1. Fractal Instances Of The Traveling Salesman Problem By Pablo Moscato.Category Science Math Combinatorics Graph Theory......Fractal Instances of the traveling salesman problem. This page containsresources on the evolving field of the generation of instances http://www.ing.unlp.edu.ar/cetad/mos/FRACTAL_TSP_home.html

Fractal Instances of the Traveling Salesman Problem This page contains resources on the evolving field of the generation of instances of combinatorial optimization problems with known optimal solution. There are currently four available papers on this subject. Papers The Euclidean Traveling Salesman Problem and a Space-Filling Curve , M. G. Norman and P. Moscato, Chaos, Solitons and Fractals , Vol. 6, pages 389-397, 1995. Using L-Systems to generate arbitrarily large instances of the Euclidean Traveling Salesman Problem with known optimal tours , A. Mariano, P. Moscato and M.G Norman, ``Anales del XXVII Simposio Brasileiro de Pesquisa Operacional'' , Vitoria, Brazil, 6-8 Nov. 1995. An Analysis of the Performance of Traveling Salesman Heuristics on Infinite-Size Fractal Instances in the Euclidean Plane. P. Moscato and M.G. Norman, first version Oct. 1994, to appear in ORSA Journal on Computing. Arbitrarily large planar ETSP instances with known optimal tours, by A. Mariano, P. Moscato, and M.G. Norman, expanded version of the paper presented at Vitoria, ES, Brazil, 1995. Paper accepted in the journal ``Pesquisa Operacional''. Using L-Systems to generate TSP Instances A software that generate TSP instances in TSPLIB format is available here . Please refer to the following paper Arbitrarily large planar ETSP instances with known optimal tours,

2. ZIP-Methode: Neue Kombinatorische Optimal-Lösung Für TSP (Traveling-Salesman-P JAVA traveling salesman problem (TSP). JAVA implementation for the symmetric traveling salesman problem (TSP). http://jochen.pleines.bei.t-online.de/

HOME INHALT DOWNLOAD AUTOR IMPRESSUM ein kombinatorischer Ansatz zur optimalen Lösung allgemeiner Traveling-Salesman-Probleme (TSP) (letzte Änderung: 12.02.2003) © Jochen Pleines. Alle Rechte vorbehalten. Nachdruck mit Quellenangabe gestattet. Belegexemplar erbeten. Kurzfassung abstract résumé Ismertetö ... resumen

3. Traveling Salesman Problem - Home Page The traveling salesman problem, or TSP for short, is this given a finite numberof cities along with the cost of travel between each pair of them, find the http://www.math.princeton.edu/tsp/

Santa's Tour 15,112-City TSP History Gallery ... Cutting-Plane Applet Test Instances World TSP National TSPs VLSI TSPs Computations The traveling salesman problem , or TSP for short, is this: given a finite number of "cities" along with the cost of travel between each pair of them, find the cheapest way of visiting all the cities and returning to your starting point. In these pages we report on our ongoing project to solve large-scale instances of the TSP. TSP Cutting-Plane Applet Interactive tool for studying the cutting-plane method for the traveling salesman problem. Solution of a 15,112-city TSP History of the TSP TSP Picture Gallery Applications ... World TSP Challenge and National TSPs VLSI TSP Test Instances Concorde Computer Code Benchmarks ... Links to the TSP Home Page Traveling Salesman Problem Links TSPLIB - Gerd Reinelt's library of TSP instances. TSPBIB - Pablo Moscato's listing of TSP references. 8th DIMACS Implementation Challenge - Testing of TSP heuristics. LKH - Keld Helsgaun's variant of the Lin-Kernighan heuristic. Jesper Larsen's Papers on the TSP A Farmer's Daughter in Our Midst Research supported by the following grants.

