81. The Traveling Salesman Problem ~ Serves An Optimal-length Ambler. 24434 the traveling salesman problem (+) HSP July 13, 2005 at 135336. 24435 A. Miller fable on poets, math, and graves = Death of a Traveling Salesman http://www.anagrammy.com/cgi-bin/displaymsg.pl?24441

82. [quant-ph/0411013] Towards Efficiently Solving Quantum Traveling Salesman Proble Towards Efficiently Solving Quantum traveling salesman problem. Authors Debabrata Goswami, Harish Karnick, Prateek Jain, Hemanta K. Maji http://arxiv.org/abs/quant-ph/0411013

Quantum Physics, abstract quant-ph/0411013 From: Debabrata Goswami [ view email ] Date: Tue, 2 Nov 2004 12:03:31 GMT (124kb) Towards Efficiently Solving Quantum Traveling Salesman Problem Authors: Debabrata Goswami Harish Karnick Prateek Jain Hemanta K. Maji Comments: 4 pages, 3 tables, PRL (submitted) We present a framework for efficiently solving Approximate Traveling Salesman Problem (Approximate TSP) for Quantum Computing Models. Existing representations of TSP introduce extra states which do not correspond to any permutation. We present an efficient and intuitive encoding for TSP in quantum computing paradigm. Using this representation and assuming a Gaussian distribution on tour-lengths, we give an algorithm to solve Approximate TSP (Euclidean) within BQP resource bounds. Generalizing this strategy for any distribution, we present an oracle based Quantum Algorithm to solve Approximate TSP. We present a realization of the oracle in the quantum counterpart of PP. Full-text: PDF only References and citations for this submission: SLAC-SPIRES HEP (refers to , cited

83. [cs/0204024] The Geometric Maximum Traveling Salesman Problem We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, http://arxiv.org/abs/cs.DS/0204024

Computer Science, abstract cs.DS/0204024 From: Sandor P. Fekete [ view email ] Date ( ): Wed, 10 Apr 2002 18:56:09 GMT (35kb) Date (revised v2): Thu, 29 May 2003 12:05:41 GMT (38kb) The Geometric Maximum Traveling Salesman Problem Authors: Alexander Barvinok Sandor P. Fekete David S. Johnson Arie Tamir ... Russ Woodroofe Comments: 24 pages, 6 figures; revised to appear in Journal of the ACM. (clarified some minor points, fixed typos) Subj-class: Data Structures and Algorithms; Computational Complexity ACM-class: F.2.2 Journal-ref: Journal of the ACM, 50 (5) 2003, 641-664. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv cs find abs

84. Traveling Salesman Problem In short, the traveling salesman problem is a good and classical mathematical and practical example in network or graph optimization, where one imagines a http://wiki.tcl.tk/9034

Traveling Salesman Problem by Theo Verelst In short, the traveling salesman problem is a good and classical mathematical and practical example in network or graph optimization, where one imagines a salesman, maybe with a car or a horse, who needs to visit a set of customers, and wants to take the shortest route. We could take a map, draw circles around every destination city, draw lines between all reasonable adjacent or all next cities, and look up or measure the distance between pairs of cities, and write them in kilometers along all connecting lines. Then we give the thus constructed graph to computer wizard, and tell him or her to solve the problem. This picture is a graph in the works, which is wrong, although it is getting there. Can you spot the error in the code? I agree this is like motherfucking code together, but so what; it is fun and relevant. This procedure generates a list of names made of a base name prepended with an increasing number, possibly with an offset: The blocks were made in Bwise like this: The last line is repeated 5 times, to generate 6 blocks in total.

85. Phys. Rev. E 51, R1 (1995): Penna - Traveling Salesman Problem And... traveling salesman problem and Tsallis statistics. TJP Penna; Instituto de Física, Universidade Federal Fluminense, Outeiro de São João Batista, s/n, http://link.aps.org/doi/10.1103/PhysRevE.51.R1

Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST AB Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article: MyArticles: View Collection Help (Click on the to add an article.) Previous article Next article Issue 1 contents View Page Images PDF (492 kB), or Buy this Article Traveling salesman problem and Tsallis statistics T. J. P. Penna Received 16 August 1994 A generalization of the stochastic method of simulated annealing algorithm based on Tsallis statistics is proposed. This algorithm is considerably faster than the traditional ones in solving the traveling salesman problem. Acceptable solutions are found in fewer steps and higher temperatures than both the classical and the fast simulated annealings. Recent developments in solving NP -complete problems can be incorporated and improve the performance even more. URL: http://link.aps.org/abstract/PRE/v51/pR1 DOI: 10.1103/PhysRevE.51.R1 PACS: 02.50.Ey, 02.60.Pn, 05.70.Ln, 02.70.-c View Page Images PDF (492 kB), or

