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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/

Extractions: 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.

2. Fractal Instances Of The Traveling Salesman Problem
By Pablo Moscato.

Extractions: 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. 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,

3. 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. Excerpt fromThe Algorithm Design Manual The traveling salesman problem is the most notorious NPcomplete problem1.5.4 traveling salesman problem. INPUT OUTPUT. Input
http://www.cs.sunysb.edu/~algorith/files/traveling-salesman.shtml

Extractions: 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.

4. The Traveling Salesman Problem
The traveling salesman problem. The traveling salesman problem, or TSP for short, is this given a
http://www.cs.rutgers.edu/~chvatal/tsp.html

Extractions: 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.

5. 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

Extractions: 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)

6. Traveling Salesman Problem
MA29.2The traveling salesman problem a Reformulation of the MillerTucker-Zemlin ConstraintsJose M MA29.3Prize-Collecting traveling salesman problemSantosh N
http://www.informs.org/Conf/WA96/TALKS/MA29.html

7. 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

Extractions: 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)

8. 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

9. Traveling Salesman Problem From MathWorld
traveling salesman problem from MathWorld 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.
http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/TravelingSalesmanP

Elastic Net Method for the TSP, by Alexander Budnik and Tatyana Filipova. Asymmetrictraveling salesman problem. Ktemplate traveling salesman problem.
http://www.densis.fee.unicamp.br/~moscato/TSPBIB_home.html

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/

Extractions: 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.

Algorithm based solver of the traveling salesman problem written in GNU C++ linked to based on Dynamic Programming. traveling salesman problem solving program (TSPSolver), by Victor

13. Traveling Salesman Problem -- From MathWorld
traveling salesman problem. Kruskal, J. B. On the Shortest Spanning Subtreeof a Graph and the traveling salesman problem. Proc. Amer. Math. Soc.
http://mathworld.wolfram.com/TravelingSalesmanProblem.html

Extractions: 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 ... search

14. Traveling Salesman Problem
Definition of traveling salesman problem any mathematical problem that involves determination of the shortest path through several points.

15. The Code Project - Genetic Algorithms And The Traveling Salesman Problem - C++ /
Free source code and tutorials for Windows developers. An example of using Genetic Algorithms for solving the traveling salesman problem The traveling salesman problem, or TSP for short, is
http://www.codeproject.com/cpp/tspapp.asp

Extractions: An example of using Genetic Algorithms for solving the Traveling Salesman Problem Advanced VC 4-6, MS PSDK Apr 2001, Win95-98, NT4, W2K, STL Posted 27 Sep 2001 Articles by this author views Search: Articles Authors Toolbox Broken links? VS.NET 2003 for \$899 MSDN Univ. from \$1950 Print version ... Send to a friend 39 members have rated this article. Result: Popularity: 6.97 . Rating: out of 5. Genetic Algorithm Genome of Travel TSP Application 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

16. Travelling Salesman's Problem
be a comprehensive listing of papers, source code, preprints, technical reports,etc, available on the Internet about the traveling salesman problem (TSP) and
http://w1.859.telia.com/~u85905224/tsp/TSP.htm

Extractions: Home email The Travelling Saleman's Problem an unfinished story This page is about what is known as the "Travelling Salesman's Problem". A travelling salesman is to visit a number of cities; how to plan the trip so every city is visited once and just once and the whole trip is as short as possible ? The problem is old and still unsolved. It's clear that some of all possible trips has to be the shortest (there might be more than one beeing equally short), but at the present no other method is known but to calculate all possible tours. And the number of trips grows very rapidly with the number of cities - and eventually the computation of the trips overwhelms any computer. Below are some Java Applets to visualize the problem. They start with a routine that is in practical use, and explore the efficiency of it and some variations. You can point with the mouse and click to locate cities as you wish. (Limits: at most 150 cities and at least 3 pixels apart) Click on the "solve" button and the applet shows how its algorithm solves the problem. The length given for the so constructed tour presumes that the size of the area is 100 * 100 length units. The "random" button gives 100 cities randomly located.

17. Branch And Cut For The Traveling Salesman Problem
Branch Cut and Price Applications traveling salesman problem. Home. Software. Applications TSP Solver of Applegate, Bixby, Chvatal, and Cook. traveling salesman problem Links
http://www.branchandcut.org/TSP

Extractions: Branch Cut and Price Applications : Traveling Salesman Problem Home Software Applications FAQ ... Links We now offer a basic TSP solver, implemented with SYMPHONY , that uses separation subroutines from the CONCORDE TSP Solver of Applegate, Bixby, Chvatal, and Cook. Traveling Salesman Problem Links This page maintained by Ted Ralphs ( ted@branchandcut.org Last updated October 9, 2003

18. Traveling Salesman Problem - Wikipedia, The Free Encyclopedia
http://en.wikipedia.org/wiki/Traveling_salesman_problem

Extractions: 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. Table of contents 1 Problem statement 2 Computational complexity 3 Algorithms 3.1 Exact algorithms ... edit 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 and then returns to the starting city? An equivalent formulation in terms of graph theory is: Find the shortest Hamiltonian cycle 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 classical example is in

19. Traveling Salesman Problem - Wikipedia, The Free Encyclopedia
traveling salesman problem. (Redirected from Travelling salesman problem). Thebottleneck traveling salesman problem is also NPhard. Algorithms.
http://en.wikipedia.org/wiki/Travelling_salesman_problem

Extractions: edit 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 and then returns to the starting city? An equivalent formulation in terms of graph theory is: Find the shortest Hamiltonian cycle 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 classical example is in

20. 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

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