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Finding the right cutting planes for the TSP

Matthew S. Levine
<span title="2000-12-31">2000</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jel7xxopxbgztkbj4qv7b6iz3u" style="color: black;">ACM Journal of Experimental Algorithmics</a> </i> &nbsp;
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/351827.384248">doi:10.1145/351827.384248</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vozqkkjbd5h5vo6ykqxadkhi3e">fatcat:vozqkkjbd5h5vo6ykqxadkhi3e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070306044634/http://www.acm.org:80/jea/ARTICLES/Vol5Nbr6.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/b8/43/b8439aaf02f44b2ecffc92d7d33d672dce97b36d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/351827.384248"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

A cutting plane method for risk-constrained traveling salesman problem with random arc costs

Zhouchun Huang, Qipeng Phil Zheng, Eduardo Pasiliao, Vladimir Boginski, Tao Zhang
<span title="2018-09-29">2018</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dpj4kespnjdflemhwaulft4tm4" style="color: black;">Journal of Global Optimization</a> </i> &nbsp;
A novel cutting plane algorithm is developed to deal with the difficulty of solving such model, and exhibits superior computational performance in our numerical experiments over other solution approaches  ...  In the presence of uncertainty, the optimal route achieved from solving the deterministic model might be exposed to a high risk that the actual cost exceeds the available resource.  ...  Compared to the branch and cut algorithm that is expected to obtain the optimal solution by visiting the search tree only once, the cutting plane method would visit the tree for more times before finding  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10898-018-0708-0">doi:10.1007/s10898-018-0708-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ai6ozmkpazhije42nfo4mda4zy">fatcat:ai6ozmkpazhije42nfo4mda4zy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200508160123/https://link.springer.com/content/pdf/10.1007/s10898-018-0708-0.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/16/58/1658cb09d805e1783a631ab83807a43b0bc43591.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10898-018-0708-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Three surgical planes identified in laparoscopic complete mesocolic excision for right-sided colon cancer

Da-Jian Zhu, Xiao-Wu Chen, Man-Zhao OuYang, Yan Lu
<span title="">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ay6phj7bp5h57fnt5kutpaz6ya" style="color: black;">World Journal of Surgical Oncology</a> </i> &nbsp;
Conclusions: The laparoscopic complete mesocolic excision surgical plane for right-sided colon cancer is composed of three surgical planes.  ...  Results: In 44 right-sided colon cancer patients, the surgical plane for laparoscopic complete mesocolic excision was found to be composed of three surgical planes that were identified by computed tomography  ...  The RCV is cut off and RGEV is used as the posterior boundary to expand the TSP to the medial.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s12957-015-0758-4">doi:10.1186/s12957-015-0758-4</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26754140">pmid:26754140</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4709915/">pmcid:PMC4709915</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4blbhnmcevhgzgml7uo6zsupiq">fatcat:4blbhnmcevhgzgml7uo6zsupiq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171013125612/http://publisher-connector.core.ac.uk/resourcesync/data/Springer-OA/pdf/613/aHR0cDovL2xpbmsuc3ByaW5nZXIuY29tLzEwLjExODYvczEyOTU3LTAxNS0wNzU4LTQucGRm.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/eb/eb/ebebd2e6a29049a6815c66c0afb232b89f611988.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s12957-015-0758-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> springer.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4709915" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Phase transitions of Traveling Salesperson problems solved with linear programming and cutting planes

Hendrik Schawe, Alexander K. Hartmann
<span title="2016-02-01">2016</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g5hwjttblnfj5hbaytqsfuuwtm" style="color: black;">Europhysics letters</a> </i> &nbsp;
Here, a linear programming approach together with suitable cutting planes is applied.  ...  The Traveling Salesperson problem asks for the shortest cyclic tour visiting a set of cities given their pairwise distances and belongs to the NP-hard complexity class, which means that with all known  ...  Acknowledgments The simulations were performed at the HPC Cluster HERO, located at the University of Oldenburg (Germany) and funded by the DFG through its Major Research Instrumentation Programme (INST  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1209/0295-5075/113/30004">doi:10.1209/0295-5075/113/30004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gh5a2z7bovfqdlqmbq3565atgy">fatcat:gh5a2z7bovfqdlqmbq3565atgy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200909085248/https://arxiv.org/pdf/1512.08554v1.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/40/e9/40e99e647dddf4e2c47becb07d17efa423c6b66a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1209/0295-5075/113/30004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

