61. Traveling Salesman Problem: Definition From Answers.com The problem of performing successively a number of tasks, represented by vertices of a graph, with the least expenditure on transitions from one task to another, represented http://www.answers.com/topic/traveling-salesman-problem-mathematics

62. The Problem Given a collection of cities and the cost of travel between each pair of them, the traveling salesman problem, or TSP for short, is to find the cheapest way of visiting all of http://www.tsp.gatech.edu/problem/index.html

Given a collection of cities and the cost of travel between each pair of them, the traveling salesman problem , or TSP for short, is to find the cheapest way of visiting all of the cities and returning to your starting point. In the standard version we study, the travel costs are symmetric in the sense that traveling from city X to city Y costs just as much as traveling from Y to X. The simplicity of the statement of the problem 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 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. Number of TSP Tours Santa TSP TSP Cake

63. Towards A 4/3 Approximation For The Asymmetric Traveling Salesman File Format Adobe PostScript View as HTML http://www.cs.uic.edu/~jlillis/courses/cs594_f02/sodatsp.ps

64. Download Traveling Salesman Problem - Traveling Salesman Problem Solves The TSP Traveling Salesman Problem Traveling Salesman Problem solves the TSP by implementing a GA http://webscripts.softpedia.com/script/Miscellaneous/Traveling-Salesman-Problem-

65. On Semidefinite Programming Relaxations Of The Traveling Salesman File Format PDF/Adobe Acrobat Quick View http://homepages.cwi.nl/~vallenti/DIAMANT2009/etienne.pdf

66. Fast Marching Methods For The Continuous Traveling Salesman by J Andrews 2007 - Cited by 8 - Related articles http://www.pnas.org/content/104/4/1118.full?maxtoshow=&HITS=10&hits=10&a

67. Traveling Salesman Problem The goal is to help our traveling salesman find the shortest closed path that visits all the cities, assuming that the distance between cities is measured as the crow flies . http://www.ph.biu.ac.il/~rapaport/java-apps/travel.html

Traveling salesman problem The goal is to help our traveling salesman find the shortest closed path that visits all the cities, assuming that the distance between cities is measured "as the crow flies". The problem can be solved (in principle only) by an exhaustive enumeration of all possible paths, but a far simpler heuristical approach is based on "simulated annealing" (a form of Monte Carlo sampling). In this example, the cities are arranged at random in four clusters. The annealing process is governed by a "temperature" parameter: big values allow large global changes in the route, whereas small values tend to cause localized changes only. The temperature drops automatically as the process advances, but can be manually adjusted as well. Available user controls are the start/stop button, a button for repeating the calculation using different random numbers (the end results should be fairly similar), a button to generate a new arrangement of the cities, a pair of buttons for controlling temperature, and sliders for choosing the number of annealing iterations between updates and the time delay between display changes. (c) D. Rapaport

68. Simulated Annealing Applet | Heaton Research Jan 9, 2008 The Traveling Salesman Problem (TSP) is a common problem applied to artificial intelligence. The TSP presents the computer with a number http://www.heatonresearch.com/articles/64/page1.html

Login: User: Password: [Register] Skip to Navigation Heaton Research Home ... Simulated Annealing Simulated Annealing Applet Submitted by jeffheaton on Wed, 01/09/2008 - 23:54 in artificial intelligence Popular Articles Simulated annealing is a programming method that attempts to simulate the physical process of annealing. Annealing is a where a material is heated and then cooled (as steel or glass) usually for softening and making the material less brittle. Simulated annealing, therefore, exposes a "solution" to "heat" and cools producing a more optimal solution. The "Traveling Salesman Problem" (TSP) is a common problem applied to artificial intelligence. The TSP presents the computer with a number of cities, and the computer must compute the optimal path between the cities. This applet uses simulated annealing to produce a solution to the "Traveling Salesman Problem". Simulated Annealing Instructions Enter the number of cities the salesman much cross through. Enter a number for the starting temperature. The temperature is an arbitrary number and does not refer to Celsius or Fahrenheit. 10 is a good enough starting temperature.

