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  1. The Travelling Salesman Problem (TSP) is the challenge of finding the shortest yet most efficient route for a person to take given a list of specific destinations.[1]
  2. The traveling salesman problem was defined in the 1800s by the Irish mathematician W. R. Hamilton and by the British mathematician Thomas Kirkman.[2]
  3. The Travelling Salesman Problem describes a salesman who must travel between N cities.[2]
  4. The Traveling Salesman Problem is typical of a large class of "hard" optimization problems that have intrigued mathematicians and computer scientists for years.[2]
  5. In general, the traveling salesman problem is hard to solve.[2]
  6. The multiple traveling salesman problem (mTSP) is a generalization of the well-known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution.[3]
  7. The origins of the travelling salesman problem are unclear.[4]
  8. The travelling salesman problem was mathematically formulated in the 1800s by the Irish mathematician W.R. Hamilton and by the British mathematician Thomas Kirkman.[4]
  9. The Beardwood–Halton–Hammersley theorem provides a practical solution to the traveling salesman problem.[4]
  10. The bottleneck traveling salesman problem is also NP-hard.[4]
  11. The traveling salesperson problem is one of a handful of foundational problems that theoretical computer scientists turn to again and again to test the limits of efficient computation.[5]
  12. Unlike the regular traveling salesperson problem, this fractional problem can be solved efficiently.[5]
  13. Nevertheless, Oveis Gharan emerged from that collaboration with an unshakable belief that their algorithm should beat Christofides’ algorithm for the general traveling salesperson problem.[5]
  14. Oveis Gharan had himself cut his teeth on the traveling salesperson problem as a graduate student back in 2010.[5]
  15. As said above, these are only two of the most basic algorithms used to obtain an approximate solution to the travelling salesman problem and there are many more sophisticated methods.[6]
  16. The resulting tree is not a possible solution to the traveling salesman problem because it does not create a round-trip route.[7]
  17. However, this round-trip route is, at worst, twice as long as the best solution to the traveling salesman problem.[7]
  18. The Travelling Salesman Problem (TSP) reflects the routing decisions that a salesman has to take.[8]
  19. They therefore defined and formulated the Sequence Dependent Travelling Salesman Problem (SDTSP).[8]
  20. Travelling salesman problem is the most notorious computational problem.[9]
  21. The answer is that both problems can be formulated in terms of the mathematical problem known as the Traveling Salesman Problem (TSP).[10]
  22. For example, the Bottleneck Traveling Salesman Problem (bottleneck TSP) arises as a variant of the usual TSP by changing the objective function.[10]
  23. Garfinkel, R. and K. Gilbert, The bottleneck traveling salesman problem: algorithms and probabilistic analysis, J. Assoc.[10]
  24. Lawler, E., A solvable case of the traveling salesman problem, Math.[10]
  25. lower bound is the solution to the linear programming relaxation of the standard integer Programming formulation of the traveling salesman problem (TSP).[11]
  26. Was it called the Travelling Salesman Problem?[12]
  27. I am sure you already heard about the traveling salesman problem or TSP.[13]
  28. The traveling salesman problem is a classic problem in combinatorial optimization.[13]
  29. If you want to solve traveling salesman problem with a large number of cities the dynamic programming method is not the best choice.[13]
  30. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem.[14]
  31. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations.[14]
  32. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance.[14]
  33. The traveling salesman problem (TSP) is one of the most famous benchmarks, significant, historic, and very hard combinatorial optimization problem.[14]
  34. The traveling salesman problem: a deterministic algorithm using tabu search.[15]
  35. Keywords : tabu search; deterministic algorithm; frequencies matrix; diversification; permutation; traveling salesman problem.[15]
  36. The Travelling Salesman Problem (TSP) is a classical optimization problem that has been evolved to real-life vehicle routing problems (VRP).[16]
  37. The Traveling Salesman Problem (TSP) is among the most widely studied problems in network optimization and has a wide variety of practical applications 2), (5), (20), (24.[17]
  38. When penalty terms for unvisited nodes are also added to the objective function, the problem is known as the PrizeCollecting Traveling Salesman Problem 3), (9.[17]
  39. Other two related problems in which customers have to be selected are the Traveling Purchaser Problem and the Generalized Traveling Salesman Problem.[17]
  40. k,i p ki x ki in the objective function of the traveling salesman problem.[17]

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