86. Traveling Salesman Problem - Computing Reference - ELook.org spelling US spelling of travelling salesman problem. Previous Terms, Terms Containing traveling salesman problem, Next Terms http://www.elook.org/computing/traveling-salesman-problem.htm

eLook Home eLook Computing Reference Search Computing Reference More Resources Information US City Data Worldwide Weather Entertainment Video Game Cheats Food Nutrition Recipes Literature Literature Reference Computing Dictionary Internet Encyclopedia Programming Reference ... Thesaurus By Letter: Non-alphabet A B C ... Z Traveling salesman problem travelling salesman problem Terms Containing traveling salesman problem trap trap door trap-door function trash ... Contact

87. Traveling Salesman Problem From FOLDOC traveling salesman problem. spelling US spelling of travelling salesman problem. (199612-13). Try this search on OneLook / Google http://foldoc.hld.c64.org/foldoc.cgi?traveling salesman problem

88. IMPRS Publications: Thesis Curve Reconsturction and teh traveling salesman problem. School*. Universität des Saarlandes. Type of Thesis*. PhD thesis. Month. December http://domino.mpi-sb.mpg.de/imprs/imprspubl.nsf/0/c021c8a5671bb3b9c1256e4b004af6

89. The Traveling Salesman Problem The traveling salesman problem is the problem of finding the shortest cyclical itinerary for a traveling salesman who must visit each of N cities in turn. http://home.ku.edu.tr/~dyuret/pub/aitr1569/node23.html

Next: Summary and future Up: Results and related Previous: Refraction tomography The traveling salesman problem The traveling salesman problem is the problem of finding the shortest cyclical itinerary for a traveling salesman who must visit each of N cities in turn. This problem has a very different nature from the above problems, it is an example of combinatorial optimization . There is an objective function to be minimized, but the search space is the discrete space of all permutations of N cities. The combinatorial optimization problems are challenging because the number of elements in the search space is factorially large, thus they cannot be exhaustively searched. Also it is hard to define a concept of ``direction'' in a permutation space. The representation one chooses to use might make it possible to define concepts of ``distance'' and ``direction'' in non-cartesian spaces. One can carefully define various mutations such that ``moving further in the same direction'' is meaningful. It is also possible to define a notion of ``size'' in carefully selected operations. I will not present a detailed study of the application of my program on combinatorial problems. However, I thought it desirable to include one example, to show that the same key ideas apply even when one does not have a cartesian space. I compared the results I obtained from a very simple implementation of my algorithm with results from simulated annealing. The simulated annealing program [

90. 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, http://foldoc.doc.ic.ac.uk/foldoc/foldoc.cgi?travelling salesman problem

91. IBM Technical Journals The classical travelingsalesman problem is to determine a tour that will minimize the total distance or cost involved in visiting several cities and http://domino.research.ibm.com/tchjr/journalindex.nsf/0/38eb497ae3a3360985256bfa

92. CBS - Pagina Niet Gevonden English, travelling salesman problem. French, . German, Rundfahrtproblem ; traveling-salesman-problem. Dutch, handelsreizigers-probleem http://www.cbs.nl/isi/glossary/term3333.htm

Spring naar inhoud Centraal Bureau voor de Statistiek Home Thema's Cijfers Publicaties ... Terug naar standaardweergave Pagina niet gevonden De pagina waar u naar zoekt is niet gevonden. Het CBS heeft 1 september 2005 zijn website geheel vernieuwd. Mogelijk volgde u een link naar de oude site. Terug naar standaardweergave Laatst gewijzigd: maandag 29 augustus 2005 11:55 Zoeken in CBS.nl Paginaopties Voeg toe aan favorieten Printversie Vaste breedte Snelkoppelingen StatLine databank FAQ's RSS Newsfeed Bedrijvenloket ... Huuraanpassing Dossiers Allochtonen Europese Unie Vergrijzing Vrouwen en mannen ... Contact

93. The Travelling Salesman Problem The Travelling salesman problem (TSP) is a deceptively simple combinatorial problem. It can be stated very simply. ncity tour. A salesman spends his time 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 reset and start. Left Side. Legend. Red path should be the shortest path to reach all 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. The Travelling Salesman Problem Software illustrating, and implementing a solution to, the Travellng salesman problem. http://www.hermetic.ch/misc/ts3/ts3demo.htm

The Travelling Salesman Problem by Peter Meyer The travelling salesman problem consists in finding the shortest (or a nearly shortest) path connecting a number of locations (perhaps hundreds), such as cities visited by a travelling salesman on his sales route. 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. World-Record Traveling Salesman Problem for 3038 Cities Solved In 1992 I came upon an article in a physics journal (I don't remember where or by whom it was written) which described the use of the so-called Simulated Annealing Algorithm to solve this problem. The algorithm is so named because it can be seen as a simulation of the physical process of annealing (in which a hot material cools slowly, allowing its constituent atoms to assume arrangements that would not be possible with rapid cooling). I then wrote a program to implement this algorithm. A good explanation of the simulated annealing algorithm is given by Robert C. Williams:

