The 4-OPT neighborhood for the TSP contains Θ(n4) moves so that finding the best move effectively requires some ingenuity. Recently, de Berg et al. have given a Θ(n3) dynamic program, but the cubic complexity is still too large for using 4-OPT in practice. We describe a new procedure which behaves, on average, slightly worse than a quadratic algorithm. This is much faster than the DP procedure, achieving speedups of two to three orders of magnitude on all instances we tested.
CITATION STYLE
Lancia, G., & Dalpasso, M. (2019). Algorithmic Strategies for a Fast Exploration of the TSP 4-OPT Neighborhood. In AIRO Springer Series (Vol. 3, pp. 457–470). Springer Nature. https://doi.org/10.1007/978-3-030-34960-8_40
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