George Dantzig's contributions to integer programming

Martin Grötschel, George L. Nemhauser
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s6sw62lf6zcxrghfhvjqhycu5y" style="color: black;">Discrete Optimization</a> </i> &nbsp;
This paper reviews George Dantzig's contributions to integer programming, especially his seminal work with Fulkerson and Johnson on the traveling salesman problem.  ...  But how do we find the right ones?  ...  Finding such algorithms is still an active research area, and the progress in this respect is, to a large extent, responsible for the enormous success of the cutting plane approach to the TSP; see [1]  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disopt.2007.08.003">doi:10.1016/j.disopt.2007.08.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m3wyvuym6jcqxdnr2xrilwkuna">fatcat:m3wyvuym6jcqxdnr2xrilwkuna</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808080549/http://www.zib.de/groetschel/pubnew/Dantzig_integer_progr.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/80/8f/808f87e7a113e3afc8b747b6da566f83d8300fd8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disopt.2007.08.003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

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.  ...  His thesis A Linear Programming Approach for the Traveling Salesman Problem appeared in 1972, and reports the first fully automatic version of the cutting-plane method for the TSP.  ... 
<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>

TSP- Infrastructure for the Traveling Salesperson Problem

Michael Hahsler, Kurt Hornik
<span title="">2007</span> <i title="Foundation for Open Access Statistic"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yr3cv2yayvhvdcoj6lb4qw36kq" style="color: black;">Journal of Statistical Software</a> </i> &nbsp;
The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions.  ...  In this paper we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem.  ...  Acknowledgments The authors of this paper want to thank Roger Bivand for providing the code to correctly draw tours and paths on a projected map.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.18637/jss.v023.i02">doi:10.18637/jss.v023.i02</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v66e5drlarhtvbr3dhf54hjmfi">fatcat:v66e5drlarhtvbr3dhf54hjmfi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810161008/http://dirichlet.mat.puc.cl/web/packages/TSP/vignettes/TSP.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/56/f6/56f622a40b41d4f2a8861fb8be97548412f0a3ee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.18637/jss.v023.i02"> <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>

Augmentative Message Passing for Traveling Salesman Problem and Graph Partitioning [article]

Siamak Ravanbakhsh, Reihaneh Rabbany, Russell Greiner
<span title="2014-06-04">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In particular for TSP we are able to find near-optimal solutions in the time that empirically grows with N^3, demonstrating that augmentation is practical and efficient.  ...  The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs.  ...  [10] manually applied the cutting plane method to 49-city problem, a combination of more sophisticated cuts, used with branch-and-bound techniques [16] , has produced the state-of-the-art TSP-solver  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.0941v1">arXiv:1406.0941v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wi6uk7n2anfqtamlihuzhe2loy">fatcat:wi6uk7n2anfqtamlihuzhe2loy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191015161038/https://arxiv.org/pdf/1406.0941v1.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/75/95/75951786ea12e73a14b51822b3378450097b2bf4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.0941v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Computing in Combinatorial Optimization [chapter]

William Cook
<span title="">2019</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We give a tour of this work, focusing on the early development of the subject and the central role played by linear programming.  ...  The paper concludes with a short wish list of future research directions.  ...  The approach they invented in this TSP work is called the cutting-plane method.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-91908-9_3">doi:10.1007/978-3-319-91908-9_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zcyzrmfzrraa3cg53srp6gqnm4">fatcat:zcyzrmfzrraa3cg53srp6gqnm4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200113065342/https://link.springer.com/content/pdf/10.1007%2F978-3-319-91908-9_3.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/a6/4b/a64bf34bf1a9ba81db3f06d5c88ea35d262f2819.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-91908-9_3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Robot Path Planning by Traveling Salesman Problem with Circle Neighborhood: modeling, algorithm, and applications [article]

Arman Nedjatia, Béla Vizvárib
<span title="2020-03-14">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The problem is to find the minimum length Hamiltonian cycle connecting the circles.  ...  The Models are coded in Cplex and Knitro and solved for small and medium sized instances.  ...  Moreover, instead of a circle, one can consider the neighbors as a cut of the hemisphere, while the complexity of problem is arisen, the accuracy is increased.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2003.06712v1">arXiv:2003.06712v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7w7hbuwvfbg77ioteur2s6a73q">fatcat:7w7hbuwvfbg77ioteur2s6a73q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200320200626/https://arxiv.org/ftp/arxiv/papers/2003/2003.06712.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] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2003.06712v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Branch-and-Bound [chapter]