69. FOR THE TRAVELING SALESMAN PROBLEM File Format Microsoft Word View as HTML http://leeds-faculty.colorado.edu/glover/TSP - Multilevel TS - June 91.doc

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70. A FAST ALGORITHM FOR THE EUCLIDEAN TRAVELING SALESMAN PROBLEM File Format PDF/Adobe Acrobat Quick View http://ftp.cs.wisc.edu/pub/techreports/1980/TR401.pdf

71. Applegate, D., Bixby, R., Chvátal, V., Et Al.: The Traveling Salesman Problem: by DL Applegate Cited by 301 - Related articles http://press.princeton.edu/titles/8451.html

72. Happy News - Bumblebees Solve "Traveling Salesman Problem" With Ease They might look like they wander aimlessly from flower to flower, but bumblebees actually solve a complex mathematical problem to find the shortest possible route between http://www.happynews.com/news/10252010/bumblebee-shortcuts.htm?utm_source=twitte

73. Neil Simonetti's Traveling Salesman Problem Page Traveling Salesman Problem Homepage (Applegate, Bixby, Chvatal, and Cook) TSPBIB Comprehensive listing of publications and code for the TSP. http://www.andrew.cmu.edu/~neils/tsp

Neil Simonetti's Traveling Salesman Problem Page Results for the Job Shop Scheduling Problems Results here were found using a Sun Ultra 60 (UltraSPARC-II processors, 360MHz) Test data for classic problems are found here Results for classic problems: Summary Test data for semiconductor problems are found here Results for semiconductor problems: Summary Test data for reentrant flow problems are found here Results for reentrant flow problems: Summary Test data for t2-ps and t2-pss instances are here Results for t2-ps and t2-pss instances Code for the Multi-Run SB-RGLS10 procedure 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

74. Traveling Salesman Problem See Part 1 The Mathematics of Dotto Dot. Well it is summer, and that means Baseball is in season again. It also means school is out and people are traveling. http://members.cox.net/mathmistakes/travel.htm

Discrete Math 2: The Traveling Salesman Problem See Part 1: The Mathematics of Dot-to Dot Well it is summer, and that means Baseball is in season again. It also means school is out and people are traveling. A couple of years ago, Master Card ran a series of ads about a couple of guys who drove a VW Van cross country to see every baseball stadium in the country. This might be something other people might find fun to do, so why not set it up as a problem to solve: What is the shortest distance one needs to travel to visit all 30 teams in 28 major league cities? If this is something you might like to try, you may want to hurry. If the Expos move to San Juan, it will make it impossible to drive to all the major league cities. But, keeping the Expos in Montreal, here is a map of the 28 major league cities: Our goal is to find the shortest path that hits all 28 cities. We will do an open path, which means we do not need to stat and end at the same place. So lets start by creating a procedure to solve this problem. This seems like a reasonable way to solve it: Starting in Seattle, go to the

75. On The Space Lling Curve Heuristic For The Euclidean Traveling File Format PDF/Adobe Acrobat Quick View http://www.mit.edu/~dbertsim/papers/ApproximationAlgorithms/Worst case examples

76. Traveling Salesman Problem -- From Wolfram Library Archive The traveling salesman problem is a classic example of combinatorial minimization. It involves finding the shortest itinerary for a traveling salesman who must visit each of N http://library.wolfram.com/infocenter/MathSource/589/

PRODUCTS Mathematica Mathematica Home Edition Mathematica for Students ... Stephen Wolfram Title Traveling Salesman Problem Author Terry Robb Organization: RMIT University Department: Department of Mathematics Old MathSource # Revision date Description The traveling salesman problem is a classic example of combinatorial minimization. It involves finding the shortest itinerary for a traveling salesman who must visit each of N cities in turn. One technique for solving this problem is the method of simulated annealing, and this notebook uses InterCall to access an external subroutine that implements the annealing algorithm. An example in which an additional constraint, such as adding a penalty for a river crossing, is also given. Subject Mathematics Discrete Mathematics Graph Theory Keywords high school courseware, college courseware, graduate courseware, data analysis, tutorial, chemical engineering, civil engineering, communications engineering, electrical engineering, industrial engineering, graphics examples, interfacing, life sciences, biology, pure mathematics, applied mathematics, InterCall, intercall, MathLink , annealing Downloads Traveling.txt