96. Travelling Salesman Problem Using Genetic Algorithms A fast unique solution for the travelling salesman problem using genetic algorithms. http://www.lalena.com/ai/tsp/

Travelling Salesman Problem Using Genetic Algorithms I have developed a method of solving the Travelling Salesman Problem (TSP) using Genetic Algorithms (GA) . In the Travelling Salesman Problem, the goal is to find the shortest distance between N different cities. The path that the salesman takes is called a tour. Testing every possibility for an N city tour would be N! math additions. A 30 city tour would be 2.65 X 10 additions. Assuming 1 billion additions per second, this would take over 8,000,000,000,000,000 years. Adding one more city would cause the number of additions to increase by a factor of 31. Obviously, this is an impossible solution. A genetic algorithm can be used to find a solution is much less time. Although it probably will not find the best solution, it can find a near perfect solution in less than a minute. There are two basic steps to solving the travelling salesman problem using a GA. First, create a group of many random tours in what is called a population . These tours are stored as a sequence of numbers. Second, pick 2 of the better (shorter) tours parents in the population and combine them, using

97. The Code Project - Solution To Travelling Salesman Problem - C++ / MFC Solution to a Travelling salesman problem using Hamiltonian circuit, the efficieny is O(n^4) and I think it gives the optimal solution. http://www.codeproject.com/cpp/TravellingSalesman.asp

View our advertisers Advertise with us document.write(""); All Topics MFC / C++ C++ / MFC Algorithms Solution to Travelling Salesman Problem By omkar joshi Solution to a Travelling Salesman problem using Hamiltonian circuit, the efficieny is O(n^4) and I think it gives the optimal solution. C++ (VC5, VC6), MC++ Windows (NT4, Win2K, WinXP, Win98), .NET Win32, VS (VS6) Dev Posted 22 Jan 2005 5:34 Articles by this author views Search: Articles Authors Help! Articles Message Boards StoreFront ... Send to a friend Sign in / Sign up Email Password Remember me Lost your Password? document.write(""); 9 members have rated this article. Result: Popularity: 1.49 . Rating: out of 5. Download source files - 2.08 Kb Introduction Hereby, I am giving a program to find a solution to a Traveling Salesman Problem using Hamiltonian circuit, the efficiency is O (n^4) and I think it gives the optimal solution. Though I have provided enough comments in the code itself so that one can understand the algorithm that I m following, here I give the pseudocode. Problem Statement Find the order of cities in which a salesman should travel in order to start from a city, reaching back the same city by visiting all rest of the cities each only once and traveling minimum distance for the same.

98. Travelling Salesman's Problem The Travelling salesman s problem, four simple algorithms in Java Applets. http://web.telia.com/~u85905224/tsp/TSP.htm

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.

99. Learning By Simulations: Travelling Salesman topology which can be used to optimize the classical travelling salesman problem. applies a circular Kohonen map to the travelling salesman problem. http://www.vias.org/simulations/simusoft_travsalm.html

Learning by Simulations has been developed by Hans Lohninger to support both teachers and students in the process of knowledge transfer and acquisition . Click here for more information. Learning by Simulations Mathematics Travelling Salesman Index Kohonen maps are a special kind of neural networks, which try to mimic natural brains with respect to the observation which is commonly represented by the "homunculus". This representation shows that those sensory regions which are very sensitive and have a lot of nerve connections to the brain (e.g. the tongue) influence a larger area of the neo cortex than areas which have less connections (e.g. the back). Further, one can see that this representation is maintaining the topology of the body. Kohonen networks work in a similar way: the topology of the signal space is preserved, and parts of a signal with many samples are assigned to more "neurons" than parts with less details. One special feature of the Kohonen map is, that the neighborhood relationship can be set up by the user. Thus, you can, for example, set up a ring topology which can be used to optimize the classical travelling salesman problem. Download English version [320 kB] German version [320 kB] After downloading please unpack all files of the zipped packages and start the executable.

100. Travelling Salesman In the travelling salesman problem, you have to find the shortest round trip visiting every town exactly once. This program tries to solve the problem by http://mathsrv.ku-eichstaett.de/MGF/homes/grothmann/java/tsp.html

The Problem In the travelling salesman problem, you have to find the shortest round trip visiting every town exactly once. This program tries to solve the problem by local minimum search starting from random locations. You can enter your own locations, or you can generate random points or points in a rectangular grid. If you are interested, here is the source of this application. R. Grothmann, grothm@ku-eichstaett.de

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