4. TSPBIB Home Page A comprehensive listing of papers, source code and preprints. http://www.densis.fee.unicamp.br/~moscato/TSPBIB_home.html

TSPBIB Home Page This page intends to be a comprehensive listing of papers, source code, preprints, technical reports, etc, available on the Internet about the Traveling Salesman Problem (TSP) and some associated problems. Please send us information about any other work you consider it should be included in this page. Pablo Moscato email: moscato@cacr.caltech.edu email: moscato@densis.fee.unicamp.br The picture above shows an instance of the Euclidean, Planar TSP and the optimal curve among the set of cities. This instance has been named MNPeano Order 2. Do you like challenges ? The 8th DIMACS Implementation Challenge is on the way, and the TSP is its subject ! The material in this page is solely aimed for academic research purposes and we encourage the readers to contact the authors of the papers included to correctly cite their papers. To make contributions for papers, preprints, technical reports, etc., let us know the authors of the paper, its title, a very short abstract (such that we could find out what topic this paper belongs to), and, if you wish to, its current status. If you plan to leave a paper for public domain access and wish to include in our list, please leave the paper as a postscript file in compressed or uncompressed form in a public directory, and let us know the complete address of the file there such that we set a link to the file. Other pages related to TSPBIB The Hamiltonian Page , by Gregory Gutin and Pablo Moscato.

5. 1.5.4 Traveling Salesman Problem A weighted graph G. Problem Find the cycle of minimum cost visiting all of the vertices of G exactly once.......1.5.4 traveling salesman problem Input http://www.cs.sunysb.edu/~algorith/files/traveling-salesman.shtml

1.5.4 Traveling Salesman Problem INPUT OUTPUT Input Description: A weighted graph G Problem: Find the cycle of minimum cost visiting all of the vertices of G exactly once. Excerpt from The Algorithm Design Manual : The traveling salesman problem is the most notorious NP-complete problem. This is a function of its general usefulness, and because it is easy to explain to the public at large. Imagine a traveling salesman who has to visit each of a given set of cities by car. Although the problem arises in transportation applications, its most important applications arise in optimizing the tool paths for manufacturing equipment. For example, consider a robot arm assigned to solder all the connections on a printed circuit board. The shortest tour that visits each solder point exactly once defines the most efficient path for the robot. A similar application arises in minimizing the amount of time taken by a graphics plotter to draw a given figure. The best book available for this problem is The Traveling Salesman Problem : A Guided Tour of Combinatorial Optimization by E.L. Lawler (Editor) and A. H. Rinnooy-Kan.

6. Traveling Salesman Problem -- From MathWorld Traveling Salesman Solver. If you want to know what it's all about, please take a look at the information document. http://mathworld.wolfram.com/TravelingSalesmanProblem.html

Applied Mathematics Optimization Discrete Mathematics Graph Theory ... Circuits Traveling Salesman Problem A problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian circuit a salesman can take through each of n cities. No general method of solution is known, and the problem is NP-hard . Solution to the traveling salesman problem is implemented in Mathematica as TravelingSalesman g ] in the Mathematica add-on package DiscreteMath`Combinatorica` (which can be loaded with the command Chinese Postman Problem Dendrite Hamiltonian Circuit Plateau's Problem ... Traveling Salesman Constants References Applegate, D.; Bixby, R.; Chvatal, V.; and Cook, W. "Finding Cuts in the TSP (a Preliminary Report)." Technical Report 95-05, DIMACS. Piscataway NJ: Rutgers University, 1995. Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth. New York: Hyperion, pp. 168-169, 1998. Kruskal, J. B. "On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem." Proc. Amer. Math. Soc.

