41. The Travelling Salesman Problem The travelling salesman problem is quite simple a travelling salesman has to But one was able to prove that the traveling salesman problem is a kind of http://www.uni-kl.de/AG-AvenhausMadlener/tsp-eng.html

The travelling salesman problem The travelling salesman problem is an optimization problem . Therefore it is not sufficient to find an arbitrary solution. Instead, one is interested in the best (or at least a very good) solution. The travelling salesman problem is quite simple: a travelling salesman has to visit customers in several towns, exactly one customer in each town. Since he is interested in not being too long on the road, he wants to take the shortest tour. He knows the distance between each two towns he wants to visit. The picture shows two possible tours for an example with five cities. For such a small example the problem is easy to solve. But examples with 100 or 1000 cities show that a systematic search for a solution is very expensive. So far, nobody was able to come up with an algorithm for solving the traveling salesman problem that does not show an exponential growth of run time with a growing number of cities. There is a strong belief that there is no algorithm that will not show this behaviour, but no one was able to prove this (yet). But one was able to prove that the traveling salesman problem is a kind of prototypical problem for a big class of problems (the famous class NP) that show this exponential behaviour. This is the reason why many reasearch groups are interested in the traveling salesman problem, since techniques developed for this problem can be transfered to other problems of this class. Follow the links to the teamwork main page the start page of the guided tour

42. Euclidean Traveling Salesman Problem Definition of Euclidean traveling salesman problem, possibly with links to more information and implementations. http://www.nist.gov/dads/HTML/euclidntrvls.html

Euclidean traveling salesman problem (classic problem) Definition: Find a path of minimum Euclidean distance between points in a plane which includes each point exactly once and returns to its starting point. See also traveling salesman spanning tree Note: This can be generalized to higher dimensions, for instance, points in a 3-dimensional space. This problem is a special case of traveling salesman since the cost between points is the planar distance instead of arbitrary weights. Author: PEB Go to the Dictionary of Algorithms and Data Structures home page. If you have suggestions, corrections, or comments, please get in touch with Paul E. Black (paul.black@nist.gov). Entry modified Fri Dec 17 12:03:57 2004. HTML page formatted Wed Aug 24 11:22:59 2005. Cite this as: Paul E. Black, "Euclidean traveling salesman problem", from Dictionary of Algorithms and Data Structures , Paul E. Black, ed., NIST http://www.nist.gov/dads/HTML/euclidntrvls.html

43. Traveling Salesman Problem -- Facts, Info, And Encyclopedia Article traveling salesman problem. Categories NPcomplete problems, Optimization, The traveling salesman problem or travelling salesman problem (TSP), http://www.absoluteastronomy.com/encyclopedia/t/tr/traveling_salesman_problem.ht

Traveling salesman problem [Categories: NP-complete problems, Optimization, Graph theory] The traveling salesman problem or travelling salesman problem TSP ), also known as the traveling salesperson problem is a problem in (Click link for more info and facts about discrete) discrete or (Click link for more info and facts about combinatorial optimization) combinatorial optimization . It is a prominent illustration of a class of problems in (Click link for more info and facts about computational complexity theory) computational complexity theory which are hard to solve. Problem statement Given a number of cities and the costs of traveling from any city to any other city, what is the cheapest round-trip route that visits each city once and then returns to the starting city? An equivalent formulation in terms of (Click link for more info and facts about graph theory) graph theory is: Given a (Click link for more info and facts about complete weighted graph) complete weighted graph (where the vertices would represent the cities, the edges would represent the roads, and the weights would be the cost or distance of that road), find the (Click link for more info and facts about Hamiltonian cycle) Hamiltonian cycle with the least weight.

