Geometry.Net - Theorems_And_Conjectures: Traveling Salesman Problem

The Travelling Salesman Problem
The travelling salesman problem is quite simple a travelling salesman has to But one was able to prove that the traveling salesman problem is a kind of
http://www.uni-kl.de/AG-AvenhausMadlener/tsp-eng.html

Extractions: 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. 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
Euclidean Traveling Salesman Problem
Definition of Euclidean traveling salesman problem, possibly with links to more information and implementations.
http://www.nist.gov/dads/HTML/euclidntrvls.html

Extractions: (classic problem) Definition: Find a path of minimum Euclidean distance between points in a plane which includes each point exactly once and returns to its starting point. See also traveling salesman spanning tree Note: This can be generalized to higher dimensions, for instance, points in a 3-dimensional space. This problem is a special case of traveling salesman since the cost between points is the planar distance instead of arbitrary weights. Author: PEB Go to the Dictionary of Algorithms and Data Structures home page. If you have suggestions, corrections, or comments, please get in touch with Paul E. Black (paul.black@nist.gov). Entry modified Fri Dec 17 12:03:57 2004.
Traveling Salesman Problem -- Facts, Info, And Encyclopedia Article
traveling salesman problem. Categories NPcomplete problems, Optimization, The traveling salesman problem or travelling salesman problem (TSP),
http://www.absoluteastronomy.com/encyclopedia/t/tr/traveling_salesman_problem.ht

Extractions: is a problem in (Click link for more info and facts about discrete) discrete or (Click link for more info and facts about combinatorial optimization) combinatorial optimization . It is a prominent illustration of a class of problems in (Click link for more info and facts about computational complexity theory) computational complexity theory which are hard to solve. Given a number of cities and the costs of traveling from any city to any other city, what is the cheapest round-trip route that visits each city once and then returns to the starting city? An equivalent formulation in terms of (Click link for more info and facts about graph theory) graph theory is: Given a (Click link for more info and facts about complete weighted graph) complete weighted graph (where the vertices would represent the cities, the edges would represent the roads, and the weights would be the cost or distance of that road), find the (Click link for more info and facts about Hamiltonian cycle) Hamiltonian cycle with the least weight.
Traveling Salesman Problem - Maple Application Center - Maplesoft
The traveling salesman problem (TSP) is a fascinating optimization problem in which a salesman wishes to visit each of N cities exactly once and return to
http://www.maplesoft.com/applications/app_center_view.aspx?AID=966
IMA PUBLIC LECTURE The Traveling Salesman Problem By William J. Cook, October 16
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,
http://www.ima.umn.edu/public-lecture/tsp/

Extractions: 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.
Traveling Salesman Problem - Definition Of Traveling Salesman Problem In Encyclo
The traveling salesman problem (TSP), also known as the traveling salesperson problem,is a problem in discrete or combinatorial optimization.
http://encyclopedia.laborlawtalk.com/Traveling_salesman_problem

Extractions: 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. Contents showTocToggle("show","hide") 1 Problem statement 7 External links 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 once and then returns to the starting city? An equivalent formulation in terms of graph theory is: Find the Hamiltonian cycle with the least weight 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 classic example is in
PCGrate -> Traveling Salesman Problem
International Intellectual Group, Inc. (IIG, Inc.) is a small private company which was established in 1996 by specialists from the USA and Russia for
http://www.pcgrate.com/about/npcomprb/tsp
Interactive Genetic Algorithms For The Traveling Salesman Problem
Interactive Genetic Algorithms for the traveling salesman problem.
http://www.cse.unr.edu/~sushil/papers/conference/newpapers/99/gecco99/iga/GECCO/

Extractions: tang@cs.unr.edu We use an interactive genetic algorithm to divide and conquer large traveling salesperson problems. Current genetic algorithm approaches are computationally intensive and may not produce acceptable tours within the time available. Instead of applying a genetic algorithm to the entire problem, we let the user interactively decompose a problem into subproblems, let the genetic algorithm separately solve these subproblems and then interactively connect subproblem solutions to get a global tour for the original problem. Our approach significantly reduces the computing time to find high quality solutions for large traveling salesperson problems. We believe that an interactive approach can be extended to other visually decomposable problems.
Generation5 - Genetic Algorithm And Traveling Salesman Problem
Generation5 aims to be the most comprehensive Artificial Intelligence site on the Internet. Communityorientated, Generation5 deals with all AI topics
http://www.generation5.org/content/2001/tspapp.asp

Extractions: By Konstantin Boukreev Printable Version Title: Genetic Algorithm and Traveling Salesman Problem Author: Konstantin Boukreev Email: konstantin@mail.primorye.ru Environment: VC++ 6.0. SP5, Win2k SP2, MS Platform SDK April 2001 Description: The example of using Genetic Algorithm for solving Traveling Salesman Problem Genetic Algorithm Base implementation, Template class GA and GA Selection classes Genome of Travel TSP Application Environment Reference I am not a GA guru and I do not have any degree in GA so this article can't be used as GA book or GA tutorial. There aren't any mathematics nor logic nor algebra about GA. It's only a programmer's view on Genetic Algorithms and only example of GA coding. Use it carefully! Any comments and criticism are highly appreciated. Genetic Algorithm, Theory
Traveling Salesman Problem
Discussion The traveling salesman problem is the most notorious NPcomplete The TSPLIB library of test instances for the traveling salesman problem is
http://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE175.HTM

