A dual ascent algorithm for the 1-tree relaxation of the symmetric traveling salesman problem

Authors:
Kavindra Malik;Marshall L. Fisher
Affiliations:
Johnson Graduate School of Management, Cornell University, USA;Department of Decision Sciences, The Wharton School, University of Pennsylvania, USA
Venue:
Operations Research Letters
Year:
1990

Citing 3
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Abstract

A dual ascent algorithm is described for the 1-tree relaxation of the symmetric traveling salesman problem. The ascent directions correspond to increasing (decreasing) the dual variables for the nodes of a set that is out of kilter high (low) for all 1-trees that are optimal at the current dual solution. This algorithm is shown to obtain near optimal bounds in about one-quarter of the time required by the subgradient method on a sample of well-known test cases.