Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem |
Vicky Mak, Tommy Thomadsen
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| 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. |
| Keywords | Quadratic Knapsack; Quadratic Selective Travelling Salesman; Polyhedral Analysis; Facets |
| Type | Technical report |
| Year | 2004 Month November |
| Publisher | Informatics and Mathematical Modelling, Technical University of Denmark, DTU |
| Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby |
| Series | IMM-Technical Report-2004-19 |
| Electronic version(s) | [pdf] [ps] |
| BibTeX data | [bibtex] |
| IMM Group(s) | Operations Research |