41. Traveling Salesman Problem From FOLDOC Free Online Dictionary of Computing. traveling salesman problem. spelling US spelling of travelling salesman problem. (1996-12-13). http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?traveling salesman problem

42. Traveling Salesman Problem traveling salesman problem. The traveling salesman problem (TSP),also known as the traveling salesperson problem, is a problem in http://www.fact-index.com/t/tr/traveling_salesman_problem.html

Main Page See live article Alphabetical index Traveling salesman problem 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 The problem can be stated as: 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 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 Table of contents 1 Computational complexity 2 Algorithms 2.1 Exact algorithms 2.2 Heuristics ... 3 External Links Computational complexity The most direct solution would be to try all the combinations and see which one is cheapest, but given that the number of combinations is N! (the factorial of the number of cities), this solution rapidly becomes impractical.

43. Traveling Salesman Problem Discrete Math 2 The traveling salesman problem. The traveling salesman problemis classified as an NP Complete problem which I have talked about before. 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

44. 1.5.4 Traveling Salesman Problem Aweighted graph G . Problem Find the cycle of minimum cost visiting......1.5.4 traveling salesman problem. INPUT OUTPUT. Input http://www2.toki.or.id/book/AlgDesignManual/WEBSITE/FILES/TRAESMAN.HTM

1.5.4 Traveling Salesman Problem INPUT OUTPUT Input Description: A weighted graph G Problem: Find the cycle of minimum cost visiting all of the vertices of G exactly once. Implementations TSP solvers (C) (rating 8) Netlib / TOMS Collected Algorithms of the ACM (FORTRAN) (rating 6) Discrete Optimization Methods (Pascal) (rating 5) Combinatorica (Mathematica) (rating 3) ... Xtango and Polka Algorithm Animation Systems (C++) (rating 3) Related Problems Convex Hull Hamiltonian Cycle Minimum Spanning Tree Satisfiability ... Go to Main Page This page last modified on Tue Jun 03, 1997 .

45. Traveling Salesman Problem traveling salesman problem. Input description A weighted graph G. DiscussionThe traveling salesman problem is the most notorious NPcomplete problem. http://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE175.HTM

Next: Hamiltonian Cycle Up: Graph Problems: Hard Problems Previous: Vertex Cover Traveling Salesman Problem Input description : A weighted graph G Problem description : Find the cycle of minimum cost that visits each of the vertices of G exactly once. Discussion : 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. What is the shortest route that will enable him to do so and return home, thus minimizing his total driving? 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. Several issues arise in solving TSPs: Is the graph unweighted?

46. Traveling Salesman Problem Type of the traveling salesman problem......The traveling salesman problem Type Brian T. Luke (btluke@aol.com) LearningFromTheWeb.net MyWeb Pages http://btluke.members.easyspace.com/tspprob.html

The Traveling Salesman Problem Type Brian T. Luke ( btluke@aol.com LearningFromTheWeb.net Suggested Books E.L. Lawler (Ed.), A.H. Rinnooy-Kan Scheduling in Parallel Computing Systems: Fuzzy and Annealing Techniques S. Salleh, A.Y. Zomaya Background Though classified as a Traveling Salesman Problem (TSP), many other problems require exactly the same mathematical formalism. Therefore, along with the well-studied TSP, the links below describe other types of problems: the Complete Bin Packing Problem and the general area of Scheduling. Each of these can use the same method to describe the solution; the only difference is in determining the cost of a putative solution. My Web Pages Description of the Traveling Salesman Problem Description of the Complete Bin Packing Problem Description of Ordering from Multiple Suppliers Description of Scheduling Problems Other Web Pages None at present

47. Traveling Salesman Problem Definition Of Traveling Salesman Problem In Computing Computer term of traveling salesman problem in the Computing Dictionary andThesaurus. Provides search by definition of traveling salesman problem. http://computing-dictionary.thefreedictionary.com/traveling salesman problem

Dictionaries: General Computing Medical Legal Encyclopedia Traveling salesman problem Word: Word Starts with Ends with Definition (spelling) traveling salesman problem - US spelling of travelling salesman problem Some words with "Traveling salesman problem" in the definition: -endian 0/1 knapsack problem 8 queens problem AI-complete ... TSP Previous Computing Dictionary Browser Next Transport Layer Interface Transport Layer Security protocol Transport Level Interface ... treeware Full Dictionary Browser Travel-tainted travel-worn travelable Travelator (enc.) Travelcards (enc.) traveled Traveler Traveler (enc.) Traveler (Colin James) (enc.) traveler's check traveler's joy traveler's letter of credit traveler's tree ... Travelers Group (enc.) Travelers Rest, South Carolina (enc.) Travelers' Diarrhea (med.) traveling traveling bag Traveling crane traveling salesman ... Traveling salesperson problem (enc.) traveling wave Traveling Wilburys (enc.) travelled Traveller Traveller (enc.) Traveller (role-playing game) (enc.) Traveller (rpg) (enc.) traveller's check traveller's joy traveller's letter of credit traveller's tree ... Travelling salesman (enc.) Travelling salesman problem (comp.)