Extractions: Next: Hamiltonian Cycle Up: Graph Problems: Hard Problems Previous: Vertex Cover 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?
World-Record Traveling Salesman Problem For 3038 Cities Solved
The problem is commonly referred to as the traveling salesman problem. The traveling salesman problem is typical of a large class of hard
http://nhse.cs.rice.edu/CRPC/newsletters/jan93/news.tsp.html

Extractions: January 1993 Finding an optimal route becomes more challenging as the number of cities involved increases. For instance, to solve for the most economical way for a traveling salesman to tour five cities the researcher can take a straightforward method, having the computer calculate the lengths of all 120 different routes to find the shortest one. This calculation could be performed in a fraction of a second. However, using the same method to figure the optimal route for a hundred cities could take billions of years. How can a more efficient solution be reached? The researchers designed an algorithm based on a technique called "branch and cut," which steadily improves the collection of linear inequalities describing the set of feasible solutions. Many other groups have created algorithms that can reach approximate (within 2%) solutions for this problem, calculating approximate optimal routes for 1000 cities in a few minutes. Improved versions of those techniques were used here to get upper bounds. The difficult part was to drive up the lower bound and prove optimality. Calculations for the 3038 cities problem required one and one-half years of computer time. 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.
Traveling Salesman Problem
traveling salesman problem. Session MA29 Date/Time Monday 08000930 Type Contribute Sponsor Track Cluster Room Room 326 Chair John Mittenthal
http://www.informs.org/Conf/WA96/TALKS/MA29.html
Problem 54: Traveling Salesman Problem In Solid Grid Graphs
Problem 54 traveling salesman problem in Solid Grid Graphs.
http://maven.smith.edu/~orourke/TOPP/P54.html

Extractions: Problem 54: Traveling Salesman Problem in Solid Grid Graphs ] show that Hamiltonicity of a solid grid graph can be decided in polynomial time. Thus we can decide whether there is a tour of length equal to the number of vertices. In contrast, deciding Hamiltonicity is NP-hard in general planar grid graphs [ ABD+01 ] observe that finding the shortest tour is polynomially solvable when restricted to thin grid graphs, i.e., grid graphs that do not contain an induced
Citations: The Traveling Salesman Problem With Distances One And Two - Papadimit
C. Papadimitriou and M Yannakakis. The traveling salesman problem with distances one and two. Mathematics of Operations Research. To appear.
http://citeseer.ifi.unizh.ch/context/24035/0

Extractions: Light Spanners and Approximate TSP in Weighted Graphs with - Forbidden Minors.. (Correct) ....by NSF Grant number CCR9820931. Department of Mathematics and Computer Science, Emory University, Atlanta GA 30322, USA. Email : mic mathcs.emory.edu. Same support and address. Email : psissok emory.edu. that is polynomial (or quasi polynomial) in n. Even the approximation problem is MAXSNP hard , so we do not expect an efficient approximation scheme for general graphs (even sparse graphs) However, there are approximation schemes running in polynomial time when G is planar [2, 6] and in quasi polynomial time when G has bounded genus [5] In this paper we show that the approximation .
On The Approximability Of The Traveling Salesman Problem - Papadimitriou, Vempal
We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than when the edge lengths are allowed to be
http://citeseer.ifi.unizh.ch/papadimitriou00approximability.html
The Geometric Maximum Traveling Salesman Problem
We consider the traveling salesman problem when the cities are points in num The traveling salesman problem for a maximum in finitedimensional real
http://portal.acm.org/citation.cfm?id=876640
Traveling Salesman Problem - Permutation City
The travelling salesman problem involves planning a route from city to city for a For this implementation of the Travelling Salesman Problem only a new
http://www.permutationcity.co.uk/projects/mutants/tsp.html
Combinatorial Optimization And The Traveling Salesman Problem :: SADIO :: Socied
Sociedad Argentina de Informática e Investigación Operativa.
http://www.sadio.org.ar/pn750/modules.php?op=modload&name=News&file=article&sid=
Hybrid Genetic Algorithms For The Traveling Salesman Problem
Hybrid Genetic Algorithms for the traveling salesman problem Hybrid Genetic Algorithms for the traveling salesman problem, International Conference on
http://www.cad.polito.it/FullDB/exact/icnnga.html

Extractions: http://www.cad.polito.it/staff/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
CodeGuru: Genetic Algorithm And Traveling Salesman Problem
A programmer s view and example on Genetic Algorithms. By Konstantin Boukreev.
http://www.codeguru.com/Cpp/misc/misc/article.php/c3795/

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