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An extended approach for lifting clique tree inequalities

Anja Fischer(anja.fischer***at***mathematik.tu-chemnitz.de)
Frank Fischer(frank.fischer***at***mathematik.tu-chemnitz.de)

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

Category 1: Combinatorial Optimization

Category 2: Combinatorial Optimization (Polyhedra )

Citation: Preprint 2012-13, Fakultaet fuer Mathematik, Technische Universitaet Chemnitz, D-09107 Chemnitz, November 2012

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Entry Submitted: 11/15/2012
Entry Accepted: 11/15/2012
Entry Last Modified: 11/15/2012

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