61. 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.

62. The Landscape Of The Traveling Salesman Problem 9201-003 The Landscape of the traveling salesman problem. Peter F.Stadler, Wolfgang Schnabl. The landscapes of Traveling Salesman http://www.tbi.univie.ac.at/papers/Abstracts/92-01-003abs.html

The Landscape of the Traveling Salesman Problem Peter F. Stadler, Wolfgang Schnabl The landscapes of Traveling Salesman Problems are investigated by random walk techniques. The autocorrelation functions for different metrics on the space of tours are calculated. The landscape turns out to be AR(1) for symmetric TSPs. For asymmetric problems there can be a random contribution superimposed on an AR(1) behaviour. Return to 1992 working papers list.

63. 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

64. Traveling Salesman Problem - Startseite Translate this page The traveling salesman problem. Zum Start bitte hier klicken Copyright1997 by Matthias Hoffmann (TFH Berlin) letzte Änderung 5-1-1997. http://www.f4.fhtw-berlin.de/people/weberwu/diplom/tsp/START.HTM

The Traveling Salesman Problem Zum Start bitte hier klicken Matthias Hoffmann (TFH Berlin)

65. The Travelling Salesman Problem An efficient solution to this problem reduces production costs for the manufacturer.— WorldRecord traveling salesman problem for 3038 Cities Solved. http://hermetic.magnet.ch/misc/ts3/ts3demo.htm

The Travelling Salesman Problem Program 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:

66. New Solution For Traveling Salesman Problem New Solution Determined for traveling salesman problem. BY GretchenJacobson Special to the Rice News June 25, 1998. Rice University http://www.rice.edu/projects/reno/rn/19980625/tsp.html

New Solution Determined for Traveling Salesman Problem BY Gretchen Jacobson Special to the Rice News June 25, 1998 Rice University researchers David Applegate, Robert Bixby and William Cook and Vasek Chvatal of Rutgers University have determined a breakthrough solution to the Traveling Salesman Problem (TSP), a method for finding an optimal path for a salesman to take when traveling through a specified number of cities. The researchers have solved the TSP for 13,509 U.S. cities with populations of more than 500 people, a dramatic step beyond their previous solution for 7,397 cities, set in 1994. The TSP is typical of a class of hard optimization problems with applications in science and engineering that has intrigued mathematicians and computer scientists for years. Finding an optimal route for the TSP becomes more challenging as the number of cities increases. For example, to solve the most economical way a salesman can tour five cities, a computer can be used to calculate the lengths of all possible routes and find the shortest one in a fraction of a second. However, using the same method to figure the optimal route for 100 cities could take billions of years. The research team has been developing mathematical models and using high-performance computing since 1988 to develop a more efficient solution. The researchers' first breakthrough was a record 3,038 cities set in 1992, using 50 workstations and an algorithm they designed based on a technique called "cutting planes." The technique steadily improves the collection of linear inequalities describing the set of feasible solutions. This achievement was recognized by Discover magazine as one of its top 50 science stories that year. By 1993, the team had solved the TSP for 4,461 cities. This year, the TSP researchers surpassed their 1994 record by using a cluster of three Digital AlphaServer 4100s (a total of 12 processors) and a cluster of 32 Pentium-II PCs located in Rice University's Duncan Hall. The calculation took approximately three months from start to finish.

67. Researchers Forge New Optimal Path For Traveling Salesman Problem 98123. RESEARCHERS FORGE NEW OPTIMAL PATH FOR traveling salesman problem(TSP). HOUSTON, June 4, 1998 Rice University researchers http://www.rice.edu/projects/reno/Newsrel/1998/19980604_tsp.html

Rice University News Office News Release DATE: June 4, 1998 CONTACT: Lia Unrau PHONE: (713) 831-4793 E-MAIL: mcinelli@rice.edu RESEARCHERS FORGE NEW OPTIMAL PATH FOR TRAVELING SALESMAN PROBLEM (TSP) HOUSTON, June 4, 1998 Rice University researchers David Applegate, Robert Bixby and William Cook, and Vasek Chvatal of Rutgers University have determined a breakthrough solution to the Traveling Salesman Problem (TSP), a method for finding an optimal path for a salesman to take when traveling through a specified number of cities. The researchers have solved the TSP for 13,509 U.S. cities with populations of more than 500 people, a dramatic step beyond their previous record of 7,397 cities, set in 1994. The TSP is typical of a class of hard optimization problems with applications in science and engineering that has intrigued mathematicians and computer scientists for years. Finding an optimal route for the TSP becomes more challenging as the number of cities increases. For example, to solve for the most economical way a salesman can tour five cities, a computer can be used to calculate the lengths of all 120 possible different routes and find the shortest one in a fraction of a second. However, using the same method to figure the optimal route for 100 cities could take billions of years. The research team has been developing mathematical models and using high-performance computing since 1988 to develop a more efficient solution. The researchers' first breakthrough was a record 3,038 cities set in 1992, using 50 workstations and an algorithm they designed based on a technique called "cutting planes." The technique steadily improves the collection of linear inequalities describing the set of feasible solutions. This achievement was recognized by Discover magazine as one of its top 50 science stories that year. By 1993, the team had solved for 4,461 cities. This year, the TSP researchers surpassed their 1994 record by using a cluster of three Digital AlphaServer 4100s (a total of 12 processors) and a cluster of 32 Pentium-II PCs located in Rice University's Duncan Hall. The calculation took approximately three months from start to finish.