44. Traveling Salesman Problem - Maple Application Center - Maplesoft The traveling salesman problem (TSP) is a fascinating optimization problem in which a salesman wishes to visit each of N cities exactly once and return to http://www.maplesoft.com/applications/app_center_view.aspx?AID=966

45. IMA PUBLIC LECTURE The Traveling Salesman Problem By William J. Cook, October 16 The traveling salesman problem, or TSP for short, is easy to state given a number of cities along with the cost of travel between each pair of them, http://www.ima.umn.edu/public-lecture/tsp/

Homepage About the IMA What's Happening Programs/Activities ... Join our Mailing Lists Search 2002-2003 Program: Optimization IMA PUBLIC LECTURE The Traveling Salesman Problem William J. Cook Industrial and Systems Engineering Georgia Institute of Technology wcook@isye.gatech.edu http://www.isye.gatech.edu/~wcook/ Wednesday, October 16, 2002, 7:00 PM Moos Tower, Room 2-650 University of Minnesota , East Bank Poster pdf jpg http://www.math.princeton.edu/tsp/ Talk 58 mins. RealAudio(SureStream) USA 13509 Cities USA 13509 Maze USA 13509 Tour The traveling salesman problem, or TSP for short, is easy to state: given a 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. The simplicity of the statement is deceptive - the TSP is one of the most intensely studied problems in computational mathematics and yet no effective solution method is known for the general case. Indeed, the resolution of the TSP would settle the P versus NP problem and fetch a $1,000,000 prize from the Clay Mathematics Institute. Although the complexity of the TSP is still unknown, for over 50 years its study has led the way to improved solution methods in many areas of mathematical optimization. We will discuss the history of the TSP and examine the role it has played in modern computational mathematics. We will also present a collection of TSP applications, ranging from genome sequencing to on-line grocery shopping. Finally, we will present a survey of recent progress in algorithms for large-scale TSP instances, including the solution of a million-city instance to within 0.09% of optimality and the exact solution of a 15,112-city instance.

46. Traveling Salesman Problem - Definition Of Traveling Salesman Problem In Encyclo The traveling salesman problem (TSP), also known as the traveling salesperson problem,is a problem in discrete or combinatorial optimization. http://encyclopedia.laborlawtalk.com/Traveling_salesman_problem

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law The traveling salesman problem TSP ), also known as the traveling salesperson problem , is a problem in discrete or combinatorial optimization . It is a prominent illustration of a class of problems in computational complexity theory which are hard to solve. Contents showTocToggle("show","hide") 1 Problem statement 2 Computational complexity 3 NP-hardness 4 Algorithms ... 7 External links Problem statement Given a number of cities and the costs of travelling from one to the other, what is the cheapest roundtrip route that visits each city once and then returns to the starting city? An equivalent formulation in terms of graph theory is: Find the Hamiltonian cycle with the least weight in a weighted graph It can be shown that the requirement of returning to the starting city does not change the computational complexity of the problem. A related problem is the Bottleneck traveling salesman problem (bottleneck TSP): Find the Hamiltonian cycle in a weighted graph with the minimal length of the longest edge The problem is of considerable practical importance, apart from evident transportation and logistics areas. A classic example is in

47. PCGrate -> Traveling Salesman Problem International Intellectual Group, Inc. (IIG, Inc.) is a small private company which was established in 1996 by specialists from the USA and Russia for http://www.pcgrate.com/about/npcomprb/tsp

Traveling Salesman Problem

48. Interactive Genetic Algorithms For The Traveling Salesman Problem Interactive Genetic Algorithms for the traveling salesman problem. http://www.cse.unr.edu/~sushil/papers/conference/newpapers/99/gecco99/iga/GECCO/

Next: INTRODUCTION Interactive Genetic Algorithms for the Traveling Salesman Problem Sushil J. Louis Genetic Adaptive Systems Lab Dept. of Computer Science/171 University of Nevada, Reno Reno, NV 89557 sushil@cs.unr.edu Rilun Tang Genetic Adaptive Systems Lab Dept. of Computer Science/171 University of Nevada, Reno Reno, NV 89557 tang@cs.unr.edu Abstract: We use an interactive genetic algorithm to divide and conquer large traveling salesperson problems. Current genetic algorithm approaches are computationally intensive and may not produce acceptable tours within the time available. Instead of applying a genetic algorithm to the entire problem, we let the user interactively decompose a problem into subproblems, let the genetic algorithm separately solve these subproblems and then interactively connect subproblem solutions to get a global tour for the original problem. Our approach significantly reduces the computing time to find high quality solutions for large traveling salesperson problems. We believe that an interactive approach can be extended to other visually decomposable problems. INTRODUCTION METHODOLOGY Genetic Algorithm for TSP Analysis ... About this document ...

