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DOI: 10.7155/jgaa.00400
A Binomial Distribution Model for the Traveling Salesman
Problem Based on Frequency Quadrilaterals
Vol. 20, no. 2, pp. 411434, 2016. Regular paper.
Abstract We study the symmetric traveling salesman problem via frequency graphs.
One computes the frequency of edges by computing how many times
an edge occurs in an optimal path involving four vertices.
The edges that are in the Optimal Hamiltonian Cycle ($OHC$) have
a higher frequency than most edges that are not in the $OHC$ and
thus edges with a low frequency can safely be ignored when searching for the optimal solution.
A binomial distribution model is introduced for the symmetric traveling
salesman problem based on frequency quadrilaterals. When
the frequency of each edge is computed with $N$ frequency
quadrilaterals, our model suggests that the minimum frequency
of an edge in the $OHC$ is
$F_\mathrm{min} =(\epsilon_\mathrm{min}+1)N$ where $\frac{4}{3}+\frac{4}{3(n2)} < \epsilon_\mathrm{min} < 4$.
This suggests a heuristic to reduce the number of edges that
need to be considered in the search for the $OHC$ which is
to keep only those edges whose frequencies
are $\geq F_\mathrm{min}$. We explore this heuristic in several realworld examples.
An erratum for this paper has been published on August 2017 (see link on the right)

Submitted: December 2015.
Reviewed: March 2016.
Revised: April 2016.
Reviewed: May 2016.
Revised: May 2016.
Reviewed: June 2016.
Revised: June 2016.
Accepted: July 2016.
Final: July 2016.
Published: July 2016.
Communicated by
Dorothea Wagner