7. Traveling Salesman Problem Generator Generates a traveling salesman problem map and data for a given set of US cities. http://www.sju.edu/~sforman/research/usa_tsp.html

TSP Generator Research Sean Forman You Are Here When given a set of cities from the United States, this script will generate a map and data necessary to construct a Traveling Salesman Problem for the given set of cities. It determines inter-city great circle distances, and generates a matrix of inter-city distances. It will also apply a series of heuristic techniques to find approximate solutions to the given TSP problem (Repetitive Nearest Neighbor and Cheapest Link). Enter a list of up to 30 cities in the following format: Philadelphia, PA Des Moines, IA Los Angeles, CA List of Cities (City, ST) State Abbreviations AK - Alaska AL - Alabama AR - Arkansas AZ - Arizona CA - California CO - Colorado CT - Connecticut DC - District of Columbia DE - Delaware FL - Florida GA - Georgia HI - Hawaii IA - Iowa ID - Idaho IL - Illinois IN - Indiana KS - Kansas KY - Kentucky LA - Louisiana MA - Massachusetts MD - Maryland ME - Maine MI - Michigan MN - Minnesota MO - Missouri MS - Mississippi MT - Montana NC - North Carolina ND - North Dakota NE - Nebraska NH - New Hampshire NJ - New Jersey NM - New Mexico NV - Nevada NY - New York OH - Ohio OK - Oklahoma OR - Oregon PA - Pennsylvania RI - Rhode Island SC - South Carolina SD - South Dakota TN - Tennessee TX - Texas UT - Utah VA - Virginia VT - Vermont WA - Washington WI - Wisconsin WV - West Virginia WY - Wyoming Size of the Map Small (600 x 400) Medium (720 x 480) Large (1024 x 720) Area Shown by Map As big as needed Lower 48 United States All 50 United States This page is an editor's pick at Michael Trick's Operations Research Page The map technology is from the

8. TSPBIB Home Page TSPBIB Home Page This page intends to be a comprehensive listing of papers, source code, preprints, technical reports, etc, available on the Internet about the traveling salesman problem (TSP) and some associated problems. http://www.ing.unlp.edu.ar/cetad/mos/TSPBIB_home.html

TSPBIB Home Page This page intends to be a comprehensive listing of papers, source code, preprints, technical reports, etc, available on the Internet about the Traveling Salesman Problem (TSP) and some associated problems. Please send us information about any other work you consider it should be included in this page. Pablo Moscato email: moscato@cacr.caltech.edu email: moscato@densis.fee.unicamp.br The picture above shows an instance of the Euclidean, Planar TSP and the optimal curve among the set of cities. This instance has been named MNPeano Order 2. The material in this page is solely aimed for academic research purposes and we encourage the readers to contact the authors of the papers included to correctly cite their papers. To make contributions for papers, preprints, technical reports, etc., let us know the authors of the paper, its title, a very short abstract (such that we could find out what topic this paper belongs to), and, if you wish to, its current status. If you plan to leave a paper for public domain access and wish to include in our list, please leave the paper as a postscript file in compressed or uncompressed form in a public directory, and let us know the complete address of the file there such that we set a link to the file. Other pages related to TSPBIB The Hamiltonian Page , by Gregory Gutin and Pablo Moscato.

9. History Of The Traveling Salesman Problem Mathematical problems related to the traveling salesman problem were treated inthe 1800s by the Irish mathematician Sir William Rowan Hamilton and by the http://www.math.princeton.edu/tsp/histmain.html

History Home Bibliography Milestones Traveling vs Travelling Pictorial History TSP Links TSPLIB Home Page Mathematical problems related to the traveling salesman problem were treated in the 1800s by the Irish mathematician Sir William Rowan Hamilton and by the British mathematician Thomas Penyngton Kirkman . The picture below is a photograph of Hamilton's Icosian Game that requires players to complete tours through the 20 points using only the specified connections. A nice discussion of the early work of Hamilton and Kirkman can be found in the book Graph Theory 1736-1936 by N. L. Biggs, E. K. LLoyd, and R. J. Wilson, Clarendon Press, Oxford, 1976. The general form of the TSP appears to be have been first studied by mathematicians starting in the 1930s by Karl Menger in Vienna and Harvard. The problem was later promoted by Hassler Whitney and Merrill Flood at Princeton. A detailed treatment of the connection between Menger and Whitney, and the growth of the TSP as a topic of study can be found in Alexander Schrijver 's paper `` On the history of combinatorial optimization (till 1960) Annotated Bibliography Milestones in the Solution of TSP Instances Traveling versus Travelling ... Back to TSP home Last updated: March 21, 2002.

