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

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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.

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  1. University of Antwerp, Faculty of Applied Economics, Prinsstraat 13, B–2000, Antwerp, Belgium

    Kenneth Sörensen

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  1. Kenneth Sörensen
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Correspondence to Kenneth Sörensen.

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Sörensen, K. Distance measures based on the edit distance for permutation-type representations. J Heuristics 13, 35–47 (2007). https://doi.org/10.1007/s10732-006-9001-3

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  • DOI: https://doi.org/10.1007/s10732-006-9001-3

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