49. Generation5 - Genetic Algorithm And Traveling Salesman Problem Generation5 aims to be the most comprehensive Artificial Intelligence site on the Internet. Communityorientated, Generation5 deals with all AI topics http://www.generation5.org/content/2001/tspapp.asp

Home Articles Reviews Interviews ... Contribute Login Login: Password: Keep me logged in. ( help Register Why register? Lost your password? ... MobES Expert System Friends and Affiliates Home Articles Genetic Algorithms > Applications/Code Genetic Algorithm and Traveling Salesman Problem By Konstantin Boukreev Printable Version Title: Genetic Algorithm and Traveling Salesman Problem Author: Konstantin Boukreev Email: konstantin@mail.primorye.ru Environment: VC++ 6.0. SP5, Win2k SP2, MS Platform SDK April 2001 Description: The example of using Genetic Algorithm for solving Traveling Salesman Problem Download TSPApp executable - 155 Kb Download TSPApp source - 119 Kb contents Genetic Algorithm Theory GA and TSP Base implementation, Template class GA and GA Selection classes Genome of Travel TSP Application GA thread UI interface Environment Reference I am not a GA guru and I do not have any degree in GA so this article can't be used as GA book or GA tutorial. There aren't any mathematics nor logic nor algebra about GA. It's only a programmer's view on Genetic Algorithms and only example of GA coding. Use it carefully! Any comments and criticism are highly appreciated. Genetic Algorithm, Theory

50. Traveling Salesman Problem Discussion The traveling salesman problem is the most notorious NPcomplete The TSPLIB library of test instances for the traveling salesman problem is http://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE175.HTM

Next: Hamiltonian Cycle Up: Graph Problems: Hard Problems Previous: Vertex Cover Traveling Salesman Problem Input description : A weighted graph G Problem description : Find the cycle of minimum cost that visits each of the vertices of G exactly once. Discussion : 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. What is the shortest route that will enable him to do so and return home, thus minimizing his total driving? 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. Several issues arise in solving TSPs: Is the graph unweighted?

51. World-Record Traveling Salesman Problem For 3038 Cities Solved The problem is commonly referred to as the traveling salesman problem. The traveling salesman problem is typical of a large class of hard http://nhse.cs.rice.edu/CRPC/newsletters/jan93/news.tsp.html

Volume 7, Issue 1 - Spring/Summer 1999 Volume 6, Issue 3 Fall 1998 ... January 1993 World-Record Traveling Salesman Problem for 3038 Cities Solved Finding an optimal route becomes more challenging as the number of cities involved increases. For instance, to solve for the most economical way for a traveling salesman to tour five cities the researcher can take a straightforward method, having the computer calculate the lengths of all 120 different routes to find the shortest one. This calculation could be performed in a fraction of a second. However, using the same method to figure the optimal route for a hundred cities could take billions of years. How can a more efficient solution be reached? The researchers designed an algorithm based on a technique called "branch and cut," which steadily improves the collection of linear inequalities describing the set of feasible solutions. Many other groups have created algorithms that can reach approximate (within 2%) solutions for this problem, calculating approximate optimal routes for 1000 cities in a few minutes. Improved versions of those techniques were used here to get upper bounds. The difficult part was to drive up the lower bound and prove optimality. Calculations for the 3038 cities problem required one and one-half years of computer time. The Traveling Salesman Problem is typical of a large class of "hard" optimization problems that have intrigued mathematicians and computer scientists for years. Most important, it has applications in science and engineering. For example, in the manufacture of a circuit board, it is important to determine the best order in which a laser will drill thousands of holes. An efficient solution to this problem reduces production costs for the manufacturer.