10. Euphoria Programming Categorized program downloads, screenshots utilities, graphic effects, libraries, example of how to combine EuGL and Exotica, traveling salesman problem solver. http://www.cyd.liu.se/~micol972/site/euphoria.htm

Programs: Utilities: Bitmap tool (color reduction, dithering..) Interactive hiragana/katakana teacher Sample generator WAV editor Various graphic effects: Blurry Particles RotoZoomer Waving Flag Wormhole ... Voxel Other: An example of how to combine EuGL with Exotica Ant-Q Traveling Salesman Problem solver Not Quite Assembly compiler Libraries: OpenGL wrapper for Euphoria CxImage wrapper for Euphoria Lossless image codec AVI export library ... WinAmp input-plugin wrapper Get the latest version of Euphoria

11. Diane Elizabeth Vaughan Information about the author's research activities, including stochastic processes, the traveling salesman problem, simultaneous generalized hill climbing algorithms, ergodic theory, and simulated annealing. http://filebox.vt.edu/users/dvaughn/

Dr. Diane Elizabeth Vaughan Post Doctorate Research Associate Department of Mechanical and Industrial Engineering University of Illinois at Urbana-Champaign 1206 West Green Street, MC-244 vaughand@vt.edu (540) 626 5741 (Home) (540) 231-3838 (Office) Formal Curriculum Vitae pdf Research Activities ( Want to know more?) Projection Pursuit The objective of this project is to study the problem of finding an optimal projection of data contained in a high dimensional space to a lower dimensional space. The Bayes Classifier is used to classify the data in the low dimensional space. Hybrid Local Search Algorithms This research creates hybrid algorithms that combine heuristic procedures that guarantee long term convergence (globally optimal solutions) with heuristic procedures that guarantee reasonable finite-time performance (locally optimal solutions). Formulating the Meta-Heuristic Tabu Search The goal of this project is to mathematically formulate probabilistic tabu search to be used in conjunction with other heuristics (i.e., simulated annealing), in such a way that the heuristic can be easily modeled as a nonstationary Markov Chain. Discrete Manufacturing Process Design Optimization This research is motivated by the Air Force’s interest in identifying optimal manufacturing process designs, where the finished unit (e.g., a titanium integrated blade rotor) meets certain geometric and microstructural specifications, and is produced at minimum cost.

12. The Traveling Salesman Problem The traveling salesman problem. The TSPLIB is Gerhard Reinelt's libraryof 110 instances of the traveling salesman problem. Some http://www.cs.rutgers.edu/~chvatal/tsp.html

The traveling salesman problem The traveling salesman problem, or TSP for short, is this: given a finite number of ``cities'' along with the cost of travel between each pair of them, find the cheapest way of visiting all the cities and returning to your starting point. (Here, we consider just the symmetric TSP, where traveling from city X to city Y costs the same as traveling from Y to X; the ``way of visiting all the cities'' is simply the order in which the cities are visited.) To put it differently, the data consist of integer weights assigned to the edges of a finite complete graph; the objective is to find a hamiltonian cycle (that is, a cycle passing through all the vertices) of the minimum total weight. In this context, hamiltonian cycles are commonly called tours TSPLIB is Gerhard Reinelt's library of 110 instances of the traveling salesman problem. Some of these instances arise from the task of drilling holes in printed circuit boards and others have been constructed artificially. (A popular way of constructing a TSP instance is to choose a set of actual cities and to define the cost of travel from X to Y as the distance between X and Y.) None of them (with a single exception) is contrived to be hard and none of them is contrived to be easy; some of them have been solved (a few of these are shown here ) and others have not.

