1. Traveling Salesman Problem Traveling salesman problem. The traveling salesman problem (TSP), also known as the traveling salesperson problem, is a problem in discrete or combinatorial optimization. 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.

2. Traveling Salesman Problem Given a number n 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 the starting point. http://www.daviddarling.info/encyclopedia/T/traveling_salesman_problem.html

3. Traveling Salesman Problem - Discussion And Encyclopedia Article. Who Is Traveli Traveling salesman problem. Discussion about Traveling salesman problem. Ecyclopedia or dictionary article about Traveling salesman problem. http://www.knowledgerush.com/kr/encyclopedia/Traveling_salesman_problem/

4. Traveling Salesman Problem The Travelling Salesman Problem ( TSP ) is an NPhard problem in combinatorial optimization studied in operations research and theoretical computer science. http://finance.kosmix.com/topic/Traveling_salesman_problem

Kosmix One sec... we're building your guide for Traveling Salesman Problem document.k_start_apptier = "Oct 31 01:07:23.533368"; kapp.assignCol($('ads_banner_top'), 'topnav_container'); Traveling Salesman Problem Overview Images Video Reference kapp.nav_menu_container = $('refine_nav').down(".navs_container"); kapp.assignCol($('refine_nav'), 'topnav_container'); kapp.assignCol($('uc_kosmixarticles_shadow'), 'right_container'); Snapshot Wikipedia Wikipedia Reference from Wikipedia Travelling Salesman Problem The Travelling Salesman Problem TSP ) is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once. The problem was first formulated as a mathematical problem in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved. The TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips. Slightly modified, it appears as a

5. Wapedia - Wiki: Travelling Salesman Problem 3. Computing a solution 4. Human performance on TSP 5. TSP path length for random pointset in a square 6. Analyst s traveling salesman problem http://wapedia.mobi/en/Traveling_salesman_problem

Wiki: Travelling salesman problem The Travelling Salesman Problem TSP ) is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science . Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once. The problem was first formulated as a mathematical problem in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved. An optimal TSP tour through Germany ’s 15 largest cities. It is the shortest among 43 589 145 600 possible tours visiting each city exactly once. The TSP has several applications even in its purest formulation, such as planning logistics , and the manufacture of microchips . Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing . In these applications, the concept

6. Traveling Salesman Problem - Definition 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 http://www.wordiq.com/definition/Traveling_salesman_problem

Traveling salesman problem - Definition 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 2 Computational complexity 3 NP-hardness 4 Algorithms ... 7 External links Problem statement Given a number of cities and the costs of travelling 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 graph theory is: Given a 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 Hamiltonian cycle with the least weight. 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

7. Traveling Salesman Problem | Ask.com Encyclopedia The Travelling Salesman Problem (TSP) is an NPhard problem in combinatorial optimization studied in operations research and theoretical computer science. http://www.ask.com/wiki/Traveling_salesman_problem?qsrc=3044

8. Wolfram|Alpha: Traveling Salesman Problem : Statement, Proof, Status, ... Complete information and computations for traveling salesman problem basic properties, history, http://www.wolframalpha.com/entities/famous_math_problems/traveling_salesman_pro

document.write(''); Home Examples About FAQS ... Media Resources A Wolfram Web Resource Wolfram Research Wolfram Mathematica Wolfram Demonstrations ... Wolfram Tones Enter something to compute or figure out Calculate traveling salesman problem: statement, proof, status, awards, ... Input interpretation: Statement: Definition Alternate name: History: Computed by Wolfram Mathematica Download as: PDF Live Mathematica A Wolfram Research Company Participate Entity Index traveling salesman problem: statement, proof, status, awards, ... Input: traveling salesman problem traveling salesman problem Statement Alternate name TSP History

9. Traveling Salesman Problem One of the most popular combinatorial problems is the Traveling Salesman Problem (TSP). Problems of this type are often encountered in practice, and the TSP has become a benchmark http://www.wardsystems.com/manuals/genehunter/traveling_salesman_problem.htm