52. Traveling Salesman Problem traveling salesman problem. Session MA29 Date/Time Monday 08000930 Type Contribute Sponsor Track Cluster Room Room 326 Chair John Mittenthal http://www.informs.org/Conf/WA96/TALKS/MA29.html

Go to INFORMS Page ... INFORMS Home What's New Info for Members Info for Nonmembers Conferences Continuing Education Education/Students Employment Prizes Publications Subdivisions Searchable Databases Links About this Web Site INFORMS Online Bookstore Discussion Search Traveling Salesman Problem Session: Date/Time: Monday 08:00-09:30 Type: Contribute Sponsor: Track: Cluster: Room: Room 326 Chair: John Mittenthal Chair Address: A Comparison of Global Search Heuristics for the TSSP+1 John Mittenthal Jose M. Pires, Luis Gouveia Prize-Collecting Traveling Salesman Problem Santosh N. Kabadi, A. Punnen Polyhedral Analysis for the Prize Collecting TSP Ann E. Bixby, David Simchi-Levi, Collette Coullard INFORMS Online Questions on membership, subscriptions and the like should go to INFORMS Customer Service Questions/comments of a general nature about this Web site should go to Editor, IOL

53. Problem 54: Traveling Salesman Problem In Solid Grid Graphs Problem 54 traveling salesman problem in Solid Grid Graphs. http://maven.smith.edu/~orourke/TOPP/P54.html

Next: Problem 55: Pallet Loading Up: The Open Problems Project Previous: Problem 53: Minimum-Turn Cycle Problem 54: Traveling Salesman Problem in Solid Grid Graphs Statement What is the complexity of finding a shortest tour in a solid planar grid graph? A planar grid graph is a graph whose vertices are any set of points on the planar integer lattice and whose edges connect every pair of vertices at unit distance. Distances between nodes correspond to induced shortest-path distances in the graph, which corresponds to ``Manhattan'' distances. A grid graph is solid if it does not have any holes, i.e., its complement in the planar integer lattice is connected. Origin ] show that the problem is NP-complete in general planar grid graphs. Status/Conjectures Open. Motivation Partial and Related Results ] show that Hamiltonicity of a solid grid graph can be decided in polynomial time. Thus we can decide whether there is a tour of length equal to the number of vertices. In contrast, deciding Hamiltonicity is NP-hard in general planar grid graphs [ ABD+01 ] observe that finding the shortest tour is polynomially solvable when restricted to thin grid graphs, i.e., grid graphs that do not contain an induced

54. Citations: The Traveling Salesman Problem With Distances One And Two - Papadimit C. Papadimitriou and M Yannakakis. The traveling salesman problem with distances one and two. Mathematics of Operations Research. To appear. http://citeseer.ifi.unizh.ch/context/24035/0

88 citations found. Retrieving documents... C. Papadimitriou and M. Yannakakis, " The traveling salesman problem with distances one and two ," Mathematics of Operations Research 18(1993) 1-11. Home/Search Document Not in Database Summary Related Articles Check This paper is cited in the following contexts: First 50 documents Next 50 Light Spanners and Approximate TSP in Weighted Graphs with - Forbidden Minors.. (Correct) ....by NSF Grant number CCR9820931. Department of Mathematics and Computer Science, Emory University, Atlanta GA 30322, USA. Email : mic mathcs.emory.edu. Same support and address. Email : psissok emory.edu. that is polynomial (or quasi polynomial) in n. Even the approximation problem is MAXSNP hard , so we do not expect an efficient approximation scheme for general graphs (even sparse graphs) However, there are approximation schemes running in polynomial time when G is planar [2, 6] and in quasi polynomial time when G has bounded genus [5] In this paper we show that the approximation . C. H. Papadimitriou and M. Yannakakis. The Traveling Salesman Problem with distances one and two . Mathematics of Operations Research, 18:111, 1993.

55. On The Approximability Of The Traveling Salesman Problem - Papadimitriou, Vempal We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than when the edge lengths are allowed to be http://citeseer.ifi.unizh.ch/papadimitriou00approximability.html

Alternate document: Details On the Approximability of Trade-offs and Optimal Access of Web Sources (Extended Abstract) ( Christos H. Papadimitriou , Mihalis On The Approximability Of The Traveling Salesman Problem (2000) (Make Corrections) (9 citations) Christos H. Papadimitriou, Santosh Vempala Home/Search Context Related View or download: Berkeley.edu/~christos/tsp.ps Cached: PS.gz PS PDF Image ... Help From: Berkeley.edu/~christos/ (more) (Enter author homepages) Rate this article: (best) Comment on this article (Enter summary) Abstract: (Update) Cited by: More Approximation Algorithms for Some Vehicle Routing Problems - Cristina Bazgan Refael (Correct) The Primal-Dual Method for Approximation Algorithms - Williamson ... (Correct) Active bibliography (related documents): More All Approximation Hardness for Small Occurrence - Instances Of Np-Hard (Correct) ... (Correct) Similar documents based on text: More All Latent Semantic Indexing: A Probabilistic Analysis - Papadimitriou, Raghavan.. (1998) (Correct) ... (Correct) Related documents from co-citation: More All Polynomial time approximation schemes for Euclidean TSP and other geometric prob..

