Anja Fischer, Frank Fischer: An extended approach for lifting clique tree inequalities

Author(s):

Anja Fischer
Frank Fischer

Title:

Anja Fischer, Frank Fischer: An extended approach for lifting clique tree inequalities

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 13, 2012

Mathematics Subject Classification:

90C57	[Polyhedral combinatorics, branch-and-bound, branch-and-cut]
90C27	[Combinatorial optimization]

Abstract:

We present a new lifting approach for strengthening arbitrary clique tree inequalities that are known to be facet defining for the symmetric traveling salesman problem in order to get stronger valid inequalities for the symmetric quadratic traveling salesman problem (SQTSP). Applying this new approach to the subtour elimination constraints (SEC) leads to two new classes of facet defining inequalities of SQTSP. For the special case of the SEC with two nodes we derive all known conflicting edges inequalities for SQTSP. Furthermore we extend the presented approach to the asymmetric quadratic traveling salesman problem (AQTSP).

Keywords:

traveling salesman problem, quadratic traveling salesman problem, polyhedral combinatorics

Language:

English

Publication time:

11/2012