68. Hybrid Genetic Algorithms For The Traveling Salesman Problem CAD Group Publications, icnnga show related papers. HybridGenetic Algorithms for the traveling salesman problem. http://www.cad.polito.it/FullDB/exact/icnnga.html

CAD Group Publications icnnga show related papers Hybrid Genetic Algorithms for the Traveling Salesman Problem P. Prinetto M. Rebaudengo reba@polito.it http://www.cad.polito.it/~reba/ M. Sonza Reorda ... http://www.cad.polito.it/~sonza/ International Conference on Neural Networks and Genetic Algorithms, Innsbruck (A), Aprile 1993, pp.559-566 KEYWORDS: Approximate Methods Evolutionary Algorithms Genetic Algorithms ABSTRACT A comparative analysis is performed on an experimental basis among four different cross-over operators. In order to exploit the benefits of the different operators, a new one (called Mixed Cross-over) is introduced, trading-off the CPU time requirements and the obtained results. A new operator is then proposed, whose goal is to include in the genetic mechanism some heuristic knowledge drawn from the already proposed local-optimization techniques. The performance of the new operator is discussed. Related files: icnnga.zip compressed archive (with PkZip) [PRSe93] P. Prinetto, M. Rebaudengo, M. Sonza Reorda, "Hybrid Genetic Algorithms for the Traveling Salesman Problem," International Conference on Neural Networks and Genetic Algorithms , Innsbruck (A), Aprile 1993, pp.559-566

69. 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

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.

70. GSRC Calibrating Achievable Design Bookshelf: Traveling Salesman Problem Slot MARCO GSRC Calibrating Achievable Design Bookshelf. traveling salesman problemSlot. Work in progress last updated Thu Apr 12 2001 (see other slots). http://vlsicad.ucsd.edu/GSRC/Bookshelf/Slots/TSP/

MARCO GSRC Calibrating Achievable Design: Bookshelf Traveling Salesman Problem Slot Work in progress : last updated Mon Dec 16 2002 see other slots Ken Boese, Andrew B. Kahng Mike Oliver and Tim Walters Contents I. Introduction II. Data Formats III. Publicly available instances, solutions and reference performance results IV. Executable Utilities (converters, generators, statistics browsers, evaluators, constraint verifiers) V. Optimizers and other non-trivial executables VI. Common in-memory representations, parsers and other source codes I. Introduction This slot gives pointers to various TSP codes, benchmarks, and instance generators. II. Data Formats To come III. Publicly available instances, solutions and reference performance results TSPLIB DIMACS Benchmark Instances Bill Cook's TSP page IV. Executable Utilities To come V. Optimizers and non-trivial executables To come VI. Source codes DIMACS Benchmark Code and Instance Generation Codes Ken Boese's implementation of the Lin-Kernighan heuristic Keld Helsgaun's implementation of the Lin-Kernighan heuristic The Concorde TSP code (Applegate, Bixby, Chvátal, and Cook) ... abk@ucsd.edu,oliver@cs.ucla.edu

71. 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!

72. 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

73. The Traveling Salesman Problem The traveling salesman problem. Gregg Townsend The traveling salesmanproblem is a traditional computer science challenge. http://www.cs.arizona.edu/people/pete/overview/demos/salesman/

The Traveling Salesman Problem Gregg Townsend The traveling salesman problem is a traditional computer science challenge. Its goal is to find the shortest circuit through a set of points. A common approach is to construct an initial path and then improve it incrementally through local optimizations. This program illustrates several construction algorithms followed by application of the "2-opt" improvement algorithm; that algorithm deletes two segments at a time and reconnects their endpoints. If you look closely you may spot sections of a path that could be further improved by the "3-opt" algorithm which is not implemented here. This animation is written in the Icon language. Source code Icon web page

74. Traveling Salesman Problem Previous Trash80 Next travelling salesman problem. traveling salesman problem. spelling US spelling of travelling salesman problem. (1996-12-13). http://burks.brighton.ac.uk/burks/foldoc/31/119.htm

The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: Trash-80 Next: travelling salesman problem traveling salesman problem spelling travelling salesman problem

