In no way can I understand by the example of the traveling salesman problem, what is a neighborhood in the local search algorithm (denoted as N)? Can you give an example of different neighborhoods of this problem?

  • The neighborhood function for each feasible solution defines a set of neighboring solutions, in some sense close to this one - vp_arth
  • That is, on the example of the traveling salesman problem, there is only one neighborhood, which includes all the cities? Since, based on the definition, any solution can be obtained from this neighborhood ... - Sergey Vladimirovich
  • the neighborhood is determined by the function, the efficiency of the algorithm depends on the choice of this function. There is a decision graph and each solution determines the neighboring solutions by this function .. - vp_arth

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Example: an epsilon-neighborhood of a point is a set of points that are not further from this one by the amount of the epsilon