Algorithmic Strategies for a Fast Exploration of the TSP 4-OPT Neighborhood

Giuseppe Lancia,Marcello Dalpasso

doi:10.1007/978-3-030-34960-8_40

Algorithmic Strategies for a Fast Exploration of the TSP 4-OPT Neighborhood

Giuseppe Lancia, Marcello Dalpasso

Open Access

https://doi.org/10.1007/978-3-030-34960-8_40

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Publication Date: Jan 1, 2019

Citations: 4

Affiliation: University of Udine, University of Padua

#Quadratic Algorithm #Exploration Of Neighborhood + Show 4 more

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Abstract

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.

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