Using Gavish-Grave LP to Formulate the Directed Black and White Traveling Salesman Problem

Authors:
He Jiang;Xianchao Zhang;Mingchu Li;Haoyang Che
Affiliations:
School of Software, Dalian University of Technology, Dalian 116621, China;School of Software, Dalian University of Technology, Dalian 116621, China;School of Software, Dalian University of Technology, Dalian 116621, China;Institute of Software, The Chinese Academy of Sciences, Beijing 100080, China
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
Year:
2007

Citing 2
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Abstract

The black and white traveling salesman problem (BWTSP) is a new class of NP-hard problem arising from work on airline scheduling and telecommunication fiber networks. The existing Ghiani LP for the undirected BWTSP contains an exponential number of constraints. For a special case of the directed BWTSP whose L = + 驴, the LP with polynomial number of constraints could be obtained by transforming it to an asymmetric traveling salesman problem with replenishment arcs (RATSP), whereas there exists no LP for the directed BWTSP in its general form. This paper proposes a LP with 3n 2 + 2n constraints only for the directed BWTSP in such a way that, by reducing the problem to an asymmetric traveling salesman problem (ATSP), we add n 2 cardinality constraints and n 2 length constraints to the existing Gavish-Grave LP for the ATSP. The new LP is also valid for the undirected BWTSP when viewed as a special case of the directed BWTSP.