A new Lagrangean Approach for the Travelling Salesman Problem

Abstract

In this paper, we use a reformulation of the symmetric and the asymmetric travelling salesman problem more suitable for Lagrangean relaxation and analyse the new approach on examples from TSP Lib. Furthermore the Lagrangean relaxed subproblems are travelling salesman alike which means that almost all that is known on the travelling salesman polytope can be used when the subproblems are to be solved.