Transformations of generalized ATSP into ATSP
نویسندگان
چکیده
منابع مشابه
Transformations of generalized ATSP into ATSP
The Generalized Traveling Salesman Problem (GTSP) is stated as follows. Given a weighted complete digraph K∗ n and a partition V1, . . . , Vk of its vertices, find a minimum weight cycle containing exactly one vertex from each set Vi, i = 1, . . . , k. We study transformations from GTSP to TSP. The ’exact’ Noon-Bean transformation is investigated in computational experiments. We study the ’non-...
متن کاملThe m-Cost ATSP
Although the m-ATSP (or multi traveling salesman problem) is well known for its importance in scheduling and vehicle routing, it has, to the best of our knowledge, never been studied polyhedraly, i.e., it has always been transformed to the standard ATSP. This transformation is valid only if the cost of an arc from node i to node j is the same for all machines. In many practical applications thi...
متن کاملTolerance Based Algorithms for the ATSP
In this paper we use arc tolerances, instead of arc costs, to improve Branch-and-Bound type algorithms for the Asymmetric Traveling Salesman Problem (ATSP). We derive new tighter lower bounds based on exact and approximate bottleneck upper tolerance values of the Assignment Problem (AP). It is shown that branching by tolerances provides a more rational branching process than branching by costs....
متن کاملOn the relationship between ATSP and the cycle cover problem
In this paper, we study the relationship between the Asymmetric Traveling Salesman Problem (ATSP) and the Cycle Cover Problem in terms of the strength of the triangle inequality on the edge costs in the given complete directed graph instance, G = (V, E). The strength of the triangle inequality is captured by parametrizing the triangle inequality as follows. A complete directed graph G = (V, E) ...
متن کاملTwo Approximation Algorithms for ATSP with Strengthened Triangle Inequality
In this paper, we study the asymmetric traveling salesman problem (ATSP) with strengthened triangle inequality, i.e. for some γ ∈ [ 1 2 , 1) the edge weights satisfy w(u, v) ≤ γ(w(u, x) + w(x, v)) for all distinct vertices u, v, x. We present two approximation algorithms for this problem. The first one is very simple and has approximation ratio 1 2(1−γ) , which is better than all previous resul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Operations Research Letters
سال: 2003
ISSN: 0167-6377
DOI: 10.1016/s0167-6377(03)00031-2