# Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem

- Authors:
- Abstract:
- A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP (QSTSP) has the additional complications: (1) each pair of nodes have an associated reward (denoted the edge-reward) which can be gained only if both nodes are visited; and (2) a constraint on the number of nodes selected is imposed, which we refer to as the cardinality constraint. The objective of an QSTSP is to maximize the total node-reward and edge-rewards gained minus the edge-costs incurred subject to the satisfaction of the cardinality constraint.
- Type:
- Report
- Language:
- English
- Keywords:
- Quadratic Knapsack; Quadratic Selective Travelling Salesman; Polyhedral Analysis; Facets
- Main Research Area:
- Science/technology
- Publication Status:
- Published
- Review type:
- Undetermined
- Submission year:
- 2004
- Publication year:
- 2004
- Scientific Level:
- Scientific
- ID:
- 2185754487