Rafael Martí, Gerhard Reinelt
<span title="2010-09-12">2010</span> <i title="Springer Berlin Heidelberg"> The Linear Ordering Problem </i> &nbsp;
For our IP model, the objective value of any dual feasible solution to the linear-programming (LP) relaxation provides a valid bound B.  ...  The two newly created subproblems need only be considered for further exploration if their corresponding bound B is greater than the value of the best known integer solution to the original model.  ...  [21, 22] , It was Padberg and Rinaldi who coined the term branch and cut for the powerful combination of the two competing algorithms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-16729-4_4">doi:10.1007/978-3-642-16729-4_4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ee34iqzvnjgjvlpg62cclhaj5q">fatcat:ee34iqzvnjgjvlpg62cclhaj5q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705105813/https://www.math.uni-bielefeld.de/documenta/vol-ismp/38_cook-bill.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/ce/99/ce993d9230133e7ff8520b769606560ef5b57d2f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-16729-4_4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 4076 of Mathematical Reviews Vol. , Issue 92g [page]

<span title="">1992</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
For the case where the technical coefficients are normally distributed, we pre- sent a convergent cutting-plane algorithm to solve the equivalent nonlinear program, which takes advantage of the characteristics  ...  92¢:90123 92g:90123 90C15 65K05 90C08 Weintraub, Andrés (RCH-UCS); Vera, Jorge (RCH-UCS) A cutting plane approach for chance constrained linear programs. Oper. Res. 39 (1991), no. 5, 776-785.  ... 
<span class="external-identifiers"> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_mathematical-reviews_1992-07_92g/page/4076" title="read fulltext microfilm" 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> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_mathematical-reviews_1992-07_92g/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Certification of an optimal TSP tour through 85,900 cities

David L. Applegate, Robert E. Bixby, Vašek Chvátal, William Cook, Daniel G. Espinoza, Marcos Goycoolea, Keld Helsgaun
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z7xgofryqjgkxjlwzlky45v4li" style="color: black;">Operations Research Letters</a> </i> &nbsp;
We describe a computer code and data that together certify the optimality of a solution to the 85,900-city traveling salesman problem pla85900, the largest instance in the TSPLIB collection of challenge  ...  Acknowledgements The work of W. Cook was supported by ONR Grant N00014-03-1-0040 and by NSF Grant CMMI-0726370.  ...  to drive the cutting-plane implementation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.orl.2008.09.006">doi:10.1016/j.orl.2008.09.006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uk5txr6jizh7pc4x3ut6me4qiy">fatcat:uk5txr6jizh7pc4x3ut6me4qiy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130717133748/http://mgoycool.uai.cl:80/papers/09applegate_orl.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/fe/d6/fed600f1630f947921e7ff8c0132576aaa0eea5a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.orl.2008.09.006"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems

Tal Tabib
<span title="2007-10-01">2007</span> <i title="SPIE-Intl Soc Optical Eng"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wbcw6rldbvdddg6we6vhk2vvfm" style="color: black;">Optical Engineering: The Journal of SPIE</a> </i> &nbsp;
An optical method for synthesizing a binary matrix representing all feasible solutions of a bounded ͑input length restricted͒ NPcomplete combinatorial problem is presented.  ...  After the preparation of this matrix, an optical matrix-vector multiplier can be used in order to multiply the synthesized binary matrix and a grayscale vector representing the weights of the problem.  ...  Acknowledgments This research was supported by the Israel Science Foundation Grant 119គ03 as well as by Intel, Deutsche Telecom, Rita Altura Trust Chair in Computer Sciences, and the Israel Ministry of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1117/1.2799086">doi:10.1117/1.2799086</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2lirm4l5orgxzcpedwebgk2a4a">fatcat:2lirm4l5orgxzcpedwebgk2a4a</a> </span>
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Solving Large-Scale TSP Using a Fast Wedging Insertion Partitioning Approach

Zuoyong Xiang, Zhenyu Chen, Xingyu Gao, Xinjun Wang, Fangchun Di, Lixin Li, Guangyi Liu, Yi Zhang
<span title="">2015</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wpareqynwbgqdfodcyhh36aqaq" style="color: black;">Mathematical Problems in Engineering</a> </i> &nbsp;
The idea of our proposed algorithm is to cut a TSP tour into four segments by nodes' coordinate (not by rectangle, such as Strip, FRP, and Karp).  ...  The experimental results show that our proposed algorithm in this paper is more efficient for solving large-scale TSPs.  ...  For such reason, it is very difficult to find optimal solution for the TSP, especially for problems with a very large number of cities.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2015/854218">doi:10.1155/2015/854218</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5p2zsh2yi5aktb6zqccedbeggi">fatcat:5p2zsh2yi5aktb6zqccedbeggi</a> </span>
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