A note on characterzing the k-opt neighborhood via group theory

A note on characterzing the k-opt neighborhood via group theory

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Article ID: iaor20002457
Country: Netherlands
Volume: 5
Issue: 1
Start Page Number: 47
End Page Number: 51
Publication Date: Mar 1999
Journal: Journal of Heuristics
Authors: , ,
Keywords: heuristics
Abstract:

Group theory can be used to model and synthesize the neighborhood of Traveling Salesman tours reachable through k-OPT exchanges. A primary concept is that a dihedral group action partitions the sets of cut arcs so that k-OPT exchanges of orbital elements are conjugate. Also presented is a method to produce all k-OPT exchanges for a given set of cut area.

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