81. The Period Traveling Salesman Problem The period traveling salesman problem a new heuristic algorithm. The travelingsalesman problem a guided tour of combinatorial optimization. http://portal.acm.org/citation.cfm?id=635303&dl=GUIDE&coll=GUIDE&CFID=11111111&C

82. Zeal.com - United States - New - Entertainment - Games - Puzzles - Math Puzzles A great resource for United States New - Entertainment - Games - Puzzles - MathPuzzles - traveling salesman problem. traveling salesman problem Preview http://zeal.com/category/preview.jhtml?cid=10161837

83. ZIP-Methode: Neue Kombinatorische Optimal-Lösung Für TSP (Traveling-Salesman-P Mit der ZIPMethode ist es m¶glich, alle Rundreisen auf eine minimale Anzahl von Grundformen - im Vergleich zur Anzahl der m¶glichen Rundreisen - zur¼ckzuf¼hren. 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 11.05.2004: Zur Geschichte der ZIP-Methode © Jochen Pleines. Alle Rechte vorbehalten. Nachdruck mit Quellenangabe gestattet. Belegexemplar erbeten. Kurzfassung abstract résumé Ismertetö ... resumen

84. Traveling Salesman Definition of traveling salesman, possibly with links to more information and implementations. traveling salesman. ( classic problem See alsobottleneck traveling salesman, Hamiltonian cycle 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

85. 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.

86. Travelling Salesman Problem From FOLDOC Free Online Dictionary of Computing. travelling salesman problem. algorithm, complexity (TSP or shortest path , US traveling http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?travelling salesman problem

87. LookSmart - Directory - Traveling Salesman Math Problem YOU ARE HERE Home Sciences Mathematics Math Puzzles travelingsalesman problem. traveling salesman Math problem Offers http://search.looksmart.com/p/browse/us1/us317914/us328800/us281829/us10161837/

@import url(/css/us/style.css); @import url(/css/us/searchResult1.css); Home IN the directory this category YOU ARE HERE Home Sciences Mathematics Math Puzzles Traveling Salesman Math Problem - Offers sites about this famous math problem where a salesman must visit multiple cities. Directory Listings About See pictures of traveling salesman problem diagrams, and read about the official challenge to mathematicians and the published results. Delphi For Fun - Traveling Salesman Problem Introductory explanation of this problem, in which a salesman must visit cities in the most efficient manner possible, offers a downloadable test version. DENSIS - TSPBIB Home Page Departamento de Engenharia de Sistemas offers a resource with papers, discussion, problems, and examples of the traveling salesman problem. Written in English. Eric Weisstein's World of Mathematics - Traveling Salesman Defines this famous graph-theory problem, Hamiltonian circuits, and offers bibliographic resource on the topic. Fractal Instances of the Traveling Salesman Problem Find a collection of papers describing solutions to the traveling salesman problem. Includes links to related sites. Applet demonstrates the use of simulated annealing to solve this classic graph-theory math dilemma.

88. Travelling Salesman Problem Definition Of Travelling Salesman Problem In Computi Travelling salesman problem. (algorithm, complexity), travelling salesman problem (TSP or shortest path , US traveling ) Given a set of towns and the http://computing-dictionary.thefreedictionary.com/travelling salesman problem

Dictionaries: General Computing Medical Legal Encyclopedia Travelling salesman problem Word: Word Starts with Ends with Definition (algorithm, complexity) travelling salesman problem - (TSP or "shortest path", US: "traveling") Given a set of towns and the distances between them, determine the shortest path starting from a given town, passing through all the other towns and returning to the first town. This is a famous problem with a variety of solutions of varying complexity and efficiency. The simplest solution (the brute force approach) generates all possible routes and takes the shortest. This becomes impractical as the number of towns, N, increases since the number of possible routes is !(N-1). A more intelligent algorithm (similar to iterative deepening ) considers the shortest path to each town which can be reached in one hop, then two hops, and so on until all towns have been visited. At each stage the algorithm maintains a "frontier" of reachable towns along with the shortest route to each. It then expands this frontier by one hop each time. Pablo Moscato's TSP bibliography Fractals and the TSP Some words with "Travelling salesman problem" in the definition:

89. 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:

90. The Code Project - Genetic Algorithms And The Traveling Salesman Problem Using C All Topics, C , .NET C Programming General Genetic Algorithms and the TravelingSalesman problem using C and ATL COM By Kalyan S Dontharaju An article http://www.codeproject.com/csharp/gatsp.asp

All Topics C# .NET C# Programming ... General Genetic Algorithms and the Traveling Salesman Problem using C# and ATL COM By Kalyan S Dontharaju An article on Travelling SalesMen Problem Solving by GA VC7, VC6, XP, W2K, Win9X, MFC Posted 25 Nov 2002 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 Sign in / Sign up Email Password Remember me Lost your Password? 3 members have rated this article. Result: Popularity: 2.27 . Rating: out of 5. Download demo project - TSPGA_Demo - 78.5Kb Download source - TSPGA_SRC 99.8Kb Introduction This project is about an application used by the Traveling Salesman, given a finite number of 'cities'(I have choosen cities from 1 to a finite number) along with the distance of travel (distance between two cities is randomly choosen) between each pair of them, The aim is to find the cheapest distance of visiting all the cities and returning to the starting point. Using GA we can get an optimal solution to solve this problem. This is only an example to look at calling COM Components and accessing SAFEARRAY in C#. I don't know many things about genetic algorithm and please don't take take this code as demonstrating a problem to solve using only genetic algorithms (GA). This is just one approach. The C++ code for GA I got from the Internet.