48. Vehicle Routing - Traveling Salesman Problem traveling salesman problem. The traveling salesman problem is one of the most wellknown problems in operations research, computer science, and mathematics. http://www.isye.gatech.edu/logisticstutorial/vehicle/vr1a011_.htm

TRAVELING SALESMAN PROBLEM The Traveling Salesman Problem is one of the most well known problems in operations research, computer science, and mathematics. Many algorithms have been proposed for the solution of this problem. A typical solution process is stepwise, where first an initial tour is constructed, then any remaining unvisited points are inserted, and then the existing tour is improved. There are many possible algorithms for each step. Create an initial tour convex hull, sweep, nearest neighbor algorithms Insert remaining free points cheapest, farthest insertion algorithms Improve existing tour two, three, or Or exchange algorithms In the next section, a demonstration of the TSP algorithms will be presented using the TOURS software package.

49. Minimum Spanning Trees A less obvious application is that the minimum spanning tree canbe used to approximately solve the traveling salesman problem. http://www.ics.uci.edu/~eppstein/161/960206.html

ICS 161: Design and Analysis of Algorithms Lecture notes for February 6, 1996 Minimum Spanning Trees Spanning trees A spanning tree of a graph is just a subgraph that contains all the vertices and is a tree. A graph may have many spanning trees; for instance the complete graph on four vertices has sixteen spanning trees: Minimum spanning trees Now suppose the edges of the graph have weights or lengths. The weight of a tree is just the sum of weights of its edges. Obviously, different trees have different lengths. The problem: how to find the minimum length spanning tree? This problem can be solved by many different algorithms. It is the topic of some very recent research. There are several "best" algorithms, depending on the assumptions you make: A randomized algorithm can solve it in linear expected time. [Karger, Klein, and Tarjan, "A randomized linear-time algorithm to find minimum spanning trees", J. ACM, vol. 42, 1995, pp. 321-328.] It can be solved in linear worst case time if the weights are small integers. [Fredman and Willard, "Trans-dichotomous algorithms for minimum spanning trees and shortest paths", 31st IEEE Symp. Foundations of Comp. Sci., 1990, pp. 719725.] Otherwise, the best solution is very close to linear but not exactly linear. The exact bound is O(m log beta(m,n)) where the beta function has a complicated definition: the smallest i such that log(log(log(...log(n)...))) is less than m/n, where the logs are nested i times. [Gabow, Galil, Spencer, and Tarjan, Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica, vol. 6, 1986, pp. 109122.]

50. David Eppstein - Publications Includes sections on the traveling salesman problem, Steiner trees, minimumweight triangulation, clustering, and separation problems. http://www.ics.uci.edu/~eppstein/pubs/tsp.html

David Eppstein - Publications Traveling salesman and hamiltonian cycle problems Worst-case bounds for subadditive geometric graphs M. Bern and D. Eppstein. 9th ACM Symp. Comp. Geom., San Diego, 1993, pp. 183-188. For many geometric graph problems for points in the unit square, such as minimum spanning trees matching , and traveling salesmen , the sum of edge lengths is O(sqrt n ) and the sum of d th powers of edge lengths is O(log n ). We provide a "gap theorem" showing that if these bounds do not hold for a class of graphs, both sums will instead be Omega( n ). For traveling salesmen the O(log n ) bound is tight but for some other graphs the sum of d th powers of edge lengths is O(1). BibTeX Citations Preprint of SCG version CiteSeer Approximation algorithms for geometric problems M. Bern and D. Eppstein. Approximation Algorithms for NP-hard Problems D. Hochbaum , ed., PWS Publishing, 1996, pp. 296-345. Considers problems for which no polynomial-time exact algorithms are known, and concentrates on bounds for worst-case approximation ratios, especially those depending intrinsically on geometry rather than on more general graph theoretic or metric space formulations. Includes sections on the traveling salesman problem , Steiner trees, minimum weight triangulation , clustering, and separation problems.

