Erratum: On Semidefinite Programming Relaxations of the Traveling Salesman Problem

On Semidefinite Programming Relaxations of the Traveling Salesman Problem

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP), that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in the paper: [D. Cvetković, M. Cangalović and V. Kovačević-Vujčić. Semidefinite Programming Methods for the Symmetric Traveling Salesman...

New semidefinite programming relaxations for the Linear Ordering and the Traveling Salesman Problem

In 2004 Newman [43] suggested a semidefinite programming relaxation for the Linear Ordering Problem (LOP) that is related to the semidefinite program used in the Goemans-Williamson algorithm to approximate the Max Cut problem [22]. Her model is based on the observation that linear orderings can be fully described by a series of cuts. Newman [43] shows that her relaxation seems better suited for...

Semidefinite Relaxations for the Traveling Salesman Problem

The Unbounded Integrality Gap of a Semidefinite Relaxation of the Traveling Salesman Problem

We study a semidefinite programming relaxation of the traveling salesman problem intro-duced by de Klerk, Pasechnik, and Sotirov [8] and show that their relaxation has an unboundedintegrality gap. In particular, we give a family of instances such that the gap increases linearlywith n. To obtain this result, we search for feasible solutions within a highly structured class of...

An Approach for Solving Traveling Salesman Problem

In this paper, we introduce a new approach for solving the traveling salesman problems (TSP) and provide a solution algorithm for a variant of this problem. The concept of the proposed method is based on the Hungarian algorithm, which has been used to solve an assignment problem for reaching an optimal solution. We introduced a new fittest criterion for crossing over such problems, and illu...