13. DIMACS TSP Challenge 8th DIMACS Implementation Challenge The traveling salesman problem. ChallengeNews Still Open for Business! (Including New DoIt-Yourself Feature). http://www.research.att.com/~dsj/chtsp/

8th DIMACS Implementation Challenge: The Traveling Salesman Problem Challenge News: Still Open for Business! (Including New Do-It-Yourself Feature) The original deadline for submitting results to TSP Challenge has passed, and the Johnson-McGeoch chapter that summarizes the Challenge results (as of 1 July 2001), ``Experimental analysis of heuristics for the STSP,'' has now been published in The Traveling Salesman Problem and Its Variations , G. Gutin and A. P. Punnen (Editors), Kluwer Academic Publishers, 2002, Boston, 369-443. A near-final draft, differing from the published version only in pagination and the correction of a few typographical errors, can be downloaded: ( 80 pages postscript PDF ). The deadline has also passed for the DIMACS technical report that will cover all the Challenge submissions and describe this website in detail. However, this report has not yet been completed, so there may still be time for late results to be included (new deadline: 1 September 2002). Even after the report is written we will continue to welcome submissions, and will periodically add them to the Results Page below. We hope to maintain this site indefinitely so that future TSP researchers will have a ready set of benchmarks to which they can compare their results. Moreover, software is now available ( tarfile zipfile ) so that users of UNIX/LINUX systems can generate figures and comparison charts for their data in our standard formats (gif and postscript) before they submit it to the site. Also included is code that will generate normalized results like those on our Results page, and this code should work on most platforms.

14. Traveling Salesman Problem (TSP) JAVA traveling salesman problem (TSP). JAVA implementation for thesymmetric traveling salesman problem (TSP). In this problem a http://home.planet.nl/~onno.waalewijn/tspfast.html

JAVA Traveling Salesman Problem (TSP) JAVA implementation for the symmetric Traveling Salesman Problem (TSP). In this problem a salesperson has to find the shortest possible route to visit all the cities. more information See also: Exact Traveling Salesman Problem Fast exhaustive version, runs up to 150 cities links to related sites combinatorics home

15. Exhaustive Traveling Salesman Problem Exhaustive traveling salesman problem (TSP). Exhaustive (or exact)implementation for the traveling salesman problem NEW now also http://home.planet.nl/~onno.waalewijn/tspx.html

Exhaustive Traveling Salesman Problem (TSP) Exhaustive (or exact) implementation for the Traveling Salesman Problem NEW - now also solves Asymmetric TSP's - see demo's The following actions are performed to compute the shortest path: - make an initial path by greedy or nearest neighbour assignments - improve this by Opt4, Opt2 and Opt3 moves - improve this again by Simulated Annealing - then start an exhaustive search, with the upperbound found in the previous step - here we backtrack if the lowerbound found by computing the Minimum Spanning Tree for the unassigned cities exceeds the upperbound - improve the lowerbound by Lagrangean relaxation - for 2d problems I also try to exclude crossings in the path using opt2 (still thinking about opt3/4) - I also try to find points close to but not in the path yet, that can be proven to belong in the path usage: While computing the optimal solution intermediate results are shown at 5 second intervals: The black line shows current path, red line shows MST, green is best found yet Interrupt by pressing the Break button The knights 5*6 and 8*8 are not true TSP problems, but the Knights problem for a 5*6 and a 8*8 chessboard. The Knight has to make a closed tour, touching each square exact once

16. TSPLIB TSPLIB. Symmetric traveling salesman problem (TSP). Given a not. HCP data Asymmetric traveling salesman problem (ATSP). Given a http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/

TSPLIB TSPLIB is a library of sample instances for the TSP (and related problems) from various sources and of various types. Frequently asked questions We have a small collection of answers to frequently asked questions (FAQ) Please read this and the description of the library before reporting problems with TSPLIB Symmetric traveling salesman problem (TSP) Given a set of n nodes and distances for each pair of nodes, find a roundtrip of minimal total length visiting each node exactly once. The distance from node i to node j is the same as from node j to node i. -> TSP data Best known solutions for symmetric TSPs Hamiltonian cycle problem (HCP) Given a graph, test if the graph contains a Hamiltonian cycle or not. -> HCP data Asymmetric traveling salesman problem (ATSP) Given a set of n nodes and distances for each pair of nodes, find a roundtrip of minimal total length visiting each node exactly once. In this case, the distance from node i to node j and the distance from node j to node i may be different. -> ATSP data Best known solutions for asymmetric TSPs Sequential ordering problem (SOP) This problem is an asymmetric traveling salesman problem with additional constraints. Given a set of n nodes and distances for each pair of nodes, find a Hamiltonian path from node 1 to node n of minimal length which takes given precedence constraints into account. Each precedence constraint requires that some node i has to be visited before some other node j.

