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.

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

Lancia, Giuseppe
;
2019

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.
978-3-030-34959-2
978-3-030-34960-8
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/1177881
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