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An extended approach for lifting clique tree inequalities

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  • Anja Fischer

    (Chemnitz University of Technology)

  • Frank Fischer

    (Chemnitz University of Technology)

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).

Suggested Citation

  • Anja Fischer & Frank Fischer, 2015. "An extended approach for lifting clique tree inequalities," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 489-519, October.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9647-3
    DOI: 10.1007/s10878-013-9647-3
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    References listed on IDEAS

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    1. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    2. M. Grötschel & W. R. Pulleyblank, 1986. "Clique Tree Inequalities and the Symmetric Travelling Salesman Problem," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 537-569, November.
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