81. CyberSpace Search! SEARCH THE WEB. Results 1 through 9 of 9 for traveling salesman problem. http://www.cyberspace.com/cgi-bin/cs_search.cgi?Terms=traveling salesman problem

82. NEAREST MERGER TRAVELING SALESMAN PROBLEM NEAREST MERGER traveling salesman problem. INSTANCE A distance matrix , whereis an integer or the symbol specifying the distance between vertices i and j. http://www.i.kyushu-u.ac.jp/~shoudai/P-complete/all/node56.html

Next: NEAREST INSERTION TRAVELING SALESMAN Up: Optimization Previous: NEAREST NEIGHBOR TRAVELING SALESMAN NEAREST MERGER TRAVELING SALESMAN PROBLEM I NSTANCE : A distance matrix , where is an integer or the symbol specifying the distance between vertices i and j P ROBLEM : Find a nearest merger heuristic tour Reference: [Kindervater, Lenstra and Shmoys, 1989]. Comment: The nearest merger heuristic is described as follows: Start with n partial tours, each consisting of a single vertex with a self-loop. 2. Find tours C and C ' such that the distance dist C C ') between C and C ' is minimum, where . Let be an edge of C and an edge of C ' for which is minimum. Then merge C and C ' by replacing edges and by and , respectively. Repeat this step until a complete tour is obtained. Since tours C C ' and edges are not necessarily uniquely determined, the resulting tour depends on the choices of C C , and . Therefore the above heuristic does not specify a unique tour. A nearest merger heuristic tour is a tour obtained by the above heuristic by appropriately specifying the choices in step 2. However, the reduction is given from CVP so that a circuit is transformed to an instance of NEAREST MERGER TRAVELING SALESMAN PROBLEM for which the nearest merger heuristic is unique. The problem is still P-complete even if the distance matrix satisfies the triangle inequality.

83. Traveling-Salesman-Problem Translate this page Das traveling-salesman-problem (TSP) gilt als eines der klassischen kombinatorischenprobleme. Optimale Lösungen für TSP mit großer http://jochen.pleines.bei.t-online.de/german/1_tsp.htm

HOME INHALT DOWNLOAD AUTOR ... IMPRESSUM 1. Das Traveling-Salesman-Problem (TSP) Das Traveling-Salesman-Problem (TSP), auch als Rundreiseproblem oder Problem des Handelsreisenden (bzw. Handlungsreisenden) bezeichnet, ist eines der berühmtesten Probleme in der kombinatorischen Optimierung. In der Regel unterscheidet man zwischen nicht-symmetrischen TSP und dem sehr häufig auftretenden Fall von symmetrischen TSP. Dabei sind die Wege, eine Lösung für TSP zu finden, oft von der räumlichen Vorstellung einer Rundreise geprägt. Der Weltrekord Untersucht man bekannte Optimallösungen von symmetrischen TSP mit vielen Orten Anders verhält es sich für den allgemeinen Fall von symmetrischen TSP, bei denen keine zusätzlichen Merkmale für die Lösung herangezogen werden und die Ausprägungen des interessierenden Merkmals beliebige positive und negative Werte annehmen können. Alle bekannten Verfahren zur Ermittlung einer Optimallösung laufen auf eine vollständige Analyse der n! möglichen Rundreisen hinaus. Bis heute ist noch kein Algorithmus bekannt, der weniger als exponentiellen Zeitaufwand (bezogen auf die Anzahl der Orte) benötigt, um eine optimale Rundreise zu ermitteln. So sind nach herrschender Ansicht für symmetrische TSP strikt kombinatorische Lösungsansätze wie die enumerative Berechnung von symmetrischen Rundreisen mit 25 Orten nicht möglich.