Traveling Salesman Problem Top Previous Next One of the most popular combinatorial problems is the Traveling Salesman Problem (TSP). Problems of this type are often encountered in practice, and the TSP has become a benchmark for the different algorithms of combinatorial optimization. Its solution is computationally difficult though the problem itself is easily expressed. The Problem Imagine a salesperson who must make a closed complete tour of a given number of cities. He wishes to minimize the length of the route. All cities are connected to each other by roads, and each of the cities should be visited only once. The main obstacle to solving the problem is that the map is not available to the salesman. The only information that he has is the table of distances between the cities. These circumstances make the solution of the problem very difficult. Having a map makes it relatively easy to construct a quasi-optimal route, while shuffling the cities according to the table of distances is a very complicated task. The total number of possible alternative tours in this problem is (N-1)!/2, where N stands for the number of cities. The TSP Program Fig. 7.1 View of TSP main form

10. Traveling Salesman Problem Example GHSAMPLE.XLS, TSP worksheet. Solution Type Enumerated Chromosomes . This example is located in a tab labeled TSP in the GHSAMPLE.XLS worksheet that was installed in the C http://www.wardsystems.com/manuals/genehunter/example_traveling_salesman_problem

Traveling Salesman Problem Top Previous Next Example: GHSAMPLE.XLS, TSP worksheet Solution Type: Enumerated Chromosomes The Traveling Salesman Problem is a well known problem which has become a comparison benchmark test for different computational methods. Its solution is computationally difficult, although the problem is easily expressed. A salesperson must make a closed complete tour of a given number of cities. All cities are connected by roads, and each city can be visited only once. GeneHunter solves this problem by minimizing the value in cell D23, the total tour length, and by changing the order of the city numbers in cells B7:B21, the adjustable cells. Each city is assigned an ordinal number from 1 to N, where N is the number of cities. The city names and numbers are listed in a range called Map in Cells B26:E40. The tour is represented as the entire sequence of city numbers. The tour length is computed using a look-up table located in cells H26:V40, in a range named Distances. The example uses Excel’s Index function for arrays in cells D7:D21 to compute the distance between each city pair listed in Column B. For example, the distance between the two city numbers currently listed in cells B7 and B8 is computed with the following function: Index(Distances,B7,B8) in cell D7

11. Traveling Salesman Problem The Travelling Salesman Problem ( TSP) is a problem in combinatorial optimization studied in operations research and theoretical computer science. http://www.kosmix.com/topic/Traveling_salesman_problem

Kosmix One sec... we're building your guide for Traveling Salesman Problem document.k_start_apptier = "Oct 31 01:07:28.851561"; kapp.assignCol($('ads_banner_top'), 'topnav_container'); Traveling Salesman Problem Overview Images Video Reference kapp.nav_menu_container = $('refine_nav').down(".navs_container"); kapp.assignCol($('refine_nav'), 'topnav_container'); kapp.assignCol($('uc_kosmixarticles_shadow'), 'right_container'); Snapshot Wikipedia Wikipedia Reference from Wikipedia Travelling Salesman Problem The Travelling Salesman Problem TSP ) is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once. The problem was first formulated as a mathematical problem in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved. The TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips. Slightly modified, it appears as a

12. Traveling Salesman Problem The Traveling Salesman Problem is one of the most intensively studied problems in computational mathematics. These pages are devoted to the history, http://www.tsp.gatech.edu/

13. Travelling Salesman Problem - Wikipedia, The Free Encyclopedia This problem is known as the analyst s traveling salesman problem. On the approximability of the traveling salesman problem, Combinatorica 26(1)101–120 http://en.wikipedia.org/wiki/Travelling_salesman_problem

Travelling salesman problem From Wikipedia, the free encyclopedia Jump to: navigation search An optimal TSP tour through Germany ’s 15 largest cities. It is the shortest among possible tours visiting each city exactly once. The Travelling Salesman Problem TSP ) is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science . Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once. The problem was first formulated as a mathematical problem in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved. The TSP has several applications even in its purest formulation, such as planning logistics , and the manufacture of microchips . Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing . In these applications, the concept

14. Traveling Salesman Problem -- From Wolfram MathWorld Oct 11, 2010 Solution to the traveling salesman problem is implemented as TravelingSalesmang in the Mathematica package Combinatorica` and http://mathworld.wolfram.com/TravelingSalesmanProblem.html

