English

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

Data Structures and Algorithms 2023-03-28 v1

Abstract

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(n3)\Theta(n^3) algorithm by de Berg's et al. and one of a Θ(n2)\Theta(n^2) algorithm by Glover, for finding the best 4-OPT move via dynamic programming.

Cite

@article{arxiv.2303.14424,
  title  = {Orbits, schemes and dynamic programming procedures for the TSP 4-OPT neighborhood},
  author = {Giuseppe Lancia and Marcello Dalpasso},
  journal= {arXiv preprint arXiv:2303.14424},
  year   = {2023}
}
R2 v1 2026-06-28T09:33:23.206Z