56. The Geometric Maximum Traveling Salesman Problem We consider the traveling salesman problem when the cities are points in num The traveling salesman problem for a maximum in finitedimensional real http://portal.acm.org/citation.cfm?id=876640

57. Traveling Salesman Problem - Permutation City The travelling salesman problem involves planning a route from city to city for a For this implementation of the Travelling Salesman Problem only a new http://www.permutationcity.co.uk/projects/mutants/tsp.html

58. Combinatorial Optimization And The Traveling Salesman Problem :: SADIO :: Socied Sociedad Argentina de Informática e Investigación Operativa. http://www.sadio.org.ar/pn750/modules.php?op=modload&name=News&file=article&sid=

59. Hybrid Genetic Algorithms For The Traveling Salesman Problem Hybrid Genetic Algorithms for the traveling salesman problem Hybrid Genetic Algorithms for the traveling salesman problem, International Conference on http://www.cad.polito.it/FullDB/exact/icnnga.html

CAD Group Publications icnnga show related papers Hybrid Genetic Algorithms for the Traveling Salesman Problem P. Prinetto M. Rebaudengo maurizio rebaudengo polito ... http://www.cad.polito.it/staff/sonza/ International Conference on Neural Networks and Genetic Algorithms, Innsbruck (A), Aprile 1993, pp.559-566 KEYWORDS: Approximate Methods Evolutionary Algorithms Genetic Algorithms ABSTRACT A comparative analysis is performed on an experimental basis among four different cross-over operators. In order to exploit the benefits of the different operators, a new one (called Mixed Cross-over) is introduced, trading-off the CPU time requirements and the obtained results. A new operator is then proposed, whose goal is to include in the genetic mechanism some heuristic knowledge drawn from the already proposed local-optimization techniques. The performance of the new operator is discussed. Related files: icnnga.zip compressed archive (with PkZip) [PRSe93] P. Prinetto, M. Rebaudengo, M. Sonza Reorda, "Hybrid Genetic Algorithms for the Traveling Salesman Problem," International Conference on Neural Networks and Genetic Algorithms , Innsbruck (A), Aprile 1993, pp.559-566

60. CodeGuru: Genetic Algorithm And Traveling Salesman Problem A programmer s view and example on Genetic Algorithms. By Konstantin Boukreev. http://www.codeguru.com/Cpp/misc/misc/article.php/c3795/

IT MANAGEMENT CIO Update Datamation eCRMGuide ... IT NEWS CodeGuru.com -Articles -Comments -Forums Earthweb User ID: Password: Remember Me: Forgot Password? Not a member? Click here for more information and to register. Auto Insurance ... Quotes internet.commerce Mortgage Refinance Laptop Reviews Compare MP3 Players Search Engine Ranking ... Online Colleges RSS Feeds All VC++/C++ .NET/C# VB See more EarthWeb Network feeds Home Whitepaper: Compliance Requirements AssessmentIBM DB2 Records Manager and Record-Enabled Solutions. Genetic Algorithm and Traveling Salesman Problem Rating: none Konstantin Boukreev view profile September 27, 2001 (continued) FREE Symantec Data Recovery and Patch Management Whitepapers! Whitepaper: Successfully Managing Both Normal and Disrupted IT Operations Enable client resilience by ensuring that devices are secure, available, and compliant with corporate standards. Whitepaper: Eliminating Overlooked System Vulnerabilities Efficiently combat attacks, eliminate vulnerabilities, and respond to and recover from disruptive events in less time, with less effort, and with greater success. Whitepaper: Intuitive and Robust Patch Management Protect your infrastructure from vulnerabilities with the ability to scan, identify, and install missing patches on hundreds of clients and servers in minutes.

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