75. PS Algorithmen Für Das Traveling Salesman Problem - SoSe 2002 Translate this page Algorithmen für das traveling salesman problem. Dozent Dr. Anusch Taraz. Lawler,Lenstra, Rinnooy Kan, Shmoys The traveling salesman problem, Wiley, 1985 back. http://www.informatik.hu-berlin.de/Institut/struktur/algorithmen/lehre/lvss02/PS

Arbeitsgruppe Algorithmen Proseminar Dozent: Dr. Anusch Taraz Termine: Mi 16-18 (DOR 24, 311) Beginn und Themenvergabe: Mi 8. Mai 2002 Zuordnung: Grundstudium Inhalte und Lernziele Voraussetzungen Empfohlen: Theoretische Informatik 2 Vortragsthemen Exakte Algorithmen Nearest Neighbour und Minimum spanning tree Heuristik Christofides Approximation Approximationsschemata Probabilistische Analyse Empfohlene Literatur Lawler, Lenstra, Rinnooy Kan, Shmoys: The Traveling Salesman Problem, Wiley, 1985 Last modified: 2002-04-29 Mon 13:48:18 (cg)

76. Two Solvable Cases Of The Traveling Salesman Problem Günter Rote Two solvable cases of the traveling salesman problem. Ph.D. thesis, May 1988, 55 pages. (Supervisor Prof. Dr. RE Burkard). http://www.inf.fu-berlin.de/~rote/Papers/abstract/Two solvable cases of the trav

77. Traveling Salesman Problem traveling salesman problem. As mentioned before, these types of hamiltoniancircuit problems can get extremely difficult to solve. http://www.lehigh.edu/~inmath/tsp.html

Traveling Salesman Problem As mentioned before, these types of hamiltonian circuit problems can get extremely difficult to solve. The tree method will give you the optimal solution but you can't use this method for several vertices for it will get too long. The traveling salesmen problem (TSP) determine the trip of minimum cost that a person can make to visit the cities he or she is trying to visit in the most efficient way, then returning home. This is the same type of problem like the vacation planning problem. The method of trees can't be used with many vertices since the comutations have such a huge running time. Computers can actually solve optimal solutions up to around 1000 vertices. Once you have around 2000 or more vertices, computers can't handle them anymore. They use a variation of the method of trees with several shortcuts which are very hard to explain and gets rather difficult. They can take a huge amount of time to solve. So how do they do it? Mathematicians had to come up with some kind of algorithm or algorithms to solve this extremely tough question. So the next question that naturally arises is can they come up with a solution quickly without having to use trees, that is still very efficient. The key here to be pointed out is we are no longer going to get THE optimal solution (it could turn out to be but it doesn't have to be). Now we are looking for a solution which is still useful that just choosing a path at random.

78. Traveling Salesman Problem From FOLDOC Guides Tutorials. Online Computing Dictionary. Register a Domain. traveling salesmanproblem. spelling US spelling of travelling salesman problem. (199612-13). http://www.instantweb.com/foldoc/foldoc.cgi?traveling salesman problem

79. The Euclidean Traveling Salesman Problem With Neighborhoods And A Connecting Fen Doctoral thesis / 200036. TITEL The Euclidean traveling salesman problem with neighborhoodsand a connecting fence FöRFATTARE Jonsson, Håkan. DATUM 200011-10. http://epubl.luth.se/1402-1544/2000/36/

Förstasida Sök In English Doctoral thesis TITEL The Euclidean traveling salesman problem with neighborhoods and a connecting fence FöRFATTARE Jonsson, Håkan DATUM INSTITUTION Systemteknik / Datalogi SAMMANFATTNING An important class of problems in robotics deals with the planning of paths. In this thesis, we study this class of problems from an algorithmic point of view by considering cases where we have complete knowledge of the environment and each solution must ensure that a point-sized robot capable of moving continuously and turning arbitrarily accomplishes the following: (1) visits a given set of objects attached to an impenetrable simple polygon in the plane, and (2) travels along a path of minimum length over all the possible paths that visit the objects without crossing the polygon. In its general form, this is The (Euclidean) Traveling Salesman Problem with Neighborhoods and a Connecting Fence. ISSN 1402-1544 / ISRN LTU-DT00/36SE / NR 2000:36 Förstasida Sök Universitetet Biblioteket LULEÅ UNIVERSITETSBIBLIOTEK

80. Traveling Salesman Problem New Search Articles. Home Help Index On/Off traveling salesmanproblem,. Index an optimization problem http://www.cs.auc.dk/~luca/FS2/salesman.html

New Search : Articles Index Dictionary traveling salesman problem, an optimization problem in graph theory, in which the nodes (cities) of a graph are connected by directed edges (routes), where the weight of an edge is the distance between two cities. The problem is to find a path that visits each city once, returns to the starting city, and minimizes the distance traveled. The only known solution that guarantees the shortest path requires a solution time that grows exponentially with the problem size ( i.e., number of cities). This is an example of an NP-complete problem q.v. ), for which no known efficient ( i.e., polynomial time) algorithm exists.

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