Series in Operations Research and Management Science</a> </i> &nbsp;
Dantzig in the preface to his book, Linear Programming and Extensions, a now classic work published in 1963, some sixteen years after his formulation of the linear programming problem and discovery of  ...  The three passages quoted above represent essential components of Dantzig's outlook on linear programming and, indeed, on mathematics generally.  ...  It pointed the way to several approaches to combinatorial optimization and integer programming problems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-1-4419-6281-2_13">doi:10.1007/978-1-4419-6281-2_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cc4lfxmnhfbyfibwc3v7tmxqjq">fatcat:cc4lfxmnhfbyfibwc3v7tmxqjq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170817050518/http://www.ams.org/journals/notices/200703/fea-cottle.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9e/5c/9e5caa9c447df046cce55e0572ef4f055ed8115a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-1-4419-6281-2_13"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Mathematical Programming in Computational Biology: an Annotated Bibliography

Giuseppe Lancia
<span title="2008-11-24">2008</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/63zsvf7vxzfznojpqgfvpyk2lu" style="color: black;">Algorithms</a> </i> &nbsp;
The field of computational biology has experienced a tremendous growth in the past 15 years.  ...  In this bibliography, we survey some of the most significant contributions that were made to the field and which employ mathematical programming techniques, while giving a broad overview of application  ...  Acknowledgements Part of this work was supported through MIUR's grant P.R.I.N. "Algoritmi di ottimizzazione per l'analisi comparativa di dati genomici di grandi dimensioni ".  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/a1020100">doi:10.3390/a1020100</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3umbzue6irgizahqanwt56or4q">fatcat:3umbzue6irgizahqanwt56or4q</a> </span>
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Stochastic Integer Programming [chapter]

Leen Stougie
<span title="">1992</span> <i title="Springer Berlin Heidelberg"> Operations Research Proceedings 1991 </i> &nbsp;
However, over the last twenty years also some studies on performance analysis of approximation algorithms for stochastic programming have appeared.  ...  Recently the complexity of stochastic programming problems has been addressed, indeed confirming that these problems are harder than most combinatorial optimization problems.  ...  integer linear program.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-46773-8_100">doi:10.1007/978-3-642-46773-8_100</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nu2euvyzfre6tfvqt2dkxk2xy4">fatcat:nu2euvyzfre6tfvqt2dkxk2xy4</a> </span>
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Stochastic Integer Programming [chapter]

A. R. Kan, L. Stougie
<span title="">1988</span> <i title="Springer Berlin Heidelberg"> Springer Series in Computational Mathematics </i> &nbsp;
However, over the last twenty years also some studies on performance analysis of approximation algorithms for stochastic programming have appeared.  ...  Recently the complexity of stochastic programming problems has been addressed, indeed confirming that these problems are harder than most combinatorial optimization problems.  ...  integer linear program.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-61370-8_8">doi:10.1007/978-3-642-61370-8_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k46jjqnrbzdp5iua7s4dgfdkse">fatcat:k46jjqnrbzdp5iua7s4dgfdkse</a> </span>
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Flexibility in generation planning: Identifying key operating constraints

Bryan Palmintier
<span title="">2014</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tdi7xjd3hzbibgwqlwgje432bm" style="color: black;">2014 Power Systems Computation Conference</a> </i> &nbsp;
However, relaxing integers provides the best accuracy vs. performance trade-offs, but only when the linear program (LP) relaxation includes the full problem with UC constraints.  ...  This paper utilizes the recent methodology of clustered integer unit commitment (UC)-which tractably captures operational flexibility within generation expansion planningto explore which operating constraints  ...  Computationally, the integer variables provide structure that both reduces the dimensionality of and guides the search through the combinatorial commitment state space by eliminating identical or very  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/pscc.2014.7038323">doi:10.1109/pscc.2014.7038323</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/pscc/Palmintier14.html">dblp:conf/pscc/Palmintier14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rdl4dr52ibdc7c43fm6zssvru4">fatcat:rdl4dr52ibdc7c43fm6zssvru4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808222836/https://www.pscc-central.org/uploads/tx_ethpublications/pscc2014_477.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/42/c5/42c50d05d8b6889127b0c93a12f0aa095bfd363a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/pscc.2014.7038323"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Designing a Combinatorial Financial Options Market [article]

Xintong Wang, David M. Pennock, Nikhil R. Devanur, David M. Rothschild, Biaoshuai Tao, Michael P. Wellman
<span title="2021-09-14">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We generalize our single-asset mechanism to match options written on different combinations of assets, and prove that optimal clearing of combinatorial financial options is coNP-hard.  ...  As option prices reveal the market's collective belief of an underlying asset's future value, a combinatorial options market enables the expression of aggregate belief about future correlations among assets  ...  Dudík et al. show how to employ constraint generation in linear programming to keep complex related prices consistent [10] . Kroer et al. generalize this approach using integer programming [19] .  ... 
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An annotated bibliography of combined routing and loading problems

Manuel Iori, Silvano Martello
<span title="">2013</span> <i title="National Library of Serbia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fvyaou32obesvjklyww2bwmzhu" style="color: black;">Yugoslav Journal of Operations Research</a> </i> &nbsp;
Transportation problems involving routing and loading at the same time are currently a hot topic in combinatorial optimization.  ...  The interest of researchers and practitioners is motivated by the intrinsic difficulty of this research area, which combines two computationally hard problems, and by its practical relevance in important  ...  Pinson, editors, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, volume 7298 of Lecture Notes in Computer Science, pages 260-274.  ... 
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