84. Travelling Salesman Problem From FOLDOC travelling salesman problem. algorithm, complexity (TSP or shortest path , US traveling ) Given a set of towns and the distances between them, determine http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?travelling salesman problem

85. Traveling Salesman NIST. traveling salesman. (classic problem). Definition Find a paththrough a weighted graph which starts and ends at the same vertex http://www.nist.gov/dads/HTML/travelingSalesman.html

traveling salesman (classic problem) Definition: Find a path through a weighted graph which starts and ends at the same vertex , includes every other vertex exactly once, and minimizes the total cost of edges Also known as TSP. See also bottleneck traveling salesman Hamiltonian cycle optimization problem Christofides algorithm , similar problems: all pairs shortest path minimum spanning tree vehicle routing problem Note: Less formally, find a path for a salesman to visit every listed city at the lowest total cost. The above described path is always a Hamiltonian cycle , or tour, however a Hamiltonian cycle need not be optimal. The problem is an optimization problem, that is, to find the shortest tour. The corresponding decision problem asks if there is a tour with a cost less than some given amount. See [CLR90, page 969] If the triangle inequality does not hold, that is d ik ij + d jk for some i, j, k, there is no possible polynomial time algorithm which guarantees near-optimal result (unless P=NP). If the triangle inequality holds, you can quickly get a near-optimal solution by finding the minimum spanning tree . Convert the tree to a path by traversing the tree, say by

86. Traveling Salesman Heuristics Welcome. This applet implements some simple, but effective heuristics for the TravelingSalesman problem with Euclidian distances ie in a 2D plane. Directions. http://riot.ieor.berkeley.edu/~cander/cs270/

Welcome This applet implements some simple, but effective heuristics for the Traveling Salesman Problem with Euclidian distances - i.e. in a 2D plane. Directions In the applet below, add points to the graph by clicking anywhere besides where the buttons are. You must enter three or more points. When you are done entering points, click on a button to solve the TSP problem. MST uses the minimum spanning tree algorithm to build a tour. The algorithmic analysis says this generates a 2-approximation - i.e. at worst, the solution is only twice that of the optimal solution. We found that it's usually much better. All MST is a heuristic that tries the MST algorithm from all possible starting verticies and returns the best one. Greedy is the simplist possible heuristic - always go the the closest neighbor until you have visited all of the nodes. Brute Force performs a brute-force enumeration of all possible tours. It always finds the optimal solution, but it runs very slowly. Therefore, you can only use it for small graphs (i.e. less than ten nodes). For more info on the Traveling Saleman Problem, check out the following:

87. KVV / Das Traveling-Salesman-Problem Translate this page Kommentiertes Vorlesungsverzeichnis Vorlesung. Das traveling-salesman-problem.Dr. J. Vygen. Beschreibung. Gegenstand dieser zweistündigen http://www.informatik.uni-bonn.de/kvv/ws0203/ver85.html

K ommentiertes V orlesungs v erzeichnis Vorlesung Das Traveling-Salesman-Problem Dr. J. Vygen Beschreibung Gegenstand dieser zweistündigen Spezialvorlesung ist das bekannte Rundreiseproblem, besser bekannt unter dem englischen Namen Traveling-Salesman-Problem. Es diente in den vergangenen 50 Jahren in vielerlei Hinsicht als das Problem, für das völlig neue Methoden der Diskreten Optimierung entwickelt wurden, die dann auch bei ganz anderen Problemen zum Einsatz kamen. Ein genaues Studium des Traveling-Salesman-Problems beinhaltet daher ein vielseitiges Themenspektrum wie Komplexität und Approximationsalgorithmen, LP-Relaxierungen und polyedrische Kombinatorik, Branch-and-Cut-Verfahren und Lokale Suche. Auch in jüngster Zeit gab es noch beachtliche Fortschritte, von denen wir einige in der Vorlesung kennenlernen werden. Zeit und Ort: Datum Von Bis Ort Beginn Bereich Di 12:00 ct Institut fuer Diskrete Mathematik, Lennestrasse 2 15. Okt. 2002 C Keine Unterlagen Als Einführung und Überblick mag dienen Kapitel 21 des Buches Combinatorial Optimization: Theory and Algorithms (B. Korte, J. Vygen), Algorithms and Combinatorics 21, Springer-Verlag, 2. Auflage 2002, sowie die dort zitierte Literatur. Die Vorlesung wird jedoch vielfach über den in diesem Kapitel enthaltenen Stoff hinausgehen. Uni Bonn Informatikinstitut KVV KVV WiSe 2002/2003 ... Vorlesungen Please report errors to: kvv@informatik.uni-bonn.de

88. Travelling Salesman Problem GUEST BOOK Visitors since 10.06.97 Elastic Net Method for the Travellingsalesman problem. If THE TRAVELLING salesman problem If http://nuweb.jinr.dubna.su/~filipova/tsp.html

