Abstract
The quadratic traveling salesman problem asks for a tour of minimal total costs where the costs are associated with each of two arcs that are traversed in succession. This structure arises, e.g., if the succession of two arcs represents loading processes in transport networks or a switch between different technologies in communication networks. Based on an integer program with quadratic objective function we present a linearized integer programming formulation and study the corresponding polyhedral structure of the asymmetric quadratic traveling salesman problem (AQTSP), where the costs may depend on the direction of traversal. The constructive approach that is used to establish the dimension of the underlying polytope allows us to prove the facetness of several classes of valid inequalities. Some of them are related to the Boolean quadric polytope. Two new classes are developed that exclude conflicting configurations. Among these the first one is separable in polynomial time, and the separation problem f...
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.