The Traveling Salesman Problem is one of the most well known problems in the class of optimization problems and is still a challenge for many computer scientists today. One approach used to attack this problem is the use of Neighborhood Search Techniques (or Improvement Algorithms) that improve a solution by making a move to a neighbor if it is a better solution. Neighborhood Search Techniques are used either independently itself or plugged in other algorithms such as Iterated Algorithm, Local Search, or Evolutionary Algorithm. At the same time, the running time gets slower quickly as the size of neighborhood grows exponentially. In this paper, we introduce the Slide Edge Algorithm (SEA), which is supposed not to find a move as Neighborhood Search Techniques do but to improve the quality of a move that a Neighborhood Search Technique finds out. While the time to find a move is exponential, the time of SEA is approximately to linear. In experiment results, with the support of SEA in improving a have-just-found move, Neighborhood Search Techniques achieve a better quality of the tour in a reasonable amount of time.
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