Geodesic
The traveling salesman problem: approximate algorithm by branch-and-bound method with~guaranteed precision
Prikladnaâ diskretnaâ matematika, no. 3 (2019), pp. 104-112

Voir la notice de l'article provenant de la source Math-Net.Ru

To solve the traveling salesman problem with distance matrix of order $n$, we propose an approximate algorithm based on the branch-and-border method. For clipping, an increased least estimate of the current partial solution is used. This guarantees a predetermined value $\varepsilon$ of the whole solution error. A computational experiment for distance matrices of four kinds of distributions was carried out. A uniform random (asymmetric) distribution as well as matrices of Euclidean distances between random points (a symmetric distribution) were used. In the latter case, a local search was additionally applied. Estimates for the power $p$ in the polynomial computational complexity $O(n^p)$ of the algorithm for various kinds of distributions and various values of error $\varepsilon$ are obtained. For a uniform random distribution and $n\leq 1000$, the obtained estimate of the power $p$ turned out to be close to $2.8$ and of an average value of error to be $1\,\%$.
Keywords: traveling salesman problem, branch-and-border method, approximate algorithm, local search, computational experiment. 
@article{PDM_2019_3_a12,
     author = {Yu. L. Kostyuk},
     title = {The traveling salesman problem: approximate algorithm by branch-and-bound method with~guaranteed precision},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {104--112},
     publisher = {mathdoc},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2019_3_a12/}
}
TY  - JOUR
AU  - Yu. L. Kostyuk
TI  - The traveling salesman problem: approximate algorithm by branch-and-bound method with~guaranteed precision
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2019
SP  - 104
EP  - 112
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2019_3_a12/
LA  - ru
ID  - PDM_2019_3_a12
ER  - 
%0 Journal Article
%A Yu. L. Kostyuk
%T The traveling salesman problem: approximate algorithm by branch-and-bound method with~guaranteed precision
%J Prikladnaâ diskretnaâ matematika
%D 2019
%P 104-112
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2019_3_a12/
%G ru
%F PDM_2019_3_a12
Yu. L. Kostyuk. The traveling salesman problem: approximate algorithm by branch-and-bound method with~guaranteed precision. Prikladnaâ diskretnaâ matematika, no. 3 (2019), pp. 104-112. http://geodesic.mathdoc.fr/item/PDM_2019_3_a12/