15. Traveling Salesman Problem Traveling Salesman Problem . Karla Hoffman. George Mason University. Manfred Padberg. New York University . Introduction The traveling salesman problem (TSP) is one which has commanded much http://iris.gmu.edu/~khoffman/papers/trav_salesman.html

Traveling Salesman Problem Karla Hoffman George Mason University Manfred Padberg New York University Introduction: The traveling salesman problem (TSP) is one which has commanded much attention of mathematicians and computer scientists specifically because it is so easy to describe and so difficult to solve. The problem can simply be stated as: if a traveling salesman wishes to visit exactly once each of a list of m cities (where the cost of traveling from city i to city j is c ij ) and then return to the home city, what is the least costly route the traveling salesman can take? A complete historical development of this and related problems can be found in Hoffman and Wolfe (1985). The importance of the TSP is that it is representative of a larger class of problems known as combinatorial optimization problems . The TSP problem belongs in the class of combinatorial optimization problems known as NP-complete. Specifically, if one can find an efficient algorithm (i.e., an algorithm that will be guaranteed to find the optimal solution in a polynomial number of steps) for the traveling salesman problem, then efficient algorithms could be found for all other problems in the NP-complete class. To date, however, no one has found a polynomial-time algorithm for the TSP. Does that mean that it is impossible to solve any large instances of such problems? Many practical optimization problems of truly large scale are solved to optimality routinely. In 1994, Applegate, et. al. solved a traveling salesman problem which models the production of printed circuit boards having 7,397 holes (cities), and, in 1998, the same authors solved a problem over the 13,509 largest cities in the U.S. So, although the question of what it is that makes a problem "difficult" may remain open, the computational record of specific instances of TSP problems coming from practical applications is optimistic.

16. Xkcd: Travelling Salesman Problem There is a linked black web, with a path in red Bruteforce solution O(n!) The web continues in this one. A man with a hat and a case is drawing it http://xkcd.com/399/

Archive Forums News/Blag Store ... About A webcomic of romance, sarcasm, math, and language. XKCD updates every Monday, Wednesday, and Friday. You can preorder the new communities map poster here Travelling Salesman Problem Random Random Permanent link to this comic: http://xkcd.com/399/ Image URL (for hotlinking/embedding): http://imgs.xkcd.com/comics/travelling_salesman_problem.png RSS Feed Atom Feed Comics I enjoy: Dinosaur Comics A Softer World Perry Bible Fellowship Copper ... Buttercup Festival Warning: this comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors). We did not invent the algorithm. The algorithm consistently finds Jesus. The algorithm killed Jeeves. The algorithm is banned in China. The algorithm is from Jersey. The algorithm constantly finds Jesus. This is not the algorithm. This is close. This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License

17. Traveling Salesman Problem Traveling Salesman Problem (Simulated Annealing) The Traveling Salesman Problem is to find the shortest circuitous path connecting N cities (meaning that a traveling salesman 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.

18. The Travelling Salesman Problem Discussion of this problem using simulated annealing. Downloadable program by Peter Meyer demonstrates solutions of the problem for particular cases. 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:

19. Traveling Salesman Problem - C++ Hi, I'm supposed to write a code of my TSP assignment using brute force algorithm. Although there are still some darkness about how to do it. I know what is TSP but I don't know http://www.daniweb.com/forums/thread242008.html

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20. Computational Science Essays on computational physics and modelling magnetic material. Software for simulating the Belousov-Zhabotinsky chemical reaction and for solving the travelling salesman problem. http://www.hermetic.ch/compsci.htm

Computational Science Humans think arithmeticly, but God thinks logarithmicly. Computational science is different from computer science. The latter is the science of computation (e.g., the invention of efficient search and sort algorithms, techniques of parallel processing, etc.). The former is the use primarily of computation, rather than of theorizing or experimentation, to attain scientific knowledge. Computational science has been made possible by the development of high-speed computers, and is still at an early stage of development. Five Cellular Automata , software which allows exploration of several cellular automata: (a) A generalization of Conway's Life, called q-state Life (b) A simulation of the Belousov-Zhabotinsky chemical reaction in which, beginning from a random state of the system, spirals and curlicues emerge spontaneously. (c) A process called Togetherness in which colored cells, starting from a random distribution, rearrange themselves so as to form clusters of cells of the same color. (d) A simulation of the population dynamics of dividing cells subject to viral infection

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