Orbits, schemes and dynamic programming procedures for the TSP 4-OPT neighborhood

03/25/2023

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by   Giuseppe Lancia, et al.

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We discuss the way to group all 25 possible 4-OPT moves into 7 orbits of equivalent moves. We then describe two implementations, one for a Θ(n^3) algorithm by de Berg's et al. and one of a Θ(n^2) algorithm by Glover, for finding the best 4-OPT move via dynamic programming.