GUEST BOOK Visitors since 10.06.97 Elastic Net Method for the Travelling Salesman Problem If you were using a Java-enabled browser, you would see animating picture instead of this paragraph. The elastic net is a kind of artificial neural networks which is used for optimization problems. Let us demonstrate the elastic net method on a simple example of solving a travelling salesman problem. The travelling salesman problem is a classical problem in the field of combinatorial optimization, concerned with efficient methods for maximizing or minimizing a function of many independent variables. Given the positions of N cities, what is the shortest closed tour in which each city can be visited once? All exact methods known for determining an optimal route require a computing effort that increases exponentially with number of cities, so in practice exact solutions can be attempted only on problems involving a few hundred cities or less. The travelling salesman problem belongs to the large class of nondeterministic polynomial time complete problems.

89. The Travelling Salesman Problem Caveat This has been very much an occasional hobby over recent years, and I have not had the time to keep abreast of the literature. Some of what I say might be out of date. The Travelling salesman problem (TSP) is a deceptively simple combinatorial problem. A salesman spends his time visiting n cities (or 2 cities then the problem is trivial, since only http://www.pcug.org.au/~dakin/tsp.htm

Introduction Caveat This has been very much an occasional hobby over recent years, and I have not had the time to keep abreast of the literature. Some of what I say might be out of date. The Travelling Salesman Problem (TSP) is a deceptively simple combinatorial problem. It can be stated very simply: A salesman spends his time visiting n cities (or nodes) cyclically. In one tour he visits each city just once, and finishes up where he started. In what order should he visit them to minimise the distance travelled? Many TSP's are symmetric - that is, for any two cities A and B, the distance from A to B is the same as that from B to A. In this case you will get exactly the same tour length if you reverse the order in which they are visited - so there is no need to distinguish between a tour and its reverse, and you can leave off the arrows on the tour diagram. If there are only 2 cities then the problem is trivial, since only one tour is possible. For the symmetric case a 3 city TSP is also trivial. If all links are present then there are (n-1)! different tours for an n city asymmetric TSP. To see why this is so, pick any city as the first - then there are n-1 choices for the second city visited, n-2 choices for the third, and so on. For the symmetric case there are half as many distinct solutions - (n-1)!/2 for an n city TSP. In either case the number of solutions becomes extremely large for large n, so that an exhaustive search is impractible. The problem has some direct importance, since quite a lot of practical applications can be put in this form. It also has a theoretical importance in complexity theory, since the TSP is one of the class of "NP Complete" combinatorial problems. NP Complete problems have intractable in the sense that no one has found any really efficient way of solving them for large n. They are also known to be more or less equivalent to each other; if you knew how to solve one kind of NP Complete problem you could solve the lot.

90. Travelling Salesman Problem Travelling salesman problem. CLICK inside to stop; CLICK again to resetand start. Left Side Legend Red path should be the shortest http://www.patol.com/java/TSP/

Travelling Salesman Problem CLICK inside to stop CLICK again to reset and start Left Side: Legend: Red path should be the shortest path to reach all towns A-B% where A is the town number, B is the percent respect all trains that this town has been presented to the network. A-B% where A is the neuron number and B is the percentage respect all trains that this neuron has been chosed as reference. Right Side: Legend: still to implement. Books Enter keywords... ALGORITHMS ... The main idea of Kohonen Neuronal Networks is to leave the network organise himself. To do this we have to present patterns continuously and randomly until a stability is reached. Such of networks are composed by two groups of neurons. In the first group each neuron is connected with each neuron (himself too) of this group and the weight value depends on the distance between neurons. The weight r(i,j) between neuron i and j is given by: 2 ( - dist(i,j) ) / ( 2 theta ) r[i,j] = e Where dist(i,j)

91. IMA Public Lecture: The Traveling Salesman (TSP) By William Cook, October 16, 20 20022003 Program Optimization. IMA PUBLIC LECTURE. The traveling SalesmanProblem. William J. Cook Industrial and Systems Engineering http://www.ima.umn.edu/public-lecture/tsp/

Search Contact Information Program Registration Postdoc/Membership Application Program Feedback ... 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.

92. The Travelling Salesman Problem So far, nobody was able to come up with an algorithm for solving the travelingsalesman problem that does not show an exponential growth of run time with a 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

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