Vol 4 No 2 (2009)
Articles

Generalized Traveling Salesman Problem Reduction Algorithms

Gregory Gutin
Royal Holloway, University of London
Bio
Daniel Karapetyan
Royal Holloway, University of London
Published September 16, 2009
Keywords
  • generalized traveling salesman problem,
  • preprocessing,
  • reduction
How to Cite
Gutin, G., & Karapetyan, D. (2009). Generalized Traveling Salesman Problem Reduction Algorithms. Algorithmic Operations Research, 4(2), Pages 144 - 154. Retrieved from https://journals.lib.unb.ca/index.php/AOR/article/view/5660

Abstract

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The aim of this paper is to present a problem reduction algorithm that deletes redundant vertices and edges, preserving the optimal solution. The algorithm’s running time is O(N3) in the worst case, but it is significantly faster in practice. The algorithm has reduced the problem size by 15–20% on average in our experiments and this has decreased the solution time by 10–60% for each of the considered solvers.