51. Das Bipartite Travelling-Salesman-Problem traveling salesman problem and its Assignment Relaxation. Preprint, 2001. http://www.numerik.uni-kiel.de/~aba/TSP-Projekt.html

Das bipartite Travelling-Salesman-Problem Leitung: Prof. Dr. A. Srivastav Mitarbeiter: Dr. Andreas Baltz Dr. Tomasz Schoen Aufgabe: Anwendung: Wir untersuchen: Effiziente Approximationsalgorithmen a) Die B2-Baum-Strategie Verdopple Kanten und durchlaufe Baum mittels Tiefensuche. Experimentell: Implementierung mit Matroid-Schnitt-Algorithmus hat hohe Laufzeit. Theoretische Analyse: berechnen. b) Die Matching-Methode Bestimme Tour durch blaue Punkte mit Approximationsschema von Arora. Experimentell: Implementierungen mit sehr geringen Laufzeit durch Austausch-Heuristiken und LP-Formulierung des Matchingproblems Theoretische Analyse: , wobei OPT-Schranke angenommen. c) Das Kreiszerlegungsverfahren Bestimme eine optimale Kreiszerlegung mittels linearer Programmierung oder durch einen kombinatorischen 2-Matching-Algorithmus. Experimentell: LP-Formulierung erlaubt Implementierungen mit geringer Laufzeit. Theoretische Analyse: Schranke OPT kann erreicht werden Asymmetrisches Bipartites TSP Frieze, Karp und Reed zeigen: Frieze und Sorkin beweisen: gilt ATSP(M)-AP(M) und Offene Fragen Literatur A. Baltz, T. Schoen, A. Srivastav;

52. Traveling Salesman Problem traveling salesman problem (Simulated Annealing). The Traveling SalesmanProblem is to find the shortest circuitous path connecting http://www.svengato.com/salesman.html

Traveling Salesman Problem (Simulated Annealing) The Traveling Salesman Problem is to find the shortest circuitous path connecting N cities (meaning that a traveling salesman following that path would visit each city only once). Although it can in principle be solved by brute force (by calculating the length of every possible circuit), this is not practical because the number of circuits grows so fast that even for N = 25 cities, it would take longer than the age of the universe (~10 billion years) to check every path, at a rate of one million paths per second! However, the method of simulated annealing quickly gives a reasonable answer, where "reasonable" means close enough to the true minimum path for practical purposes. Simulated annealing starts with the cities connected in a random order, and then considers making random changes in that order. If changing the order of cities leads to a shorter path, we accept that change. If the modification yields a longer path, we give ourselves a certain probability of accepting the modification less likely the larger the proposed increase in path length. We then gradually reduce this probability over time, in order to rule out shorter and shorter path increases thereby converging toward a path length close to the absolute minimum. The term "simulated annealing" comes from the analogy with annealing of metal, in which the metal is heated to a high temperature to give its atoms a lot of thermal motion, then is slowly cooled to give them a chance to align themselves into their lowest-energy (generally crystalline) configuration. Annealing makes the metal stronger than does rapid cooling (e.g. by plunging it into cold water), which would freeze the atoms wherever they happened to be, leaving microscopic cracks that make the metal brittle.

53. The Traveling Salesman Problem next up previous Next About this document Up dynnotes Previous The ShortestPath Problem. The traveling salesman problem. See section 3.6 from the text. http://www.cs.pitt.edu/~kirk/cs1510/notes/dynnotes/node14.html

Next: About this document ... Up: dynnotes Previous: The Shortest Path Problem The Traveling Salesman Problem See section 3.6 from the text. The input to this problem is a directed edge weighted graph with a designated vertex s . The edge weights may be positive or negative. The problem is to find the shortest simple path from s that visits all of the vertices. Here feasible solutions are simple paths that start from the source vertex s . The nodes in level k of the tree represent all paths from s of exactly k . Note that by simplicity we we need only consider the tree to depth n , the number of vertices. The pruning rule is that if two paths end at the same vertex and contain the same vertices then we may prune the shorter one. We thus get the following code. Here D k S i ] is the shortest path from s to i of k or less hops that visits exactly the vertices in S For k= 1 to n do For i= 1 to n do For S= 1 to 2^n do for each edge e = (i, j) do if j is not in S then D[k, S+ j, j]=min( D[k, S+j, j], D[k, S, i] + the length of e ) The running time of this code is O VE V ), where