17. Neil Simonetti's Traveling Salesman Problem Page Neil Simonetti's traveling salesman problem Page. Results for the DIMACSChallenge Res. 1983 (J. Tama). More traveling salesman problem Links http://www.andrew.cmu.edu/~neils/tsp/

Neil Simonetti's Traveling Salesman Problem Page Results for the DIMACS Challenge Results in HTML tables Results in separate text files: Benchmark Runs Brief text description of the algorithm Dynamic Programming Code for the TSP: Linear Time Dynamic Programming Algorithms for New Classes of Restricted TSPs: A Computational Study gzipped postscript Adobe pdf INFORMS Journal on Computing My Thesis: Applications of a Dynamic Programming Approach to the Traveling Salesman Problem gzipped postscript Adobe pdf Conference Procedings, IPCO V: Implementation of a Linear Time Algorithm for Certain Generalized TSP's gzipped postscript Adobe pdf The Code: ag.h agtw.h dynopt.h solver.h (Instructions are contained in an appendix to my thesis) Sample Shells: regtsp.c twdist.c twtime.c uscity.c (Instructions are contained in an appendix to my thesis) Building the Auxiliary Structure: auxgraph.c Selected Test Data Sites for the TSP: U. S. Cities : Symmetric TSP's based on the layout of America's Largest Cities. (Neil Simonetti) TSPLIB : Largest catalog of TSP related problems on the web. (Gerhard Reinelt) [

18. MP-TESTDATA - Traveling Salesman Problem Instances traveling salesman problem Instances. ATSPTW, Instances of the asymmetric travelingsalesman problem with time windows, contributed by N. Ascheuer (ZIB). http://elib.zib.de/pub/Packages/mp-testdata/tsp/

MP-TESTDATA Assignment Integer/Mixed Integer Programming Linear Programming ... Matrix decomposition (MADLIB) Maximum Flow Minimum Cost Flow/ Transportation Min-Cut Clustering ... Steiner Tree Packing (SteinLib) Traveling Salesman (TSPLIB) Vehicle Routing (VRPLIB) Instance Generators References to other MP data collections MP-TESTDATA Traveling Salesman Problem Instances ATSPTW Instances of the asymmetric traveling salesman problem with time windows, contributed by N. Ascheuer (ZIB). SOP Instances of the sequential ordering problem (asymmetric traveling salesman problem with precedence constraints), see TSP Information on resources for solving Traveling Salesman problems including benchmarks, by D. Applegate, R. Bixby, V. Chvatal, W. Cook. TSPLIB Mirror of TSPLIB by G. Reinelt, see: TSPLIB - A Traveling Salesman Problem Library , ORSA Journal on Computing 3 (1991), pp. 376-384 Last update: March 13, 2000 Georg Skorobohatyj ZIB Homepage URL: http://elib.zib.de/pub/Packages/mp-testdata/tsp/index.html

19. World-Record Traveling Salesman Problem For 3038 Cities Solved WorldRecord traveling salesman problem for 3038 Cities Solved. The problemis commonly referred to as the traveling salesman problem. . http://www.crpc.rice.edu/CRPC/newsletters/jan93/news.tsp.html

20. CRPC Researchers Solve Traveling Salesman Problem For Record- CRPC Researchers Solve traveling salesman problem for RecordBreaking13,509 Cities. 13,509 US cities with populations of more than http://www.crpc.rice.edu/CRPC/newsletters/sum98/news_tsp.html

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