Distance measures based on the edit distance for permutation-type representations

  • Authors:
  • Kenneth Sörensen

  • Affiliations:
  • University of Antwerp, Faculty of Applied Economics, Antwerp, Belgium

  • Venue:
  • Journal of Heuristics
  • Year:
  • 2007

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Abstract

In this paper, we discuss distance measures for a number of different combinatorial optimization problems of which the solutions are best represented as permutations of items, sometimes composed of several permutation (sub)sets. The problems discussed include single-machine and multiple-machine scheduling problems, the traveling salesman problem, vehicle routing problems, and many others. Each of these problems requires a different distance measure that takes the specific properties of the representation into account. The distance measures discussed in this paper are based on a general distance measure for string comparison called the edit distance. We introduce several extensions to the simple edit distance, that can be used when a solution cannot be represented as a simple permutation, and develop algorithms to calculate them efficiently.