54. Zuse Institute Berlin - MP-Testdata - Traveling Salesman Problem Instances Translate this page http://elib.zib.de/pub/Packages/mp-testdata/tsp/

55. Traveling Salesman Problem Definition Meaning Information Explanation traveling salesman problem definition, meaning and explanation andmore about traveling salesman problem. traveling salesman problem. http://www.free-definition.com/Traveling-salesman-problem.html

A B C D ... Contact Beta 0.71 powered by: akademie.de PHP PostgreSQL Google News about your search term Traveling salesman problem 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. Inhaltsverzeichnis 1 Problem statement 2 Computational complexity 3 Algorithms 3.1 Exact algorithms ... 6 External Links Problem statement 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 printed circuit manufacturing scheduling of a route of the drill machine to drill holes in a PCB. In robotic machining or drilling applications, the "cities" are parts to machine or holes (of different sizes) to drill, and the "cost of travel" includes time for retooling the robot (single machine job sequencing problem).

56. OPL Model Details: Traveling Salesman Problem traveling salesman problem. The traveling salesman problem (TSP)is a classic problem in combinatorial optimization. The goal is http://www2.ilog.com/oplmodels/display.cfm?ID=41

57. Traveling Salesman Problem next up previous Next Conclusions Up Nature s Way of OptimizingPrevious Graph Partitioning. traveling salesman problem. In the http://cnls.lanl.gov/Highlights/1998-12/html/node3.html

Next: Conclusions Up: Nature's Way of Optimizing Previous: Graph Partitioning Traveling Salesman Problem In the traveling salesman problem (TSP), N points (``cities'') are given, and every pair of cities i and j is separated by a distance . The problem is to connect the cities with the shortest closed ``tour'', passing through each city exactly once. For our purposes, take the distance matrix to be symmetric. Its entries could be the Euclidean distances between cities in a plane, or alternatively random numbers drawn from some distribution making the problem non-Euclidean. (The former case might correspond to a business traveler trying to minimize driving time; the latter to a traveler trying to minimize expenses on a string of airline flights, whose prices do not necessarily obey triangle inequalities!) For the TSP, we implement EO in the following way. Consider each city i as a degree of freedom, with a fitness based on the two links emerging from it. Ideally, a city would want to be connected to its first and second nearest neighbor, but is often ``frustrated'' by the competition of other cities, causing it to be connected instead to (say) its th and th neighbors

58. OperationsResearch.com - 'Traveling Salesman Problem (TSP)' Next Prev Top. traveling salesman problem (TSP). Asymmetric TravelingSalesman Problem 1, 2; The traveling salesman problem - 1, 2; http://opsresearch.com/OR-Links/P10.html

Next Prev Top Traveling Salesman Problem (TSP) Asymmetric Traveling Salesman Problem The Traveling Salesman Problem David Neto's TSP reading list TSPLIB ... The Travelling Salesperson Problem

59. OpenTS Tutorial - Traveling Salesman Problem (TSP) OpenTS Tutorial traveling salesman problem. Introduction. In thistutorial we will be build a tabu search that solves the famous http://www-124.ibm.com/developerworks/opensource/coin/OpenTS/docs/tutorial/simpl

i Harder.net OpenTS Tutorial Summary Download now! Documentation Installation ... Contact Robert Harder OpenTS Tutorial - Traveling Salesman Problem Introduction In this tutorial we will be build a tabu search that solves the famous Traveling Salesman Problem (TSP). In the TSP, a salesman wants to visit all of his customers once, traveling the least distance possible. There are many variations on this basic problem. Our problem will be this: There is a list of customers. Each customer has an (x,y) coordinate in the range [0,200) generated by multiplying random numbers from zero (0) to 0.9999... by 200. The salseman may start at the first customer, must visit each customer exactly once, and returns to the original customer at the end (we can assume the first customer is "home"). All the tutorial files are available here Tutorial Agenda After having just introduced the problem, however briefly, we will look at the main program to give us a high-level overview before looking at the details of actually building our tabu search objects. Introduction Main Program source Solution source ... Tabu List [Using built-in tabu list] Putting it All Together Making the Move Manager Adaptive - Coming Soon!

60. Travelling Salesman Problem doc.ic.ac.uk . Previous traveling salesman problem Next trawl. travellingsalesman problem. algorithm, complexity (TSP or shortest http://burks.brighton.ac.uk/burks/foldoc/32/119.htm

The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: traveling salesman problem Next: trawl travelling salesman problem algorithm complexity 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

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