77. The Traveling Salesman Problem With Distances One And Two -- Papadimitriou And Y by CH Papadimitriou 1993 - Cited by 272 - Related articles http://mor.journal.informs.org/cgi/content/abstract/18/1/1

78. Science Fair Projects - Traveling Salesman Problem The Ultimate Science Fair Projects Encyclopedia Traveling salesman problem http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Trav

All Science Fair Projects Science Fair Project Encyclopedia for Schools! Search Browse Forum Coach ... Dictionary Science Fair Project Encyclopedia For information on any area of science that interests you, enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.). Or else, you can start by choosing any of the categories below. Science Fair Project Encyclopedia Contents Page Categories Graph theory Optimization ... NP-complete problems Traveling salesman problem (Redirected from Traveling salesperson problem The traveling salesman problem or travelling 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 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 graph theory is: Given a 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

79. MIT Press Journals - Neural Computation - Abstract Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.mitpressjournals.org/doi/abs/10.1162/neco.1990.2.3.261

Hello. Sign in to personalize your visit. New user? Register now Home List of Issues Table of Contents Quick Tools Email to a Colleague Add Article to Favorites Alert Me When new articles cite this article RSS (TOC Alert) RSS (Citation Alert) Download to Citation Manager Most Downloaded Articles Most Cited Articles View Related Articles Quick Search In MIT Press Journals CrossRef By author Carsten Peterson Monthly 288 pp. per issue                      6 x 9, illustrated Founded: 1989 ISSN 0899-7667 E-ISSN 1530-888X 2009 ISI Impact Factor: 2.175 Inside the Journal About NECO Peer Review site Editorial Info Abstracting and Indexing ... Publication Agreement  Fall 1990, Vol. 2, No. 3, Pages 261-269 Posted Online 13 March 2008. (doi:10.1162/neco.1990.2.3.261) Parallel Distributed Approaches to Combinatorial Optimization: Benchmark Studies on Traveling Salesman Problem Carsten Peterson PDF (414.608 KB) PDF Plus (251.862 KB) We present and summarize the results from 50-, 100-, and 200-city TSP benchmarks presented at the 1989 Neural Information Processing Systems (NIPS) postconference workshop using neural network, elastic net, genetic algorithm, and simulated annealing approaches. These results are also compared with a state-of-the-art hybrid approach consisting of greedy solutions, exhaustive search, and simulated annealing. Cited by B. F. Kostenko

80. Traveling Salesman Problem Applied To Chagas - Fogarty International Center @ NI The classic traveling salesman problem has been successfully applied to address Chagas disease in Peru, dramatically increasing the effectiveness of http://www.fic.nih.gov/news/publications/global_health_matters/2010/0210_chagas.

Search News Global Health Matters Newsletter Fogarty Grantee Publications ... Newsletter Traveling salesman problem applied to Chagas, may also help combat dengue and malaria Photo courtesy of Dr. Michael Levy Fogarty scientist Dr. Michael Levy and colleagues used the traveling salesman problem to improve insecticide application strategies to combat Chagas disease in Peru. The classic traveling salesman problem has been successfully applied to address Chagas disease in Peru, increasing the effectiveness of insecticide application and reducing transmission of Chagas, which is spread through bug bites. Researchers believe the strategy may also work for other vector-borne diseases such as dengue and malaria. Fogarty scientists Drs. Michael Levy and Ellis McKenzie - together with their collaborators - recently published their findings in the Journal of the Royal Society Interface. Levy and his colleagues knew the traditional contiguous approach to insecticide application, spraying one adjoining area after another, does not work well in urban settings such as Arequipa, the study site. They looked for a more effective approach and decided to explore the traveling salesman problem, a standard exercise in operations research and theoretical computer science. Solving the problem requires covering a defined territory without retracing steps, minimizing the total distance traveled. A rich library of traveling salesman algorithms exists but had never been adapted to infectious disease control.

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