Thursday, 13:45 - 14:10 h, Room: MA 041

 

Anja Fischer
The asymmetric quadratic traveling salesman problem

 

Abstract:
In the asymmetric quadratic traveling salesman problem (AQTSP) the costs are associated to any three nodes that are traversed in succession and the task is to find a directed tour of minimal total cost. The problem is motivated by an application in biology and includes the angular-metric TSP and the TSP with reload costs as special cases. We study the polyhedral structure of a linearized integer programming formulation, present several classes of facets and investigate the complexity of the corresponding separation problems. Some facets are related to the Boolean quadric polytope and others forbid conflicting configurations. A general strengthening approach is proposed that allows to lift valid inequalities for the asymmetric TSP to improved inequalities for AQTSP. Applying this for the subtour elimination constraints gives rise to facet defining inequalities for AQTSP. Finally we demonstrate the usefulness of the new cuts. Real world instances from biology can be solved up for to 100 nodes in less than 11 minutes. Random instances turn out to be difficult, but on these semidefinite relaxations improved by the cutting planes help to reduce the gap in the root node significantly.

 

Talk 2 of the invited session Thu.2.MA 041
"Convex approaches for quadratic integer programs" [...]
Cluster 14
"Mixed-integer nonlinear programming" [...]

 

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