travelling salesman problem - meaning and definition. What is travelling salesman problem
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What (who) is travelling salesman problem - definition


Travelling salesman problem         
  • 1) An ant chooses a path among all possible paths and lays a pheromone trail on it. 2) All the ants are travelling on different paths, laying a trail of pheromones proportional to the quality of the solution. 3) Each edge of the best path is more reinforced than others. 4) Evaporation ensures that the bad solutions disappear. The map is a work of Yves Aubry [http://openclipart.org/clipart//geography/carte_de_france_01.svg].
  • Ant colony optimization algorithm for a TSP with 7 cities: Red and thick lines in the pheromone map indicate presence of more pheromone
  • Solution of a TSP with 7 cities using a simple Branch and bound algorithm. Note: The number of permutations is much less than Brute force search
  • Solution to a symmetric TSP with 7 cities using brute force search. Note: Number of permutations: (7−1)!/2 = 360
  • Creating a matching
  • Nearest Neighbour algorithm for a TSP with 7 cities. The solution changes as the starting point is changed
  • An example of a 2-opt iteration
  • Using a shortcut heuristic on the graph created by the matching above
  • Symmetric TSP with four cities
  • William Rowan Hamilton
NP-HARD PROBLEM IN COMBINATORIAL OPTIMIZATION
Traveling salesperson problem; Traveling Salesman Problem; Euclidean traveling salesman problem; Euclidean TSP; Wandering salesman problem; Traveling salesman problem; Euclidian TSP; Travelling salesperson problem; Salesman problem; Tsp problem; TSP Problem; Travelling Salesman Problem; Travelling Salesman problem; Traveling Salesman problem; Travelling-salesman problem; Euclidean traveling salesman; Metric traveling salesman; Euclidean travelling salesman; Generalized travelling salesman problem; Generalized traveling salesman problem; Traveling tourist problem; Delta travelling salesman problem; Metric tsp; Willy Loman problem; Salesperson Problem; Travelling salesmen problem; Metric TSP; Traveling salesmen problem; Euclidean travelling salesman problem; Traveling salesman puzzle; Salesman Problem; TSP problem; Approximation algorithms for the traveling salesman problem; Computational complexity of the travelling salesman problem
The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research.
traveling salesman problem         
  • 1) An ant chooses a path among all possible paths and lays a pheromone trail on it. 2) All the ants are travelling on different paths, laying a trail of pheromones proportional to the quality of the solution. 3) Each edge of the best path is more reinforced than others. 4) Evaporation ensures that the bad solutions disappear. The map is a work of Yves Aubry [http://openclipart.org/clipart//geography/carte_de_france_01.svg].
  • Ant colony optimization algorithm for a TSP with 7 cities: Red and thick lines in the pheromone map indicate presence of more pheromone
  • Solution of a TSP with 7 cities using a simple Branch and bound algorithm. Note: The number of permutations is much less than Brute force search
  • Solution to a symmetric TSP with 7 cities using brute force search. Note: Number of permutations: (7−1)!/2 = 360
  • Creating a matching
  • Nearest Neighbour algorithm for a TSP with 7 cities. The solution changes as the starting point is changed
  • An example of a 2-opt iteration
  • Using a shortcut heuristic on the graph created by the matching above
  • Symmetric TSP with four cities
  • William Rowan Hamilton
NP-HARD PROBLEM IN COMBINATORIAL OPTIMIZATION
Traveling salesperson problem; Traveling Salesman Problem; Euclidean traveling salesman problem; Euclidean TSP; Wandering salesman problem; Traveling salesman problem; Euclidian TSP; Travelling salesperson problem; Salesman problem; Tsp problem; TSP Problem; Travelling Salesman Problem; Travelling Salesman problem; Traveling Salesman problem; Travelling-salesman problem; Euclidean traveling salesman; Metric traveling salesman; Euclidean travelling salesman; Generalized travelling salesman problem; Generalized traveling salesman problem; Traveling tourist problem; Delta travelling salesman problem; Metric tsp; Willy Loman problem; Salesperson Problem; Travelling salesmen problem; Metric TSP; Traveling salesmen problem; Euclidean travelling salesman problem; Traveling salesman puzzle; Salesman Problem; TSP problem; Approximation algorithms for the traveling salesman problem; Computational complexity of the travelling salesman problem
<spelling> US spelling of travelling salesman problem. (1996-12-13)
travelling salesman problem         
  • 1) An ant chooses a path among all possible paths and lays a pheromone trail on it. 2) All the ants are travelling on different paths, laying a trail of pheromones proportional to the quality of the solution. 3) Each edge of the best path is more reinforced than others. 4) Evaporation ensures that the bad solutions disappear. The map is a work of Yves Aubry [http://openclipart.org/clipart//geography/carte_de_france_01.svg].
  • Ant colony optimization algorithm for a TSP with 7 cities: Red and thick lines in the pheromone map indicate presence of more pheromone
  • Solution of a TSP with 7 cities using a simple Branch and bound algorithm. Note: The number of permutations is much less than Brute force search
  • Solution to a symmetric TSP with 7 cities using brute force search. Note: Number of permutations: (7&minus;1)!/2 = 360
  • Creating a matching
  • Nearest Neighbour algorithm for a TSP with 7 cities. The solution changes as the starting point is changed
  • An example of a 2-opt iteration
  • Using a shortcut heuristic on the graph created by the matching above
  • Symmetric TSP with four cities
  • William Rowan Hamilton
NP-HARD PROBLEM IN COMBINATORIAL OPTIMIZATION
Traveling salesperson problem; Traveling Salesman Problem; Euclidean traveling salesman problem; Euclidean TSP; Wandering salesman problem; Traveling salesman problem; Euclidian TSP; Travelling salesperson problem; Salesman problem; Tsp problem; TSP Problem; Travelling Salesman Problem; Travelling Salesman problem; Traveling Salesman problem; Travelling-salesman problem; Euclidean traveling salesman; Metric traveling salesman; Euclidean travelling salesman; Generalized travelling salesman problem; Generalized traveling salesman problem; Traveling tourist problem; Delta travelling salesman problem; Metric tsp; Willy Loman problem; Salesperson Problem; Travelling salesmen problem; Metric TSP; Traveling salesmen problem; Euclidean travelling salesman problem; Traveling salesman puzzle; Salesman Problem; TSP problem; Approximation algorithms for the traveling salesman problem; Computational complexity of the travelling salesman problem
<algorithm, complexity> (TSP or "shortest path", US: "traveling") Given a set of towns and the distances between them, determine the shortest path starting from a given town, passing through all the other towns and returning to the first town. 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. {travelling salesman problemmoscato/TSPBIB_home.html">Pablo Moscato's TSP bibliography (http://densis.fee.unicamp.br/travelling salesman problemmoscato/TSPBIB_home.html)}. {Fractals and the TSP (http://ing.unlp.edu.ar/cetad/mos/FRACTAL_TSP_home.html)}. (1998-03-24)