91. Travelling Salesman Problem From FOLDOC travelling salesman problem. algorithm, complexity (TSP or shortestpath , US traveling ) Given a set of towns and the distances http://www.swif.uniba.it/lei/foldop/foldoc.cgi?travelling salesman problem

92. Travelling Salesman Problem From FOLDOC travelling salesman problem. algorithm, complexity (TSP or shortestpath , US traveling ) Given a set of towns and the distances http://www.instantweb.com/D/dictionary/foldoc.cgi?travelling salesman problem

93. The Travelling Salesman Problem 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 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.

94. 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)

95. TravellingSalesman Travelling salesman problem Torsten Reil torsten.reil@zoology.oxford.ac.uk Thisprogram utilises a genetic algorithm to find solutions for the Travelling http://users.ox.ac.uk/~quee0818/ts/ts.html

Travelling Salesman Problem Torsten Reil torsten.reil@zoology.oxford.ac.uk This program utilises a genetic algorithm to find solutions for the Travelling Salesman Problem. Briefly, a random route is created, mutated offspring routes are produced, and the best of these (in terms of total length of route) is selected as the next generation's parent. In addition to using random city postiions (by clicking the Start button), the user can draw cities by clicking onto the white area. Green indicates the start, red the end point. JDK1.1 Patch . That should do the trick.

96. 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

97. TSP Problem. The TSP Example. EXAMPLE Heuristic algorithm for the traveling SalesmanProblem (TSP) . This is one of the most known problems http://students.ceid.upatras.gr/~papagel/project/tspprobl.htm

The T.S.P. Example. EXAMPLE: Heuristic algorithm for the Traveling Salesman Problem (T.S.P) This is one of the most known problems ,and is often called as a difficult problem.A salesman must visit n cities, passing through each city only once,beginning from one of them which is considered as his base,and returning to it.The cost of the transportation among the cities (whichever combination possible) is given.The program of the journey is requested,that is the order of visiting the cities in such a way that the cost is the minimum. Let's number the cities from 1 to n ,and let city 1 be the city-base of the salesman.Also let's assume that c (i,j) is the visiting cost from i to j .There can be c (i,j) (j,i) Apparently all the possible solutions are (n-1)! .Someone could probably determine them systematically,find the cost for each and everyone of these solutions and finally keep the one with the minimum cost.These requires at least (n-1)! steps. If for example there were 21 cities the steps required are (n-1)!=(21-1)!=20! steps.If every step required a

98. TSP Algorithms In Action Animated Examples Of Heuristic Algorithms Stephan Mertens. Abstract The travelling salesman problem (TSP) probablyis the most prominent problem in combinatorial optimization. http://itp.nat.uni-magdeburg.de/~mertens/TSP/TSP.html

Next: 1. Introduction TSP Algorithms in Action Animated Examples of Heuristic Algorithms Stephan Mertens Abstract: The travelling salesman problem (TSP) probably is the most prominent problem in combinatorial optimization. Its simple definition along with its notorious difficulty has stimulated (and still stimulates) many efforts to find an efficient algorithm. Due to the NP-completeness of the TSP, only approximate solutions can be expected. This contribution presents animated, graphical Java-Applets of some approximate algorithms for the TSP. The applets allow to watch the algorithms in action and to play around with them. 1. Introduction 1.1 Notes on the Java-Applets 1.2 Related WWW Resources 2. Construction Heuristics ... About this document ... Stephan Mertens

99. Dictionary.com/travelling Salesman Problem Get the Top 10 Most Popular Sites for travelling salesman problem . 1 entryfound for travelling salesman problem. travelling salesman problem. http://dictionary.reference.com/search?q=travelling salesman problem

100. TRAVELLING SALESMAN PROBLEM - Meaning And Definition Of The Word Search Dictionary TRAVELLING salesman problem Dictionary Entryand Meaning. Computing Dictionary. Definition (TSP or shortest http://www.hyperdictionary.com/computing/travelling salesman problem

English Dictionary Computer Dictionary Thesaurus Dream Dictionary ... Medical Dictionary Search Dictionary: TRAVELLING SALESMAN PROBLEM: Dictionary Entry and Meaning Computing Dictionary Definition: (TSP or "shortest path", US: "traveling") Given a set of towns and the distances between them, determine the shortest path starting from a given town, passing through all the other towns and returning to the first town. This is a famous problem with a variety of solutions of varying complexity and efficiency. The simplest solution (the brute force approach) generates all possible routes and takes the shortest. This becomes impractical as the number of towns, N, increases since the number of possible routes is !(N-1). A more intelligent algorithm (similar to iterative deepening ) considers the shortest path to each town which can be reached in one hop, then two hops, and so on until all towns have been visited. At each stage the algorithm maintains a "frontier" of reachable towns along with the shortest route to each. It then expands this frontier by one hop each time. Pablo Moscato's TSP bibliography Fractals and the TSP See Also: algorithm complexity HOME ABOUT HYPERDICTIONARY

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